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QUARTERLY REVIEWS COMMENTS ON THE THERMOCHEMISTRY OF THE ELEMENTS OF GROUPS IVB AND IV By E. C. BAUGHAN O.B.E. M.A. B.Sc. (PROFESSOR OF CHEMISTRY ROYAL MILITARY COLLEGE OF SCIENCE MHT~IVENHAM WILTS.) Section I THE heat of any chemical reaction is the algebraic sum of the heats of formation Qf of the compounds concerned from their elements in conven- tionally chosen standard states. Heats of formation of gaseous compounds are not complicated by interactions between molecules and such heats of formation Qf" related to free atoms in the gas phase as standard states are simpler in theory than the conventional Qj values. The problem of under- standing thermochemistry starts therefore with Qj" values. If a molecule XU has n bonds in it all the same then we may define a bond energy B(X-Y) by 1 B(X-Y) f n -Qf"(XY,) .It is found that such bond energies are often approximately the same For example the heats of the several steps (where CH + X --f CH,X + H CH,X + X -+ CI-IX + H CHX + X -+ CX + H are approximately equal so that one can consider each process as the loss of a C-H bond energy and the gain of a C-X bond energy.l The history of this bond-energy concept is divided fairly clearly into three main periods. In the first,2 the object was to investigate the constancy of bond energies as between different molecule^.^ In the second period attention became directed to the anomalies this development is mainly due to Pauling who by use of the quantum-mechanical concept of '' resonance " explained many such anomalies and the numerical values in several molecules. X = C1 Br or I) C'H,X + X -+ CH2X2 + H 1 Baughan Nature 1941 147 542.Fajtjans Ber. 1920 53 643 ; 1922 55 2836 ; see also Grimm Sidgwick and others. Cf. Sidgwick " The Covalent Link in Chemistry " Cornell Univ. Press 1934. " The Covalent Link in Chemistry " Cornell Univ. Press 1940. 103 H 104 QUARTERLY REVIEWS of many bond energies themselves. The great successes of Pauling's method has led naturally enough to the third modern development of the question. Here the real issue is to make the concept of bond energies do two things at once. Any refinements of the bond-energy concept must retain the original ability to predict the Qf values of molecules ; the problem now is to use bond energies for other purposes as well vix. to correlate bond energies with e.g. molecular ionisation potentials,5 or bond distances and force constants,6~ or dipole or with the dissociation energies of individual links to give free radicals $&,a(CH,) for example with the heat of reaction CH + CH + H.Evidently any such single-step dissociation energy can be given as the differcnce between the &fa of a molecule and those of the free radicals or atoms into which it dissociates ; the problem of dissociation energies can to begin with be reduced to that o f What is the relation between the bond energies in cases where one of the atoms is in a different valency ? To this problem quantum mechanics at present gives no simple quanti- tative answer.1° It is however a problem of great practical importance. The calculation of the heats of formation of stable well-known molecular species is a problem in which as experimental chemistry so long preceded quantum physics theory mainly reduces to order what is already known.Considering however free radicals in chain reactions surface hydrides in catalytic processes,11 compounds unknown in '' bottle " quantities at room temperature but of major importance in metallurgical and combustion reactions we see that many problems still involve unknown heats'of forma- tion of compounds of " unusual " valency ; and in the absence of any clear guide from theory we must try to see what empirical general rules can be stated about the dependence of bond energies on valency. Such a programme accentuates the great uncertainty in the heats of formation of so many elements as free gaseous atoms from their conventional standard states (" heats of atomisation ").Yet on the one hand the earlier investigations assumed many heats of atomisation which are either still the subject of controversy (e.g. carbon nitrogen) or have since been shown to be wrong (e.g. oxygen fluorine) ; on the other hand modern investigators claim to deduce heats of atomisation from bond energies. Evidently for some applications of bond energies the heats of atomisation cancel out but for others they do not. If one confines attention to Qf values for molecules conversion of these into &fa values leaves the bond energies constant as between different molecules as long as the valency may be considered constant. An error of x in the heat of atomisation of carbon for example implies an error of &X in aZZ single bonds to carbon 8x in all C-C bonds etc.It would therefore have been possible to discuss additivity relations in heats of Walsh Trans. Faruday SOC. 1946 42 56 ; 1947 43 60 158. Baughan Trans. Faraday SOC. 1048 44 845. Cottrell and Sutton Quart. Reviews 1948 2 260 ; see also ref. (4). 6 F o ~ and Martin J. 1938 2106. * Linnett ibid. 1940 36 1123. 1oCoiilson Discuss. Puraduy SOC. 1947 2 9. l 1 Cf. Eley ibid. 1950 8 34. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 105 formation without bringing in heats of atomisation a t all and this was in fact sometinies done.12 For example the " resonance energy " of the benzene molecule could either be obtained from bond energies or directly by comparing the heat of hydrogenation of benzene with those of ethylenic hydrocarbons ; the two methods agree to within the considerable uncer- tainties imposed by neglect of the vibrational and rotational energies involved.l3 When we come to the numerical values of bond energies the position becomes more subtle. The empirical issue involved in Pauling's use of " ionic-covalent resonance energies " is to compare the single bond energy B(X-Y) with the mean of B(X-X) and B(Y-Y). Provided that we consider the arithmetic mean and that the heats of atomisation A, A, of X and Y are simply related to the single-bond energies then A% A may vanish. This condition may be justified for hydrogen the halogens and the elements carbon silicon germanium and tin but it is certainly not legitimate for nitrogen for example. Further when we come to the problem of dissociation energies heats of atomisation cannot be neglected even in the first approximation.It is an obvious first simplification to suppose that the dissociation energy of CH -+ CH + H should be simply equal to the bond energy in CH, though this view cannot be justified theoretically or to suppose that they would be equal if one referred the bond energies to a spectroscopically excited state of carbon 14-although the tetrahedral symmetry of CH argues for hybridisa- tion ; but one cannot begin to check either hypothesis unless one can put a number to the bond energy of CH ; the full ax uncertainty is involved. It is therefore of crucial importance to improve our knowledge of heats of formation of atoms and radicals and more experiments are needed. But one can often improve the heats of atomisation derived from existing data on equilibrium constants and this has not always been done.High- temperature equilibrium data measure a t T a free-energy change AG;. From this we can derive AH (and hence AH the value at O'K) either from the variation of AGF with T (plot log K against 1/T and find the slope ; second-law method) or by computing from specific-heat data and the quantum-statistical theory of entropy AH? from each single value of AG'; (third-law method). It is not universally realised that the latter method is the better. First it reduces a problem in two variables to a problem in one variable. Secondly correct third-law values of AH; must agree with the correct second-law values ; we have therefore a check on the data. Thirdly high-temperature equilibria are not easy to measure and the measurements often involve systematic errors.The second-law method depends on differences usually small in AGg the third-law method on its absolute value. Evidently the latter is less sensitive to systematic errors. So far we have mentioned calorimetric and equilibrium-constant data. 12Cf. Kharasch Bull. Bur Stand. J. Re$. 1929 2 359. l3 See Dewar Trans. Faruday Soc. 1946 42 767. 14Long and Norrish Proc. Roy. Soc. 1946 A 187 337. 106 QUARTERLY REVIEWS Other methods are also available. I n a polyatomic molecule CH for example the first-stage dissociation energy (CH -+ CH 1- H - D kcal.) can often and later stages occasionally be obtained froin kinetic measure- m e n t ~ ~ ~ particularly froin low-pressure pyrolysis reactions or from niass- spectrometer experiments where electron bombardment procliices both ionisation and boiid-fission.lG The dissociation energy of the last stage (CH -+ C + H - D kcal.) is the quantity usually known as DF by spectro- scopists-the dissociation energy of a diatomic molecule into atoms in their ground states.And from Hess's law the bond energy (as defined in equation 1) is related to these dissociation energies D by C D = 1~13 . * (2) ?& It may be pointed out that errors in the spectroscopic determination of dissociation energies are of two kinds ( a ) errors of extrapolation from the highest measured state of vibrational excitation to the limit of complete dissociation ; such errors are continuous (in the matheniatical sense) A dissociation energy of a molecule may be exactly known but the products of dissociation unknown-one or both of the atoms may be in excited states.But the possible excitations of most common atoms are well known and there are theoretical rules which limit the possible atomic states into which a given diatomic molecular state can dissociate. Hence the errors of this second kind are errors of choice between a discrete set of a few possible values (such are the notorious cases of CO and N l 7 ) so that a rough thermochemical estimate may rule out all identification possibilities but one which can then in its turn make the thermochemical estimate much more precise. The use of third-law methods again increases the precision of this argument. Besides giving many such dissociation energies (and hence many heats of atomisation) molecular spectroscopy also provides the basis for another attack on the problem.For a diatomic molecule XY one can obtain the fundamental vibrational frequency (and hence the force constant) and often the interatomic distance as well though this is often impracticable because of isotopic complexity or complexity of rotational levels. 179 1s Equally for molecules XU the X-Y distances can be obtained froin electron and X-ray diffraction experiments (occasionally by spectroscopic methods) l9 and the force constants can be obtained froin the vibrational frequencies though unfortunately the results depend on the particular form of the fields of force assumed. 2o We have therefore the material for a new way of searching for an inter- pretation. I n principle there are two extreme types of variation in a series ( b ) errors of identification. 1 5 For reviews see Szwarc Ghem.Reviews 1960 47 75 ; Quurt. IZcviews 1951 5 22. 16 Stevenson Discuss. Puraday ~Soc. 1961 10 36. 17 See Gaydon " Dissociation Energies and Spectra of Diatomic Molecules " 18 Herzbcrg " Spectra of Diatomic Blolccnles " Van Nostrand Co. New Tork 19For a summary of data see Allen and Suttoii Acta Cry&. 1950 3 46. ZOLinnett QuuTt. Reviews 1947 1 73. Chapman & Hall London 1947. 1950; Table 39 in this book gives a very coriiplete summary of data. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 107 of molecules. In the one t'he energy force constant and distance all vary together the first two increasing as the distance decreases ; the difference in energy is therefore partly if not entirely due to factors which affect the equilibrium properties of the bond.It appears probable that the C-C C=C C r C and the conjugated bonds of organic chemistry are an example of this type of variation since simple empirical equations account for the phenomena.6$ Such a variation we may call an " equilibrium variation " in bond energy. The other logical extreme case is where the equilibrium properties of an X-Y bond do not vary although t'he bond energies vary considerably. Here the difference in energy must be due to factors which do not affect the bond in the molecule but affect only the products into which it dissociates. This kind of variation we may call " separation variation " in bond energy. This empirical distinction may serve as a check on theoretical interpretation ; Long and Norrish's " reorganisation energy " concept,l4 for example clearly implies some " separation variation ".But the application of these ideas to radicals XY and corresponding molecules XY involves a further complication in that the repulsion forces between " non-bonded '' Y atoms the ehlorines in CC1 for example must be considered. Such computations have been applied in the past to the calculation of force constants but the same principles can simply be extended to other equilibrium properties of the X-Y bond This introductory discussion leads to a general programme of investi- gation of bond energies in compounds of " unusual " valency and to sug- gestion of methods ( a ) To discuss bond energies as far as possible without introducing heats of atomisation at all. ( b ) In cases where heats of formation of " unusual " molecules depend on high-temperature equilibria to use third-law rather than second-law methods to deduce heats of reaction.( c ) To compare as far as possible the results of kinetic spectroscopic and thermochemical experiments on bond properties together with due regard to the effects of " non-bonding " regulations. The present Review attempts such a programme inevitably still incom- plete for the peculiarly suitable group of elements carbon silicon germanium tin lead; other elements are considered only in so far as they illuminate thc problems arising in this Group. Section I1 As already pointed out conclusions drawn from the heats of formation of series of molecules do not depend on heats of atomisation. We shall therefore not discuss such applications successful though they are. 21 There are however points worth reconsidering about '' ionic-covalent resonance " and these arc the subject of the present Section.This " semi-empirical " quantum idea of Pauling's is invoked to explain bond energies themselves. If B(X-Y) B ( X - X ) B(Y-Y) are the bond energies (equation 1) of single bonds between the elements concerned then it is generally found that B(X-Y) is greater than the mean of B(X-X) and 21 Cf. Wheland " The Theory of Resonance and its Application to Organic Chemis- try" Chapman & Hall London 1944; John Wiley New York. 108 QUARTERLY REVIEWS B(Y-Y). covalent resonance energy” R, by the equation Admittedly the geometric mean gives a better correlation but a geometric mean of bond energies implies their absolute values and hence requires heats of atomisation.The arithmetic mean however in some special cases does not require heats of atomisation. It is easy to prove that if the standard states of hydrogen and the halogens be taken as diatomic gases with dissociation energy equal to their single-bond energy and that if the standard states of C Si Ge Sn be taken as the quadrivalent diamond-type crystals (grey tin not the metallic form) with each atom the centre of four single bonds then for the halogen hydrides the interhalogen compounds (XU) and the tetrahedal Group IV halides XY where the asterisk on Q; implies this somewhat unusual choice of thermo- chemical standard states. For these particular sets of compounds the evaluation of R, is therefore independent of any knowledge of heats of atomisation provided only ( a ) that the standard states may be regarded as singly bound in the valency sense and ( h ) that the arithmetic-mean approximation is adequate.This point is indeed made by Pauling 4 but does not perhaps appear to be generally realised. It may be emphasised that no such simplification is possible for such important elements as 0 N P. I n Table 1 therefore amre given the heats of formation of these molecules in t,he ordinary convention and then Q; in the modified convention and hence the “ ionic-resonance energy ” R defined in equation (3). Considering the arithmetic mean Pauling defines an “ ionic- B(X-Y) i [ B ( X - X ) + B(Y-Y)] + R, - (3) Q,*(XY,) = n R, * (4) TABLE 121a (All compounds gaseous) HF . HCl . HBr . HI . FC1 . IC1 . BrCl . CH . CE’ . CCl . CBr . QJ 64.0 22.1 8.7 - 5.0 25.7 - 3.5 - 3.1 18.2 231 25.9 - 12 Q? = Q f = Qf 12.5 + 1.5 = Qf + 4.0 + 0.8 = Q j = Q J = Qf + 3.5 64.0 22.1 12-5 1-5 25.7 4.0 0.8 4.6 57.8 6.5 0.8 X z - Z 1.9 0.9 0.7 0.4 1.0 0.5 0-2 0-4 1.5 0.5 0.3 SiH .SiF . SiC1 . SiBr . SiI . GeC1 . GeBr GcI . SnCI . SnBr QJ 8.7 360.1 142.5 83.7 16.1 216 - - 118.4 79.7 = QJ = Q J = Qr 99.0 45.9 = Q! 83.3 42.0 119.0 94.2 I?, Iss-5yI 2-2 0.3 90.0 2.2 35.6 1.2 24.8 1-0 11.5 0-7 54.0 1.2 20.8 1.1 10.5 0-7 29.8 1.3 23.5 1.1 Z1a All Qr values are from Bichowsky and Rossini “ Thermochemistry of Chemical Suhstanccs ” Reinhold New York 1937 except CF from von TT7artenberg Nachr. Akad. Wiss. Gdttingen (Mat. Phys. Abt.) 1946 p. 57 ; GeBr4 GeI from Evans and Richards J. 1952 1293. BSUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB SNU IV 109 Pauling points out a further remarkable correlation that R, = const.I x - xy I . * ( 6 ) where x and xy are empirical coefficients (whose scale is evidently arbitrary) characteristic only of the atoms X and Y and independent of their partners in the bond. These coefficients are- called " thermal electronegativities ". The last column in Table 1 gives his values of I x - xy I and in Fig. 1 we plot dz against I x - xY 1 for these compounds ; it can be seen that a straight line passes well through these points. For I x - xy I = 1 Z/R = 4.7 or R, = 22 in excellent agreement with Pauling's value 23 recommended on the basis of many data some of which are however less certain. On this specially restricted sample of 21 R, values depending on 9 ele- ments the empirical rule fits well. As a general rulc it has been criticised by Burawoy,22 who emphasiscs two matters.( a ) A few cases appear to show negutive values of Rr,. Some of these anomalies disappear if one chooses a geometric mean; others rcmain. It may however prove sig- nificant that most of the elements concerned in these anomalies are those whose heats of atomisation are pecu- liarly difficult to measure-the ele- ments of Groups V and VB VI and VIB of the Periodic Table-and can- not be simply eliminated ; the results for oxyge'n whose heat of atomisation is accurately known are satisfactory. (0) The correlation between R and thermal electronegativity is particu- larly inexact in the case of bonds FIG. 1 involving hydrogen an important deduction for which Burawoy's factual evidence though partly unsatisfactory is still conclusive. So far the thermal electronegativities are purely empirical coefficients whose significance depends on whether from N such coefficients and N B( X-X) values we can in fact account for the single-bond energies between N elements [$N(N - 1) in number].That we are really dealing with an electrical property of a bond is made very probable by the rough correlation of x wit'h the XY bond dipole moment and the proportionality between the thermal electronegativity of an atom and the sum of its ionisation potential I and electron affinity E. 23 Hcre the empirical correlation actually 2 2 Trans. Faraday SOC. 1943 39 79. 23 Mulliken J . Chem. Phys. 1934 2 782; 1935 3 573. 110 QUaRTERLY REVIEWS given in Pauling’s book refers oiily to “ the univalent elements hydrogen the halogens the alkali metals for which the treatment is stiraightformard ”.The subsequent neglect of this very striking relationship arises from two causes. First it appears to be generally believed that although ionisation potentials are well known yet not enough is known about electron affinities in the middle of the Periodic Table for the sum ( I + E ) to be evaluated. Sccondly Mulliken’s discussion 23 points out that t’he I and E values should really refer to the “ valence states ” of the atoms not to their spectroscopic ground states. Electron affinities caiz be roughly estimated for ground-statc atoms and since I is much larger than E the sum I + E can be estimated about as precisely as the tliermal electroiiegativity itself; thr ratio E / I is highest for the lialogens where it varies from 0-23 for fluorine to 0.33 for iodine for hydrogen it is only This conclusion is incscapable.However the actual facts are surprisingly simple. Element I H I . E . I + E x( ohs.) x( calc. ) Elenien t I . . E . . I + E . x( o bs.) .r( calc . ) . . . . . . . . . . Na 5.14 0.1 5.2 0.9 1.0 13.50 0.72 14.31 2.1 2.8 Mg 7.64 - 0.9 6-7 1.2 1.3 Li 5.40 0.4 5 . s 1.0 1.1 A1 5.97 0 6.0 1.5 1.2 9.32 - 0.6 8.7 1.5 1.7 Si 8.15 0.6 8.8 1.8 1.7 8.28 0.1 8-4 2.0 1.6 1’ 10.0 0.2 11-1 2.1 2.1 11.27 1.1 12.4 2.5 2.4 s 10.36 2-0 12.4 2.5 2.4 14.55 0.1 14.6 3.0 3.0 c‘1 12.90 3-73 14-6 3.0 2.8 13.63 2.2 15.8 3.5 3-1 Er 11.76 3.52 15-3 2-8 3-0 17-43 4.1 21.5 4 .o 4.1 I 10.44 3.21 11.6 2.4 2.6 0.05 and for carbon about 0.10 ; and the sum I + E is very closely proportional to the “ thermal clectronegativity ” e u m for nhultiualent elemcnts.For the halogens accurate (& 1 or 2%) values of E can be obtained from the lattice-energies of ionic crystals and the Born-Haber cycle ; for a few other elements values are obtainable from electron- bombardment experiments. For most elements we must employ another “ semi-empirical ” argument. In the ionisation potentials of a series of atoms and ions like R C+ Nff Off+ F++++ we are concerned wifh the same number of electrons but with changes by unity in the nuclea,r charge ; hence extra- polation back would give the ionisamtion potential of Be- which is with due regard to sign the electron affinity. For atoms and ions with two external electrons the ionisation potentials calculated by a variational method agree with experiment to wit’hin a few thousandths of a volt.The results are expressible as a series in direct and inverse powers of the atomic How should this extrapolation be madc ? BADGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB ,4ND I V 111 number 2 of which all but the first two or three terins are very small.24 Glockler expressing such series of isoelectronic ionisation potentials for more complex cases as similar series in 2 but with different coefficients obtained electron affinities for the elements in the two short periods agreeing to within about 0.4 volt with the Born-Haber values for the halogens and supported in many cases by computation from Slater eigenfunctions.26 In Table 2 are shown therefore the values of I and E for those elements for which such rough estimates of E have been made and the thermal electro- negativities x (from Table 11-3 in Pauling’s book 4).are in electron-volts (1 e.v. per atom = 23-06 kcal. per g.-atom). It can be seen from Fig. 2 where these points are plotted that the graph of I + E against x is a good straight line passing through the origin -the point for I€ being badly off the line and the points for B Al and 0 The I and E values 0 7 2 3 4 Therma/ e/ectronegu tiwty x FIG. 2 significantly off it. criticisms just referred to. The hydrogen anomaly is striking in view of Burawoy’s The equation to this line is or ( I + E ) = 5-15x(I + E in volts) . . - (7) I x = 0.193 ( I + E ) = 119x ( I + E in kcal./g.-atom) and this last coefficient may be directly compared with Pauling’s 130 on the smaller sample. I n the last line of Table 2 are given the values of the thermal electronegativity calculated from this equation.Again we have a general relation with individual exceptions. Provided however the empirical relation holds one conclusion may be drawn. Mulli- ken’s arguments prove conclusively that the ( I + E ) value which should be considered as a measure of electronegativity is that related to the valency 2 4 Hylleraas 2. PI-lysik 1930 65 209. 25 Phys. Rev. 1934 38 111. 26 Hellmann and Mamotenko Acta Physiochim. U.R.S.S. 1938 7 1. 112 QUARTERLY REVIEWS state. In fact the ( I f. E’) for the groundstate is as we have scen pro- portional to Pauling’s thermal electronegativity for the usual vulcncy state (carbon quadrivalent for example). The conclusion may therefore be provisionally drawn that the thermal electronegaticity of an atom in divfferent valency states depends but little on its particular calency state.,3 For it would enable for example the bond energy in a compound AX to be estimated from that in AY if one knew the bond energies in AX and AY,.It would permit discussion of setls of bond energies for different valencics in terms of the one numerical parameter the “ excitation energy of the valency state ”. And once more if we may accept the arithmetic- mean approximation the verification of this hypothesis necd not always require a knowledge of the heats of atomisation. There is a t any rate one case where we have fairly precise data for the bond energies of molecules XY and XY the mono- and di-halides of The heats of formation of HgHal are well known (cf. Richowsky and Rossini 210) the heat of atomisation of Hg from its vapour- pressure curve which has been well established and the dissociation energies D,O of HgHal from spectroscopic data.27$ 29 If we call ,R the bond energy in the HgHal molecule and ,B that in the diatomic radical ( -0; by definition) then we may draw up the following Table This principle if true would greatly simplify our problem.28 Hg-Cl . . . . 52.2 Hg-Br . . . . Hg-I . * . . . The rough constancy of ,B-,B is encouraging (the ,B values refer to 0” K and the $B values to 291” I<) and a similar test on the tri- and penta- halides of phosphorus and the di- and tetra-halides of tin also shows rough agreement. 28 It is instructive to compare this hypothesis with a proposal for simplifying bond energies put forward by Dewar 30 who states that “ it is possible to modify the bond-energy table so that tkie values for the bond energy and the dissociation energy ” (which he there calls bond strength) “ of any bond are equal if we take the heat of formation to refer to formation from atoms in arbitrary energy states ” and that “ such energy states should be regarded as arbitrary parameters the value of which should be so chosen that the bond energies of carbon bonds should be equal to their breaking-energy (dissociation energy).” It is as we have already pointed out legitimate to reckon Qj values for molecules from any arbitrary zero provided one restricts discussion to whether bond energies are constant in a series of molecules of the same 2 i Cf.Wehrli and Milazzo €IcZv. Ghim. Act* 1039 26 1025. 28 Skinner Trans. Furadczy SOC.1949 45 20. 29 Wieland in “ Les Spectres Moleculaires ” CNRS Paris 1947. 30 “Electronic Theory of Organic Chemistry ” O.U.P. 1949 pp. 32 33 37. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 113 valency. But a dissociation energy involves a difference in bond energy between two molecules of different valency (e.g. CH and CH,). If for example one chooses the zero to give D(CH,-H) equal to B’(CH,) the bond energy of CH reckoned from this zero why should the Same choice of zero be valid for CCl and CC1 ? Clearly it will not be unless the R, terms are the same in CC1 as in CC1,. Reasons have just been given for supposing that this may be true but Dewar’s argument rests on a confusion between experimental fact and arbitrary convention. Another application of thermal electronegativities is due to Schomaker and S t e ~ e n s o n ~ ~ according to whom an X-Y bond should be shorter than corresponds to the mean of lengths of the X-X and Y-Y bonds by an amount directly proportional to 1 x - xy I.Once more *the coni- pounds of the types considered in Table 1 are particularly suitable for investigation for the single- bond distances in IT, F, Cl, Br, I, and in the halogen hydrides are well known from spectroscopic data and in carbon (diamond) silicon germanium and grey tetrahedral tin from accurate X-ray work.32 We may take from these values the following single-bond distances H 0-742 F 1.435 C1 1-988 Rr 2.284 I 2.667 C-C 1.541 Si-Si 2.346 Ge-Ge 2.446 Sn-Sn 2.811 A. In Table 3 are given therefore (a,) the observed distances,lB ( b ) the internuclear distance pre- dicted as a mean (“ additivity of covalent radii ”) ( c ) the contrac- tion of the bond (additive minus observed) (d) the difference I Ax 1 Ixx-xyI FIG.3 in electronegativity according . to Pauling. against I Ax I in Fig. 3. The contractions are plotted If Ar is the contraction in then Ar = 0.11 I X - xY 1 . (8) with a probable error in the slope of about 20% (cf. Schomaker and Stevenson’s slope 0.09) ; the two companion dotted lines correspond to & 0.02 8. It may be seen that 16 of the 23 points plotted lie round this 3 1 J . Amer. Chem. SOC. 1941 63 37. 3 2 For diamond so0 Landolt-Bornstein’s ‘‘ Tabellen ” ; for silicon Jette and Foote J. Chem. Phys. 1935 3 615 ; for germanium Nitka Physikal. Z . 1937 38 896 ; for tin Brownlee Nature 1950 166 482. 114 QTJARTERLY REVIEWS TABLE 3 HF .HCl . HBr . HI . BrF . ClF . IC1 . CF . CCl . CHr . CI . SiF . 0-9 17 1.275 1.414 1.604 1.756 1.628 2.321 1-36 1.76 1-94 2-15 1.54 1.089 1.365 1.513 1-704 1.860 1.712 2.325 1.488 1.764 1.913 2.104 1.890 Contr. 0-172 0.090 0.099 0.100 0,104 0.084 0.007 0.13 I r O - 0.03 - 0.05 0-35 1.9 0 . 9 0.7 0.3 1.2 1.0 0-6 1.5 0.5 0.3 0-0 2.3 SiCI . SiBr . Si14 . GeF . GeC1 . GcBr QeI . SnHr CH . Sr1C1 . SnI . d0lP. 2.02 2.15 2.43 1.67 2-08 2.29 2-50 2.30 2.4 1 3.61 1.093 ‘additiw Coiitx. I 2.167 2.3 15 2.506 1.941 2.217 2.365 2.556 2.‘100 2.548 2.739 1.142 0.15 0.17 0.08 0.27 0.14 0.08 0.06 0.10 0.1 1 0.10 0.049 1.2 1-0 0.6 2.3 1.3 1 . 1 0.7 1.3 1 . 1 0.7 0.4 line with deviations which are in many cases of about the magnitude to be expected. I n other cases the deviations are beyond experimental error so i t is clcar that the rule is only a good first approximation but the points badly off the line merit spccial consideration.The scatter of the points a t very high Ax may not mean anything; there is no theoretical reason for a strictly linear relationship (it is indeed rather unlikely) and it would be easy to choose some other functional form which would represent the lower points equally well and yet curve upwards. Two outstanding dis- crepancies are left (a) that the point for HI is too high and that for ICl too low (curiously enough the carbon-iodine bond also has an anomalously low resonance energy RZy) ; ( b ) that aZE the contractions for the carbon halides are too small being actually negative for CCl, CRr, and CI,. These bonds are from Fig.3 all about 0-06 A too long. We shall show later that this abnormal length of carbon-halogen bonds may be predicted from the 9‘‘ non-bonding ” repulsions. The discussion so far shows the value of the empirical concept of elcctro- negativity ; the selected facts of this Section leave little doubt as to its general applicability or on the other hand as to there being individual discrepancies. Recently there has been a discussion of these ideas before the Royal Society.33 From the theoretical side (Cottrell and Sutton Coulson and others) it is difficult to see why they should work so well yet Warhurst has applied them even to the second-order effect involved in the changes of molecular vibration frequencies of given solutes in different solvents and Walsh has pointed out some remarkable correlations between electronegativities and bond vibration frequencies.These are the more remarkable in that vibration frequencies tlhemselves appear subject to empirical regularities of very simple form.34 One may venture the opinion that the search for empirical regularities will yield yet further results. 33 Proc. Roy. Xoc. 1951 A 207 1-74. 3 4 Guggenheimcr Proc. Phys. SOC. 1946 58 456 ; Discuss. Faraday ~Soc. 1950 9 ; Baughan Trans. Faraday Soc. 1952 48 121. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 115 Section I11 derived from high-temperature equilibria. I n this Section we are concerned with improving some heats of reaction Wc may write AG? = - RT In K p ~ . * (9) where AGg is the standard Gibbs free-energy change corresponding to the equilibrium constant Kp both referring to 1’” K.Since (the Gibbs-Helmholtz equation) AGg = AH - T.ASg AGg = (AH - AH$)) - T(AX - AS’?) + AH$ - T.AXF . (10) where the subscript 0 refers to 0” K. If we know the two terms in parentheses and Ax$ the entropy change a t absolute zero we can obtain AII? the heat of reaction a t absolute zero (and AH- the heat of reaction at any desired intermediate temperature). For a condenscd phase II$? - H,O must be determined by a graphical integration Cp.dT +AH’ +- J C,.dT + AH” + Cp.ciT . (11) for example where AH’ AH” are the heat content changes due to phase changes (melting crystalline transitions occurring a t T’ T” etc.). For a gaseous phase Cp can be calculated from well-known formulz of quantum statistics. Similarly Sg - 8; can be computed from the same data needed for HOT - H$) for condensed phases and for gases from other well-known formulae of quantum statistics.Such computations though sometimes tiresome are quite straightforward the only difficulties coming from cor- rections for quantum weight and for electronic excitation [of atomic vapours in particular). Alternatively one can tabulate by the same means values of G$ - H,O or - (G? - H,O)/T the function called “ free-energy function ” by United States authors ; this is often simpler in practice. We are concerned essen- tially with ( H g - HF)dT/T2 and the inverse-square dependence on temperature inside the integral implies that the uncertain high-temperature ranges in determinations in H are not of the importance which one might at first suppose. It may be of use to quote a few general references on these computations.( a ) Theory. A logical account particularly on the quantum-weight diffi- culties is given by Fowler and G~ggenheim.3~ Another general account from a more directly practical point of view is given by J. G. A ~ t o n . ~ ~ ( 6 ) Fact. A full and accurate survey of numerical data for inorganic sub- stances has been given in a series of memoirs by K. K. Kelley under the Tt’ 7”” H$ - H,O = 5:’ T‘ JY 5 35 “ Statistical Thermodynamics ” C.U.P. 1939 Chap. V. 36 See H. S. Taylor and S. Glasstone ’* Treatise on Physical Chemistry ” Van Nostrand Co. New York 1942. 116 QUARTERLY REVIEWS general title " Contributions to the Data of Theoretical Metallurgy ".37 A survey of the heats of vaporisation and free-energy functions of elements oxides halides nitrides and carbides has been published by L.Brewer and his co-worker~,~~ based largely on Kelley's work brought up to date. The particular case of the vapour pressure of metals has also independently been discussed by E~cken.~S In some cases these discussions imke major alterations to the values for heats of atomisation quoted by Bichowsky and Rossini.21a Finally one may refer to a useful list of the quantum weights and excitation energies of low-lying atomic energy states in Landolt-Bornstein's " Tabellen " (Erganzungsband IIIc). As particular examples of these methods we shall here consider ( a ) the heat of atomisation of silicon (and the heat of formation of silicon carbide) ; ( b ) the heat of atomisation of tin ; ( c ) the heat of atomisation of germanium ; (d) the heat of formation of silicon monoxide SiO and its dissociation energy into atoms.(a) Heat of Vaporisation of Silicon.-The vapour pressure of this element has been measured by a streaming technique by von Wa~tenberg,~~ whose results are only approximate by Ruff and his co-workers by their spring- balance t e ~ h n i q u e ~ ~ and by Baur and B r ~ n n e r ~ ~ using a mercury-drop null manometer. From a graphical second-law treatment one obtains for A0 the heat of vaporisation of the solid at O " K the values (44) 150 and 106 kcal. respectively and it is evident that the second-law method gives only the roughest estimate. To use the third-law method we need data on the specific heat and heat of fusion of silicon. For low temperat,ures (20-300" I<) we have data by Andrews 43 in good agreement with older data by Nernst and Schwers ; 44 the extrapolation from 20" K t o absolute zero has been made by taking silicon to be a Debye solid with 80 = 460" K.From room temperature to 100" c there are several values quoted in Mellor's treatise 44a which have been plotted graphically. Above room temperature to 1200" K we have Magnus's data 45 for the total heat content above 300" K on a sample of known purity. Silicon melts at 1688" H (1415" C) and the range from 1200" to 1688" has been estimated by a graphical extrapolation of Magnus's data. The thermodynamic functions so obtained 37 United States Department of the Interior Bureau of Mines Bulletins ( a ) 1935 No. 383 (vapour pressures) ; ( b ) 1936 No. 393 (heats of fusion) ; ( c ) 1949 No. 176 (high-temperature heat content heat capacity and entropy data) ; ( d ) 1950 No.477 (revision of entropy data). 38 In National Nuclear Energy Series IV 19B " Chemistry and Metallurgy of Miscellaneous Materials Thermodynamics " edited by L. L. Quill 'McGraw Hill 1950. 39 Metallwirtsch. 1936 15 27 63. 40 2. anorg. Chem. 1913 79 71. *l Trans. Amer. Electrochem. s'oc. Preprint 68-32 (1935) ; 2. Elektrochern. 1926 4 2 Helv. Chirn. Acta 1934 17 958. 4 3 J. Arner. Chem. Soc. 1930 52 2301. 4 4 Nitzunpber. Preuss. Akad. Wiss. 1914 355. 44a " A Comprehensive Treatise on Inorganic and Theoretical Chemistry " Vol. VI Longmans Green and Co. London 1925. 4 5 Ann. Physik 1923 70 303. 32 515. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 117 were in excellent agreement with those deduced by Kelley 37 from essentially the same data.The heat of fusion and specific heat of liquid silicon are not precisely known. The heat of fusion may be estimated from the depression of freez- ing point by metallic solutes ; Kelley 37 so obtains the value 9470 cal./mole ; Kubaschewski et aZ.46 from similar evidence recommended 11,100 500 cal./mole. The specific heat C of liquid silicon is also not well known ; it can hardly be less than 7 cal.,/g.-atom and dircct experiment suggests the much higher value 11.2 ~al./g.-atom.~~ In spite of these uncertainties the differences implied for A are small compared with the discrepancies in the second-law treatment. Thus in the following Table the heat of vaporisation lo of silicon at 0" K has been calculated on two assumptions ( a ) Cp liquid Si = 7 cal./g.-atom latent heat of fusion 9470 cal./g.-atom ; ( b ) Cp liquid Si = 11.2 latent heat 11,200 cal./g.-atom.Authors Ruff et ul. (grouped data) Baur and Brunner T O I< 2607 2442 2373 2309 2277 2160 207 1 1980 P mm. 752 147 70 31 23 15 6.3 2 Mean of last six (84.2) (87.6) 88.9 90.5 90.7 88.5 88.9 90.0 89.6 (52.4) (86.2) 87.7 89.4 89.8 87.8 88.3 89.6 88.8 It can be seen that the values obtained for AH? are fairly steady except a t the very highest temperatures ; by analogy with carbon,48 one would expect participation of Si molecules a t the highest pressures. Similar calculations 011 the earlier approximate data of von Wartenberg 4O suggest lo 21 75 kcal./mole as opposed to the second-law value of 44 kcal. We may therefore take a value of 89-2 (& 3.0 perhaps) for the heat of vaporisa- tion of silicon at absolute zero corresponding to 89.9 kcal.at room tem- perature (18" or 25"). This calculation has been presented a t some length to show the power of the method even when the high-temperature thermal data are only approximate. The Heat of Formation of Sic (Carborund~m).-RufT~~ also quotes data for the vaporisation of Sic by the reaction Sicsolit1 + Cgrnptiite + Sivapour 40 Z . Elektrochem. 1950 54 275. 47 Chipman and Grant Trans. Amer. SOC. Metals Preprint No. 28 1942. 48 Brewer Gilles and Jenkins J . Chem. Pliys. 1948 16 797. 118 QUARTERLY REVIEWS at temperatures between 2579" and 2925" K. The thermodynamic functions of graphite have been listed up t u 1500" K by Itossini and his c o - ~ o r k e r s ~ ~ and those of carborundum by Kelley 37 50 up to 1700" K.In both cases the " free energy function " - (Up - E:g)/T is very well given by a formula T ' K V.P. mm. 2579 1.24 2683 6.05 ~ _ _ _ _ ~ - . _ _ _ _ _ _ ~ TABLE 4. Vapour pressure of silicon omr carborundurn (qroziped yesults) T 0 1; I v . p . nm. AH,. ~ 126.5 2841 15.9 125.6 123.4 2925 31.2 125-7 125.3 Mean ~~ ~ of the type A + BT - CT2 from 500" K upwards. Extrapolating these formulae up to 2500-3000" K one can obtain a rough estimatc of AH for the reaction given as shown in Table 4. Froiii this and the value just obtained we deduce Siyolid + Sivapoirr ; AH? 89.3 Sisolid + Cgrspllite -+ Sicsolid AH - 36.1 kcal. or Xisolid + Cdialrlond -+ SiCSolid AH& - 35.8 kcal. [G - Qf(SiC)] This value should be equal to - Qf,2,1n listed by Bichowsky and Rossini,21a who recommend Qf 291 = 28 kcal./mole as a mean of widely different values (the calorimetric data depend on small differences in large heats of reaction).If Si and C were of equal " thermal electronegativity " one would predict from the distances given in Section 11 a Si-C distance of 1-944 A in Sic. The observed value 51 is 1.888 8. This contraction being interpreted as due to difference in electronegativity ( Schoniaker-Stevenson) this difference would from Fig. 3 (equation 8) be equal to 0.19 (Pauling recommends 0.7 the I + E data in Table 2 and equation 7 give 0-7). An electronegativity difference of 0.49 would predict from Pig. 1 an ionic resonance energy R, of 5-3 kcal. per bond or Qj(SiC) = 21 kcal.; a difference 0.70 would predict Qj(SiC) = 44 kcal. ( b ) Heat of Vaporisation of Tin.-The vapour pressure of tin has been observed by several workers.(i) G r e e n w ~ o d ~ ~ by varying the pressure of an inert gas and measuring the temperature of visible ebullition of the liquid metal. Range temperature 2243-2543" K pressure 101-760 mm. (ii) Ruff and his c o - ~ o r k e r s ~ ~ by their " spring-balance " technique. Range temperature 2278-2543" K pressure 126-755 mm. These ale in excellent agreement with (i). (iii) Baur and B r ~ n n e r ~ ~ by the same technique as used for silicon. Range temperature 1585-2103" K pressure The agreement is reasonably satisfactory. 49 Bull. Bur. Stand. Circular 461 1947. 50 J. Amer. Chem. SOC. 1941 63 1137. 51Ta~lor and Laidler J. AppZ. Physics 1950 1 178. 5 2 Proc. Roy. s'oc. 1909 A 82 396; 53Ruff and Bergdahl 2. ccnorg Chem.1919 106 7 6 ; 1910. 83 483. Ruff and Mugdan ibid. 1921 117 147. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 119 2.6-81-7 mm. (iv) Von Wartenberg 54 obtained two isolated values from the rate at which tin is carried as vapour by a stream of nitrogen 1403" K p = 0-13 mm ; 1633" K p = 1.2 111111. (v) Harteck 5 5 a t 1264-1434" K and pressures of 5 x to 8.5 x 10-4 nlm. by Knudsen's tecliriique of effusion through a sinall hole. (vi) Granovskaya and Lyubimov 56 have measured the vapour pressure by Langmuir's method (rate of evaporation from a surface). to 3 x mm. We have here therefore data by various authors by different techniques covering a range of 15000 and a factor about los in pressure. As before attempts to deduce a second-law value for tlie heat of vaporisation lead to wide discrepancies.I n the range round 100 mm. the data of the first three investigations quoted agree very well and so do the two sets of data between 100 and 760 mm. (see Pig. 4). At lower temperatures considerable scatter is apparent and the results of (v) and (vi) are quite incompatible. On application of a third-law calculation to these data the situation becomes clearer. We have throughout ussumed the vapour to be monatomic cor- recting therefore Harteck's data and used the thermodynamic functions listed by K e l l e ~ . ~ ' For tin whose melting point is so low (605" K) tlie heat of fusion is well established but the specific heat of the liquid metal is once more very uncertain. The computations have therefore been carried through for four constant values of Cp 7.0 7-3 (favoured by many previous authors) 9.0 and 11.0 (improbably high) as an illustration of the effect of errors in this quantity.I n view of the large numbers of experi- mental points we have here taken smoothed values by plotting p against TABLE 5 Range temperature 1003-1213" K pressure 1.4 X Authors Ruff et al. Greenwood. Baur and Brunner v. Wartonberg . Harteck . . . Granovskaya and Lyubimov 1'. O R p mm. 590 31 6 1 62 78 46 13 2.9 0.39 8.9 x 1 0 - 4 1.7 x 10-4 2.9 x 10-4 1.45 x A0 r a k . for diffrreiit valucs of C for liquid t i l l 63.4 63.9 64.3 61.9 61.2 59.6 68.0 60.8 73.4 72.6 65.8 65.8 7.3 62.8 63.3 $3.8 61.5 60-8 59.3 57.8 60.7 73.3 72.4 65.7 65.7 9 69.2 55.6 57.6 56.5 59.6 72.4 71.7 65.1 65.1 11 53.4 56.5 57.5 56.4 56.1 55-7 55.0 58.3 71-3 70.8 64.4 65.0 638 385 220 63.1 30.6 5.60 0.67 0.17 4.4 x 10-2 8.3 x 10-3 1.2 x 1 0 - 3 7 .4 x 10-6 6 4 2. Elektrochem. 191 3 19 484. 55 2. phys. Chem. 1988 134 1. 513 J . Phys. Chem. V.R.S.S. 1944 22 527. 120 QUARTERLY REVIEWS 1/T for each of the references given ; tlhe data of Greenwood and of Ruff and his co-workers agree so well that they have been considered together. The results are in Table 5. It is clear from these data that Harteck’s results are incompatible with the other results which are in fairly good mutual agreement. The mean values of lo for the other work (double weight being given to the concordant high-temperature results) are for Cp = 7 61.8 ; Cp = 7.3 62.4 ; Cp = 9.0 60.2 ; Cp = 11 57.7 kcal./g.-atom. The best estimate is probably lo = 62.4 & 2-0 kcal./g.-atom and the probable error could be reduced to about a third if the specific-heat data were certain.FIG. 4 The f u l l line shows the third-law calculation for A. = 62 l i d . ; the broken lines for h = 60 and 64. In Fig. 4 therefore we have plotted the vapour-pressure curve cor- responding to lo = 62.4 (broken lines & 2-0 kcal.) Cp = 7.3 the vapour pressures corresponding to this being given in the last column of Table 5 . The agreement is sufficiently satisfactory for discrepancies to be worth special comment. These results have been much criticised as being seriously affected by porosity in the crucibles used but Partington 67 has recently denied that the crucibles ( a ) The accuracy of Greenwood’s data is noteworthy 67 “ Advanced Treatise on Physiral Chemistry ” Longmans Green and Co.London 1950 Vol. 11 p. 237. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 121 used were in fact appreciably porous. In agreement with Partington our analysis shows Greenwood's data to be not seriously in error. ( b ) Fig. 4 suggests that Baur and Brunner's results are systematically too high a t lower pressures and that second-law estimates based on these alone 5* are untrustworthy. Eucken 39 points out the same systematic trend in their work on Ag Be Al and Mn and mentions that Pischer 69 has explained such an effect as probably due to the peculiarities of their pressure- measurement device. Here as Table 5 shows the vapour pressure observed is about 50 times too low. One can only suppose that in some circumstances (surface impurities ?) tin is peculiarly difficult to vaporise.This hypothesis gains some support from the early work of von Wartenberg 60 on the vapour density of tin which is often quoted as evidence for the vapour's being Sn,. Actually however no constant value was obtained for the atomicity of the vapour the best integral value corresponding roughly to Sn (!) and von Wartenberg quotes the molecular weights as " naturally only apparent ". These two researches suggest that tin vapour is not necessarily polyatomic but that peculiar difficulties sometimes attend attainment of equilibrium on vaporisation. The good agreement of all the other data with the third-law computa- tions in which a monatomic vapour was assumed argues strongly for the vapoF's being monatomic in analogy with lead. (c) The Heat of Vaporisation of Germanium.-Only one study of the vapour pressure of pure germanium has so far been published that by Searcy 61 using Knudsen's technique between 1510" and 1882" K.These data were treated by Searcy by second-law methods giving Ge -+ Gevapour AH$ = 84.0 3 1-5 kcal. Recently by using the extremely pure germanium now of great industrial importance two independent series of measurements have been published on the specific heat between liquid-helium temperatures and 160-200" K by Estermann and Weertman 62 and by Hill and P a r k i n ~ o n . ~ ~ These two sets of results are in good agreement. Up to 200" K the errors in the thermo- dynamic functions of germanium are therefore very small. From 2 0 0 " ~ to the melting point T 11232"~) the Reviewer has calculated Cv from Debye's equation (0 = 400") and Cp - Cv from the empirical equation the curve so obtained agreeing fairly well with Kelley's estimate 37 of Cp = 4.62 + 2.27 x 10-3T(273-7130 K).The heat of melting has been estimated by Kubaschewski 46 a t 7.3 kcal./g.-atom and no data exist on the specific heat of the liquid which has been assumed to be 7.3 cal./g.-atom (analogy with tin). The high- temperature range in the " free-energy function '' is thus uncertain. Taking (c) It remains to consider Harteck's data.55 cp - cv oc C;T/T 68 Long and Norrish Phil. Trans. 1949 241 A 687. 60HeZv. Chim. Acta 1935 18 1028. 6oZ. nnorg. Chem. 1908 56 320. J . Amer. Chem. SOC. 1952 '74 4789. 62 J . Chem. Physics 1952 20. 6 3 Phil. Mag. 1952 43 309. 122 QUARTERLY REVIEWS the probable errors as (i) 0-200" K negligible (ii) 200-1232" K & lo% (iii) 1232-1700" K (mean value of v.p.data) & 30% one obtains an error of A check on the consistency of the data involves a much smaller error since the range 200-1500°~ is common. The computation of AH? is then as shown in the following Table (smoothed data) 4 kcal. in AH; if the errors in (ii) and (iii) arc of the same sign. T O K . . . . . loglop (atm.) . . . AH . . . . . 1600 1600 1700 1800 1900 -6.01 -5.24 -4.56 -3.96 -3.43 89.0 88.9 88.8 88.6 88.5 as a mean value one may recommend AH:(vap.) = 88.8 (& 4.0) and AH&(vap.) = 89.2 (* 4.0) kcal./g.-atom. The self-consistency of the data and the good agreement with the second-law value show that this unique set of data can be accepted with confidence ; once more the value of AH could be much improved if more were known about high-temperature specific heats.The lack of high-temperature specific heat data on liquid metals is indeed in general a limiting factor t o the accuracy of deduction of many heats of reaction. Such data as are available 64 suggest a remarkable constancy in Cp.65 Simple theory would predict only a high-tempeyaturc constancy in the lattice contribution to C ; but to this must be added two terms (i) The electronic specific heat which theoretically is proportional to T ; at very low temperatures (liquid helium) this term is greater than the lattice term since the latter is then proportional to T3 ; at room tempera- tures i t is negligible and at high temperatures it becomes again appreci- able since i t continues to increase while the lattice term remains constant.(ii) The difference Cp - C, which must be positive and can be calculated from coefficients of expansion and compressibility ; if Cp therefore really is roughly constant Cv must be decreasing. This decrease has becn observed for mercury and the alkali metals.66 It can be shown that such a decrease is incompatible with simple harmonic ~ i b r a t i o n s ~ ~ s o that the study of high- temperature C might throw light on problems of the liquid state as well as being of practical importance. Finally one may point out that the heats of vaporisation of silicon and germanium are practically identical. I n Group IIA also the heat of vaporisa- tion of magnesium is less than those of both Be and Ca. It is not therefore always possible simply to interpolate heats of vaporisation as a function of interatomic distance even in the same sub-group of the Periodic Table.( d ) The Heat of Formation and Dissociation Energy of Si0.-Silicoii monoxide has been known as a " spectroscopic " molecule for some time. 6 4 See e.g. Van Arkel " Reine Metalle " Springer-Verlag Berlin 1939. 65Cf. also the comments of Sir Andrew MeCanee Discziss. Fnmday SOC. No. 4 66Eyring and Kineaid J. Chem. Phys. 1937 5 591. 67 Cf. Fowler and Guggenheim ref. 35 p. 147. 1948 p. 8. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 123 It has been studied by Bonhoeffer 68 and more recently by Barrow and his c o - ~ o r k e r s . ~ ~ The equilibrium distance (1.510 8) and the fundamental frequency of vibration (1242 cm.-l) arc well known and estimates have been made of its dissociation energy.More directly chemical evidence shows that silica is unusually volatile in the presence of reducing agents (silicon itself or hydrogen for example) and powdery or resinous sublimates have been obtained of approximately the composition SiO although X-ray investigation showed many of these solid products to be intimate mixtures of silicon and silica produced presumably by disproportionation. The solubility of silica in molten iron points to the existence of SiO as a solute ; ' 0 it is possible to reduce silicates to oxides and SiO by heating them with silicon and even some oxides to metals and SiO e.g. Nb,O + 5% + 2Nb + 5SiO (vapour) and SiO may exist as a solid chemical species.71 We now use some data on high-temperature equilibria to compute by statistical methods the heat of formation of SiO vapour and hence deduce the dissociation energy.The reactions are H (gas) + SiO (quartz) Si (solid) + SiO (quartz) -+ 2 SiO (gas) -+ H,O (gas) + SiO (gas) and the " free-energy functions " required have been obtained as follows H, H,O from publications of the Bureau of Standards; 49 SiO, from Mosesman and Pitzer's data; 7 2 SiO calculated by the usual simple- harmonic rigid rotator approximation (symmetry number unity) ; Si as already explained. The first of these reactions was studied between 1200" and 1500" c by a streaming technique by Grube and S ~ e i d e l ~ ~ who determined the SiO content of the gas by decomposing it on an iron wire and analysing the product for silicon. By second-law methods they found a mean AH$ = 112 & 6 kcal. This is in reasonable agreement with the third-law calculations as shown in the following Table (pH = 1 atm.).T K 1473 1573 1673 1773 psl0 111111. 0.05 0.09 0.28 0.62 59.3 56.6 52.5 51.4 -@Go,- AH* 0) 73.9 78.6 83.1 87.8 AH (kcal./mole) 133-3 135.2 135.6 (139.2) Mean of first three 134-7 The discrepancy of the highest-pressure point would suggest that t'he method of analysis begins to break down and that about one-third of the SiO escaped detection. These observations are supported by the recent 0 8 2 . phys. Chem. 1928 131 363. For data see Herzberg ref. 18. 70 Zapffe and Sims Anzcr. Insf. Mi??. Met. Eng. Technical Publication No. 1498 1942. 7 1 Zintl Rraiining Grube Krings and hforawietz 2. anorg. Chem. 1940 245 1. 7 2 J . Amer. C'hrm. Sot, 1941 63 2352. 73 8. Elektrochem. 1949 53 339. 124 QUARTERLY REVIEWS work of Tombs and Welch,74 who analysed the gas stream for H,O by thermal conductivity.Here as these authors point out the obvious risk is that some water may be coming out of the glass etc. I n the following table a third-law calculation is shown for their data-the 23 observations given fall naturally into 5 groups. 143.2 148.4 153.1 No. of observations 170.1 170.8 172.9 Mean 171.2 T. K AG AH AH (con ) 129.7 125.8 127.8 130.5 130.4 1508 1632 1744 1836 1904 47.5 43.7 41.3 40 4 37.6 75.1 50.7 85 8 89.7 92 6 122.6 124.4 127.1 130.1 130 2 The value for AH shows a considerable drift but tends to become steady at the highest pressures where the effect of such adventitious water would be least. If one corrects the data assuming a constant adventitious water pressure of 0.2 x 10-4 atm.an almost constant AH? value is obtained (last column of the Table above). A " best " value of AH = 130.3 may be recommended. We now turn t o the reaction Si (solid) + SiO (quartz) + 2SiO (gas). This was studied by following loss of weight by Knudsen's method by The agree- Schiifer and Hornle,75 whose results are analysed in Table 6. TABLE 6 TABLE 7 AG; AH 165.3 166.8 167.6 169.2 Mean 167.2 T O K 1673 1623 1653 1713 T O K 1336 1367 1398 1429 1460 55.1 52.7 50.2 47.7 46.2 109.7 112.1 114.5 117.0 119.4 164.8 ~ 164.8 164.7 164.7 i (165.6) ~ Mean 164-7 1 37.0 34.6 33.1 30.2 128.3 132.2 134.5 139.0 ment is extremely satisfactory. Tombs and Welch 74 have also studied this reaction by measuring the weight-loss from a boat in a stream of argon; their results are shown in Table 7.By condensing the SiO as a solid on to a weighed alumina tube these authors were also able to follow the reaction to higher temperatures where direct weight loss was impracticable through spattering of liquid silicon ; these results are shown in the following Table. I' O K 26.9 23.4 10.8 1773 1853 1920 5 4 J . Iron Rtecl Inst. 1052 172 69. 75Z. anorg. Chem. 1950 263 261. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 125 The correctness of the " free-energy functions " being assumed therefore these data give the heats of certain reactions involving the gaseous SiO molecule. All the other heats of formation are known so the data can be corrected to 291 O K. to give AHf( - Q f ) of SiO a t this conventional standard temperature. Taking @for H,O (gas) as 57.8 21a and that for solid quartz as 210.3 k~al./mole,~~ we can compute the heat of formation of SiO (see Technique Si analysis H,O analysis Weight loss Weight loss Analysis of gases Table 8).TABLE 8 I AH 134.7 130-3 164.7 167.2 171.2 Reaction H, + SiO -+ H,O + SiO Si + SiO2+2Si0 . . . Authors G. & S. T. & W. S. & H. T. & W. T. & W. A f c L 135.4 131-0 166.3 168.13 172.8 Q p O J (-AH, 291') 17.1 21.5 22.0 20.8 18.8 Schafer and Hornle's data which internal consistency suggests to be the most precise are in good agreement with two of the sets of Tombs and Welch's data ; their third method and that of Grube and Speidel involve difficult analytical techniques based on heterogeneous reactions and give a slightly lower result. Qr (SiO gas) at 291" K = 21.6 & 1 kcal.whence Sicrystal + 0 -+ SiO ; = - 80.7 AH = - 80.6 Adding to this the heat of vaporisation of silicon a t absolute zero we obtain D,O (SiO) = 170 & 6 kcal. (7.39 volts) In an imprtant recent paper where such third-law methods are applied to several oxides Brewer and Mastick 77 have deduced a value of about 165 kcal./mole from other experimental data. From linear Birge-Sponer extrapolation of the lC ground state,ls one obtains 7.8 volts for the dissociation energy of SiO (private communication from Dr. R. F. Barrow) ; Gaydon l7 recommends 8 & 1 volts and Vago and Barrow 78 8.26. In all cases these authors assume the products of dissociation to be ground-state atoms. In this calculation we have used third-law methods to compute an uncertain dissociation energy of a diatomic molecule.A combination of third-law and spectroscopic methods on SnO has recently been published by Drummond and Barrow.79 In their paper a dissociation limit in SnO of We may take 76Humphrey and King J . dmer. Chem. SOC. 1952 74 2041. 77 J . Chem. Phys. 1951 19 834. 7 8 J. C'him. physique '' Contrib. Btude structure mol. Vol. comm6m. Victor Henri " 79 I'roc. Phys. ~Yoc. 1952 A 65 148. Desoer Lihge 1947 p. 201. 126 QUARTERLY REVIEWS uncertain " identification " has by third-law evaluation of the heat of vaporisation of SnO and the calculations on Sn given in this present paper been identified as very probably due to t,he process SnO (" E-state ") -j Sn (3P,) + 0 (3P) and hence not only is i t almost certain that SnO dissociates into ground-state oxygen and the triplet ground-state of tin but also t'he particular component of the tin triplet-state has been identified giving D,O (SnO) = 121 kcal.(5.25 volts). Brewer and Mastick 7 7 have also by third-law methods obtained a dissociation energy Do0 for PbO of 98 kcal. (4.25 volts). SiO SnO and PbO probably dissociate therefore into t,he 3P ground states of Si Sn Pb ; if CO does the same then the high value 170 kcal. for the heat of vaporisation of carbon follows. Section IV Before considering the bond energies and equilibrium properties of molecules containing the elements C Si Ge Sn in different valericies we shall in the present Section discuss briefly the effect of van der Waals inter- action between the " non-bonded '' atoms. Again the tetrahalides of Group IV-IV are a particularly suitable subject of investigation.The structure of such molecules as NH is largely determined by repulsion between the bonds and the " lone-pair " electrons ; but for carboq silicon etc. there are no lone-pairs to complicate the picture. Previous 'discussions on these repulsive forces have mainly considered their effect on the vibrational frequencies of the molecule. By representing the repulsion as an inverse power-function of distance it is possible to represent adequately the frequencies which otherwise do not agree with the simple valency-force field (S.V.F.F.) model. The laws of non-bonded repul- sive force so deduced agree very roughly with other approximate estimates -the force between " non-bonded " chlorine atoms being considered to be the same as between argon atoms a t the same distance for example.8l9 8 2 But the extension of these arguments has led to improbable consequences.Heath and Linnett,12 for example deduce that the C-Cl distance in CCl is stretched by no less than 0.49 A by the repulsion between the C1 atoms. This conclusion which cannot be reconciled with the C-C1 distances in CH,Cl CH,Cl, CHCl, CCl C1.781 1.77 (& 02) 1.761 1.785 (& 0*015) respectively] 2 0 ~ 8 3 or wiOh the approximate constancy of the successive substitution heats of CH with C1,l could however well arise from extra- polation of an unduly simplified potential energy function. We shall here therefore invert the problem and consider whether from what is known about potential-energy functions of " non-bonded " atoms one can deduce ( a ) the " non-bonding " force-constants in the actual mole- 80 Fuct Sidgwick and Powell Proc.Roy. h'oc. 1940 A. 176 153. Theory Cf. Lennard-Jones and Pople Discuss. Furuday Suc. 1951 10 9. 81 Urey and Bradley Phys. Reviews 1931 38 1969. a 2 Heath and Linnett Trans. Farnday SOC. 1948 44 561. 93 Mirro-wave data listed in Ann. Rev. Physicrrl Chcm. Vols. 1 and 2 (1950 1951) Annual Rcviews h e Stanford California. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 127 cules,81p g2 ( b ) the heats of formation of such molecules [t,he arguments in Section I1 suggest that the effect of repulsion is small (cf. Pauling ref. 4)] (c) the observed interatomic distances-in particular the peculiar discrepancy of carbon-halogen bond lengths. From London's theory of van der Waals forces we know that the attrac- tive potential energy can be approximately represented as an inverse sixth- power function of the interatomic distance y while the repulsive potential energy is more nearly an exponential function.To simplify the mathe- matics it is usual to replace this also by a high-power law giving for the " non-bonding )' potential energy W where m = 6. This model has been successfully applied by Lennard-Jones with n 2 12,84 to the second virial coefficient of gases and by Lennard- Jones and Devonshire 85 to the equation of state of condensed phases of the inert gases. In our discussion we shall be concerned with W dW/dy and d2W/dy2. It is convenient to transform all these in terms of W, the equilibrium energy and Yo the equilibrium distance-where the repulsive and attractive forces are equal and opposite-by using the relation From (12) and (13) we can easily deduce that T I - ahrn+B/Yn * ' (12) (d~/d?h = Yo = 0 * (13) whence n - m (14) where y is the dimensionless variable defined by y'- Yo/y I If we assume given values for m (= 6) and n (= 12)) then 4 can once and for all be calculated as functions of y ; and y being as an experimental fact the discussion then involves Wo and With this choice of the exponents m and n we have x(y) = 1276 - 12712 4(Y) = 2Y6 - y12 ~ ( y ) = 1 5 6 ~ ~ ~ - 84y6 We start by considering what is known about Yo-the equilibrium distance of two atoms in diflerent molecules.Pauling * has from the empirical data of crystallography shown that " van der Waals distances )' 8 4 P h g ~ Z . ~ ~ 1937 4 941. * ~ P T o c Roy. Soc. 1937 A 163 53, 128 QUARTEILLY REVIEWS can be roughly dissected into sums of two " van der Waals radii " and gives the following list of van der Waals radii Van der Waals radii p (from Pauling) Element .. ~ N i P i A s i S b i 0 1 S 1 Se ~ Te ~ F 1 C1 ~ Br 1 I Radius (8) . 1.5 1.9 2.0 2.2 1.40 1.85 2.00 2.20 1.35 1.80 1-05 2.15 (& 0.05-0.10 A in each case) From the geometry of the tetrahedron y = 1.633~. The force between the peripheral atoms is repulsive if y < (2 van der Waals radii) i.e. y = 1.633~ < 2p or x < 1 . 2 2 ~ . Referring to the experimental data in Table 3 we see that this condition is easily satisfied for CF, CCl, CBr, CI, just satisfied for the halides of Si and Ge and not satis- fied for those of Sn. The fact that the halides of C show unusually long bonds (Scction 11) encourages us to more detailed treatment.Let us now consider W, the equilibrium van der Waals 0 This has been computed together with the equili- brium distance Y, for simple gases by Lennard-Jones using the 6-12 potential.84 His results are given in Table 9 which also gives as a rough measure of intermolecular energy the latent heat of evaporation Lv of the liquid at its boiling point ; it can be seen that for monatomic TABLE 9." W and Yo from the 6-12 potential ; heats of vaporisation of liquids at the boiling point (Lv). 0 energy. Neon . . . . Argon . . . . Krypton . . . Xenon . . . . Nitrogen . . . Oxygen . . . . c o . . . . . C H . . . . . F . . . . . B r . . . . . C l . . . . . I . . . . . cal /g -atom lopx6 ergs 4.88 16.50 23.84 30.99 13.24 16.97 13.36 19.70 (15.1) (40.7) (68-2) (95.5) 70.6 239 346 447 192 244.9 192.8 284.3 (219) (590) (990) (1 385) 3.049 3.819 4.030 4.561 4.174 - - - - - - - L V (cal./g.-mol ) 442 1590 2010 3110 1457 1858 1470 2040 1640 4420 7420 10390 Lvl ffrJ 6.38 6.25 5.80 6.82 7.58 7.58 7.60 7.20 - - - - * T V and Yo for Ne A N, 0, CO and CH from Lennard-Jones ; Kr private communication from Professor J.A. Beattie ; Xe Beattie Barriault and Brierley J . C'hem. Phys. 1951 19 1219 ; L values from Kelle~.~'b gases Lu/Wo is roughly constant a t about 6-2 for diatomic gases a t about 7-5 from which ratio are deduced the W values quoted in Table 9 for the halogens. The W values for the halogens are considerably greater than the values BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 129 for the corresponding inert gases. If we assume the repulsiou energy func- tions to be the same in the two cases a simple calculation gives Yo for the van der Waals attraction between two non-bonded halogen atoms ; the results are compared in Table 10 with twice the Pauling (‘ van der Waals radii ” p (A 0.1-0*2).TABLE 10 Yo cnlc. 2P F . . . . . 2.78 2.70 c1 . . . . 3.54 3.60 Yo calc. 2P Br . . . . 3-69 3.90 I. . . . . 4.16 4.30 The agreement is satisfactory and we may now proceed therefore to apply equations (19) for the 6-12 potential using the W, Yo values in Tables 9 and 10 (calc. values). The application to the force con- stants themselves comes directly from equations (19). In Fig. 5 are com- pared the force constants so calculated for “ non-bonded ” chlorines at dis- tances y with those deduced by Heath and Linnett.82 The two curves agree well for the higher values of the “non- bonding ” force constant so the argu- ments adduced by Heath and Linnett from vibrational frequencies are roughly confirmed ; it would appear that Heath and Linnett’s function over-estimates the effects at longer distances.We now consider the effect on inter- atomic distances. For the molecule to be in equilibrium where C is the ( ( chemical ” bond energy acting along x (the C-C1 distance in CCl, for example). Suppose the chemical bond to be a harmonic oscil- lator with force constant I c ; then if 46 dW/dy = dC/dx * (20) Comparison of force consturLts for “non-bonded” chlorine atoms at a dis- tance y A. Ax is the lengthening of the bond along x due to the repulsion Y d6>x(y) -I W I = E Ax But for a tetrahedron y = 22/6x/3 therefore = 3 .1 1 x ( y ) 2 kx . (21) Taking for the halides of carbon the observed x values quoted in Table 5, 130 QUARTERLY REVIEWS and the values of W and Yo (and hence y ) just deduced we can calculate Ax from k the force constant of the " chemical " carbon-halogen bond. Taking for CF 6.5 CCl 3.2 CBr 2.5 CI 2-0 ( lo5 dynes/cm.) we calculate that the C-halogen bonds in these molecules are lengthened by repulsion by 0.034 0.128 0.152 and 0.180 8 respectively. Carrying through the same calculation for the silicon halides we calculate the elongations 0-004 0-011 0.028 and 0.032 A respectively. For Ge and Sn the elongations calculated are naturally smaller still. The conclusions thus reached are in satisfactory agreement with the empirical deductions from Fig. 2 vix.that the C-F bond in CF was slightly longer than expected and that the bonds in CCl, CBr, CI were all about 0.07 A too long while the other tetrahalide bonds show no significant lengthening. The predicted lengthening is roughly twice as large as that deduced from Fig. 2 which is reasonable agreement in view of the approxi- mate nature of the theory used and the sensitiveness of the function used to small changes in y . It remains therefore to consider the effect of these forces on the total energy of the molecule. When y (equation 18) is less than unity the tendency of the van der Waals forces is to shorten the bonds and increase the bond energy from what would be otherwise expected. For a tetrahedral molecule the maximum such stabilisation energy will be 6W0/4 per bond or about 1 kcal (Table 7) ; this is a maximum since the contraction of the non-bonded distance would usually imply a contraction of the bonding distance below the equilibrium value.Comparing therefore a tetrahedral molecule XY with a diatomic molecule XY we should find a small correction of the order 1 kcal. per bond ; on comparison of one tetrahedral molecule with another the correc- tion becomes still smaller since the bond energies already contain these van der Waals corrections ; and finally the effect on the means of bond energies is trivial since from the polarisability interpretation of van der Waals attraction energies 86 these also are subject to a geometric-mean rule in the first approximation. As a result of the mutual interaction the chemical bond is lengthened by Ax and its bond energy lessened by *k(Ax), the van der Waals distance is shortened from Yo to a distance y(y = Yo/y) and the energy of interaction changed from W to W,y(y) (equation 15).Hence t'he total lessening of the bond energy AB is given by if we reckon the bond energy from a standard value containing the full W contribution. As Ax is not directly measurable it is convenient to use equation (21) to deduce These conclusions hold if y 5 1. If y > 1 (CCI, for example) the corrections become appreciable. AB = ; I WoC&y) - 11 1 + *Ww2 In this way we calculate from the numerical data already quoted the follow- ing values for AB for carbon halides (in kcal. per bond) CF 3. CCl &, 8 6 London Trans. Farctduy ~Coc. 1037 33 8. BAUGHAN THERMOCHEMISTRY OF ELEMENTS OF GROUPS IVB AND IV 131 CBr 6-, CI 11.0.These considerable diminutions in the bond energies may to some extent explain the anomaly in the C-I bond energy. The theory of this Section has therefore (i) confirmed that a considerable effect on force constants is to be expected particularly for the halides of carbon ; (ii) confirmed qualitatively and roughly quantitatively the dis- crepancies of bond lengths in the carbon halides from those predicted by the Schomaker-Stevenson rule ; (iii) confirmed that ‘‘ non-bonding ” repulsive forces in tetrahedral molecules make but little difference to bond energies except once more in such cases as the halides of carbon ; and (iv) incident- ally confirmed that Pauling’s “ van der Waals radii ” agree well with those calculated by Lennard-Jones’s ‘’ 6-12 potential ” from virial coefficients.Section V We now consider together the data available for the internuclear dis- tances the force constants and the bond energies (as defined in Section I) for the compounds XY XY, and XY where X is C Si Ge Sn or Pb and Y is hydrogen or a halogen. The bond energies for carbon compounds have been calculated for two values of the latent heat of vaporisation (170 or 125 kcal./g.-atom). The problem which we are trying to illuminate is to what extent do variations in these three quantities go together (“ equilibrium variation ”) and to what extent must we consider also “ separation variation ” ? For CH CH 4r/1r = 0.976 ; for SiF SiF 0-96 ; for CF CF 1-07. From the electronegativity arguments of Section I1 we calculate for SiH ,r = 1.510 for SnH ,r = 1-731 whence for SiH SiH 4r/1r = 0.993 and for SnH SnH 0.970.Once more we have a general rule (4~/1r N 0.975) with the carbon halide anomalous and we may conclude that CF (but not SIP,) has the carbon-halogen bond lengthened by about 0.12 A [cf. 0.07 A (Sec- tion 11) 0.03 A from the repulsion theory of Section IV]. and by TJinnett,S that in a series of bonds involving the same atoms (C-C C-H for example) Ern is constant where n 1 5. From this rule we would expect then the force constants in XY to be (0~975)-~ = 1.135 times those in XY. The values so “ calculated ” (Table 11) are in good agreement with the S.V.P.F. values for CH and SiH where non-bonding repulsion is small and for the tetrahalides lie between the S.V.F.F. calculations which make no allowance for non- bonding repulsion and Heath and Linnett’s calculations which tend to overestimate it (Section IV).In the same way we might expect the bond energies in XY to be (0~975)-~ 2 1-079 times more than in XY. Since the bond energies ,B are better known than the spectroscopic dissociation energies ,B we show in Table 11 the “ calculated ” values of ,B. As far as they go the agreement is satisfactory with one marked exception that the dissociation energy of SiF quoted by Gaydon is very much less than that predicted. The rough general picture that emerges is that the properties of XY and XY can be approximately predicted one from the other in terms of The data are given in Table 11. We begin by considering the distances ,r in XY and lr in XY. It has been shown empirically particularly by Fox and Martin 132 QUARTERLY REVIEWS “ equilibrium-variation ” although the experimental data are incomplete a,nd although it would appear that a more refined theory is necessary to derive the force constants from the frequencies in XY4.87 Considering the dihalides of tin however we might expect that the distances force constants and bond energies should be intermediate between those of SnHal and SnHal,.Unfortunately the force constants in SnHal are not known; but the distances in the dihalides are larger than in the tetrahalides while the bond energies are larger (15 14 kcal. see Section 11) instead of being smaller as one might expect. It is clear therefore that we cannot explain the differences between these molecules entirely in terms of equilibrium- variation. ( a ) Pauling’s remarkable cmpirical generalisations are strongly supported by the experimental evidence chosen as it has been to ( b ) The empirical value of the concept of “ thermal electronegativity ” is discussed and a simple extension suggested which may prove of value in discussing bond energies for given atoms in diflerent valency states.The Schomaker- Stevenson rule is shown to break down for the halides of carbon but ( c ) this can be roughly accounted for in terms of a simple theory of “ non-bonding ” repulsion which based on Lennard- Jones’s work on virial coefficients also agrees with Pauling’s empirical “ van der Waals radii ”. (d) Some examples are given of the way in which third-law methods make more precise many important values for heats of reaction. ( e ) A comparison of evidence leads to the unexpected conclusion that the mono- and tetra-halides and -hydrides of these elements are closely related energetically while the dihalides of tin (at any rate) are anomalous.To sum up .avoid difficulties due to uncertain heats of vaporisation. I thank my former colleague Dr. It. R. Smith and Dr. R. F. Barrow for valuable discussions and also Mr. R. P. Bell F.R.S. for his advice on the presentation of this Review. s7Cf. Torkington Trans. Faraday SOC. 1951 47 105. Note to Table 11.-Diatomics. All data for r and k are from Herzberg except for CF which is from Anclrews and Barrow (Proc. Phys. SOC. 1951 64 481) ; all data for ,R from Gaydon 17 except for the monohalides of Pb from Wieland and Newburgh (Helv. Phys. Acta 1949 22 590) and for CF from Andrews and Barrow (loc. cit.) Polyatomics.,r from Allen and Sutton,lQ k for S.V.F.F. from Herzberg “ Infra-Red and Raman Spectra of Polyatomic Molecules ” van Nostrand Co. Inc. New York 1945 ; Heath and Linnettea Bond energies see Section I1 and the vaporisation heats of Xi Ge and Sn deduced in Section I11 ; the vaporisation heat of Pb and the dis- sociation energies of Cl, Br, and I are from Bichowsky and Rossini; 21a that of F has been taken as 39 kcal./mole (Doescher J . Chem. Physics 1952 20 330). Two values of ,B are given for carbon corresponding to L = 170 125 kcal./g.-atom ; for PbF we have used Qf (solid) 222 kcal./mole (v. Wartenberg 2. anorg. Chem. 1940 240 337) and estimated the vaporisation heat from the boiling point. CH . . . CB . . . CC1 . . CBr . . . CI . . . SiH . . . SiF . . . SlCl . . . SiBr .. . SlI . . . GeH . . . GeF . . . GeCl . . . GeBr . . . GeI . . . SnH . . . SnF . . . SnCl . . . SnBr . . . SnI . . . PbH . . . PbF . . . PbCl . . . PbBr . . . PbI . . . TABLE 11. Cornparisons of data for XY XY, and X*Y Diatomic XY 4.45 7.17 3.77 2-46 4.90 2.63 2.20 - - 3.92 2.31 1.96 - 1.46 3.28 1-98 1.71 - I a43 2.63 1.63 1.45 1.19 1H ,B calc. hcal /mole 80 - 114 - - - - 88 f 8 76 & 11 69 & 11 - - I 62 f 9 58 & 8 < 74 76 & 11 7 4 f 11 46 & 23 - - - 80 72 69 65 92 or 82 111 or 101 72 or 62 61 or 51 70 122 81 65 48 - 97 61 47 - - 69 57 - - 76 - - - Pentatomic XY ?c lo6 dyne/cm. 1.093 1.36 1-765 1-94 2.15 - 1.54 2-02 2.15 2.43 - 1.67 2-08 2.29 2-50 - - 2.30 2.44 2.64 - - 2-43 - - 5.04 N S.V.F.F. 5.05 9-14 4-32 ' (8.14) 4.38 1.79 (4-28) 3-36 1-38 - - - - 2-84 N S.V.F.F. 2.79 7-16 5.7 5.56 3.75 2.55 2.99 2.92 2.01 2.50 - - - - - - - 4.45 3-27 2.40 2.62 8-58 1.90 2.22 - 1.66 - - 3.72 2.80 2.34 2-25 2.28 1.84 1-94 I - - - - - - - - 1.62 - - 2.99 - 1-85 - - 1.65 - - 1-35 - - 99 or 88 120 or 109 78 or 67 66 or 55 76 132 87 70 52 - - 105 66 51 - - - 74 62 - - 82 - - - Triatolnic XY

ISSN:0009-2681    

DOI:10.1039/QR9530700103

出版商:RSC    

年代:1953

数据来源: RSC

摘要:

THE HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS By L. H. LONG B.Sc. PH.D.(LoNDON) PH.D.(CANTAB.) A.R.C.S. D.I.C. (DEPARTMENT OF CHEMISTRY UNIVERSITY COLLEGE EXETER) 1. Introduction THE contribution made to chemistry by an ever-increasing knowledge of heats of formation has broadly speaking been twofold. I n the firat place heats of formation may be utilised directly to compute heats of reaction and these in conjunction with other thermodynamic data such as concen- tration pressure volume temperature and specific heats used in turn to provide much useful data concerning chemical processes. Thus given enough data it is possible to predict not only the direction of a reaction but in the case of a reversible reaction the position of equilibrium its variation with temperature arid the output of mechanical or electrical work.Heats of formation have also on occasion found application in making intelligent qualitative predictions concerning the types of phase diagrams to be expected for multicomponent systems. It should be emphasised that it is only possible to obtain a knowledge of the thermodynamic possi- bilities of a reaction in this manner. Heats of formation tell us nothing concerning the probabilities or the rates of reactions since they are concerned neither with the paths a reaction may take nor with the potential barriers encountered en route. This limitation can be overcome only by resorting to reaction kinetics a subject outside the scope of the present Review. The other major contribution concerns the energetic aspect of the structures of inorganic compounds whether crystalline or molecular.True heats of formation tell us nothing concerning the structures themselves but they are nonetheless indispensable for obtaining crystal energies and bond energies. The numerical data may therefore be said to be of great importance t o the theoretical chemist as well as to the industrial chemist. Indeed interest in heats of formation extends to other fields of science than chemistry for they have been utilised in attempting to account for the composition of the earth and other planets,l as well its for elucidating the processes occurring in the upper atmosphere as a result of photodecomposition.2 In view of the advances made during the last quarter-century and more an account of the various aspects of the present subject is timely. In such a wide subject it is not possible to be comprehensive and emphasis will here be laid on those matters not conveniently summarised in text-books.2. Historical Oxides apart it is rarely possible to measure the heats of formation of Normally the heats 'Urey Geochim. Cosmochimi Acta 1951 1 209. ZSee e.g. Herzberg J . Roy. Astron. Soc. Canada 1951 45 100. 134 an inorganic compound directly and in a single step. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 135 liberated or absorbed in a number of different steps must be determined independently and the required heat of formation calculated by algebraic summation of the values obtained. This being the case the dawn of thermochemistry may be said to have occurred with the enunciation of Hess’s law in 1840 (although it had been recognised some 60 years earlier by Lavoisier and de Laplace that the heat of decomposition of a compound is in magnitude equal and opposite to its heat of formation).Hess’s law now frequently termed the “ law of constant heat summation ” states that the heat liberated or absorbed in a chemical reaction is independent of the number and nature of the steps by which the reaction is effected. The law which was originally based on a large number of calorimetric measurements is thus seen to be a special case of the first law of thermodynamics (law of conservation of energy) w ~ c h was first propounded a few years later likewise on an empirical footing. The latter half of the 19th century witnessed the measurements of the heats of reaction of thousands of chemical processes and the accumulation of a vast amount of thermochemical data.This must be accredited mainly to Thomsen and Berthelot ,4 although others also contributed. Thomsen who carried out most of his investigations between 1852 and 1886 included gas calorimetry in his studies and evolved a so-called “ universal burner ” the precursor of the modern gas calorimeter. Berthelot commenced his thermochemical studies in 1864. To him is due the development of bomb calorimetry from 1880 onward^.^ True a type of bomb had been used as early as 1846,6 but this worked a t atmospheric pressure whereas Berthelot utilised the advantages offered by working a t high pressures (ultimately exceeding 20 atm.) and by other improvements in technique. By modern standards the accuracy of the work accomplished during this period was far from high.Errors of 1-2% were common and still larger errors not infrequent. Both Thomsen and Berthelot were spurred on in their researches by the belief that in the heat of reaction they had found a measure for the “ affinity ” of a process and that in consequence they had found in calorimetry a means of attacking the then-unsolved problem of chemical affinity. To see this development in its true perspective it is necessary to recall that the whole question of chemical affinity was one which had largely preoccupied the minds of many scientists and philosophers for a very long time. For example Boyle and a number of his contempor- aries had considered it while the concept can be traced as a hazy notion at least as far back as the 13th century! In independently equating affinity with the heat of reaction therefore Thomsen and Berthelot both believed that they had opened up the way to satisfying one of the main lines of chemical enquiry.3Hess Pogg. Annulen 1840 50 386; 1841 52 97. Both experimenters summarised their work in book form. See Thomsen “ Therniochernistry ” (English translation by K. A. Burke London 1908 and 1920) ; Berthelot “ Thermochimie ” (Paris 1897). Berthelot Conapt. rend. 1880 90 779 ; 91 188. 13 hdrews Phil. Mag. 1848 32 321 ; Pogg. Annakn 1848 75 27. K 136 QUARTERLY REVIEWS One of the logical consequences of the Thomsen-Bert helot principle however is that only exothermic reactions can proceed. Quite apart from the subsequent discovery of reactions that are inescapably endothermic a moment’s reflection on the existence of numerous chemically reversible reactions-which cannot be exothermic in both directions-is sufficient to demonstrate the unsatisfactory nature of this viewpoint.Reversible reac- tions had been known for a long time and the position is the more surprising when it is reflected that before embarking 011 his thermocheniical studies Berthelot had himself made a study of the reaction between acetic a’cid and alcohol. That the inconsistency was not immediately detected is in part due to the imperfect ideas then current concerning the nature of chemical equilibria (which were widely regarded as “static ” systems though a few such as A. W. Williamson thought otherwise) and in part due to the fact that neither Thomsen nor Berthelot adopted an essentially atomistic approach to chemistry.It is doubtful if the importance of the combined effect of these two chance factors has been fully appreciated even by thermochemists themselves. Thus it was that Thomsen and Berthelot failed for a long time to recognise the untenability of their main hypothesis even after 1879 when Guldberg and Waage put the “ law of mass action ” (which they had first enunciated clearly in 1867) on a ‘‘ dynamic ” footing by the introduction of velocity constants. Had Thomsen and Berthelot come to this recognition at an early date they might well have turned their attention to other fields and the historical development of thermochemistry would have been quite different. The actual cause of the relinquishing of this false position was the discovery of the second law of thermodynamics one consequence of which was a redefinition of chemical affinity (in 1884 by van’t Hoff ’) as the maxi- mum amount of external useful work which can be obtained from a chemical process at constant temperature and pressure.Before the end of the century both Thomsen and Berthelot reluctantly accepted the new stand- point from which the data they had amassed appeared to be relegated to a position of secondary importance. The true relationship between the heat of reaction and chemical affinity was finally clarified in 1906 by Nernst.* 3. Modern Developments The first two decades of the present century witnessed only comparatively small additions to the thermochemical data compiled during the previous half-century. Nevertheless two important developments occurred during this period. One of these was the determination of specific heats down to very low temperatures on the one hand by direct measurement and on the other by applying statistical mechanics to observable spectroscopic data.Since these values could be used for the accurate experimental computation of entropies it now became possible to determine affinities at a given temperature by means of the simple relation AG = AH - TAX. Here 7 “ ktudes de dynamique chimique ” (Amsterdam 1884). 8 Nachr. K . Gee. Wiss. QBttingen 1906 1. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 137 AG AH and A# are the changes in free energy heat content and entropy respectively of the isothermal system undergoing the chemical change under consideration at temperature 2'. The true measure of the affinity is the decrease in free energy which is only equal to the heat of reaction (decrease in heat content) a t absolute zero.Heats of reaction and hence heats of formation thus took their rightful places as indispensable thermodynamic quantities and this gave to calorimetry a new impetus that became in- creasingly apparent after 1920. The other major development was a vast improvement in experimental technique and accuracy. Electrical calibration was introduced in 1 903,9 and temperatures began to be measured by thermocouples and platinum resistance thermometers. Rotary stirring the avoidance of heat losses by evaporation and the more accurate estimation of heat corrections were among the other improvements. The experimental side was largely per- fected in the hands of Dickinson,lo whose paper repays perusal.It may be noted that one important recommendation by Dickinson has unfortunately still not been adopted by instrument makers in this country namely the total avoidance of poor thermal conductors like ebonite in calorimeter construction. Such " thermal insulators " increase the time required to re-establish equilibrium and render the accurute computation of heat trans- ferred impossible. Other names which must be mentioned in connection with advances in experimental technique are T. W. Richards W. A. Roth Swarts Verkade and Swietoslawski (microcalorimetry 11-14). The various types of calorimeters evolved have been critically discussed by White.15 The several advances mentioned rapidly led to the realisation of an accuracy of 5 0.1% or better and sinoe about 1930 the National Bureau of Standards in Washington has been the source of a steady flow of data accurate to about & 0.02 yo.As high an accuracy has been attained in other laboratories.16 To achieve this very special attention has had to be paid to purity of material and purity of reaction. True heats of reaction known with such accuracy are still almost entirely confined to processes involving combustible organic substances but the fundamental obstacles in technique having been overcome there is no reason why a similar order of accuracy should not in time be achieved for many types of inorganic processes. Much research remains t o be done. Since however for a reaction to be amenable to accurate calorimetric study it must follow a single path involve only stoicheiometric compounds and go to completion rapidly,17 i t is clear Jaeger and von Xteinwehr Verh.deut. phys. Ges. 1903 5 50. l1 Swietoslawski and Dorabialska Compt. rend. 1927 185 763. l2 Xwietoslawski J. Chim. physique 1930 27 96. l 3 Swietoslawski Rybicka and Solodkowska BUZZ. Acad. Polonaise (Cl. Math. Nat.) Bull. U S . Bur. Stand. 1915 11 189. 1931 A 322. Swietoslawski and Bartoszewicz ibid. p. 336. l5 " The Modern Calorimeter " (New York 1928). l6 See e.g. Coops Van Nes Kentie and Dienske Rec. Traw. chim. 1947 66 113. l7 A calorimetric method for studying slow reactions has recently been developed by Buzzell and Sturtevant J . Amer. Chem. h'oc. 1951 73 2454. 138 QUARTERLY REVIEWS from the outset that the accuracy realisable in inorganic chemistry .will not be as uniformly high as in orgmic chemistry. Solid reactions are particularly unsuited to direct thernioclieinical Ineasurcnicnt .The increase in accuracy referred t o came at a timely juncture for meet- ing the growing chemical and thermodynamical needs of the modern era and these needs were tliemrclves a stiinulus t o thcrmoclieniical research. I n particular the calculation of equilibrium constants for industrial processes demanded thermochemical data of a hitherto unprecedented order of accuracy. The bearing of thermocheniical values on one such process and its historical significance have been briefly discussed recently by Parks,lS who has also pointed out that the sensitivity of equilibrium constants to inaccuracies in the thermocheniical data makes a further tenfold reduction in calorimetric errors desirable. The principle employed in calculating equilibrium constants is equally true in reverse so that very accurate thermodynamic data have been obtained from the experimental study of equilibria over a temperature range.Likewise the temperature-dependence of electrochemical potentials is able to provide very accurate figures for heats of reaction. These methods are of course restricted to cases providing suitable chemical equilibria or electrochemical processes respectively. Finally it must be mentioned that the determination of a number of heats of formation has been brought about to meet the requirements of certain academic studies more particularly in connection with crystal energies of heteropolar compounds on the one hand and bond energies of homopolar compounds on the other. Here the accuracies demanded are not so high.Both lines of enquiry entail a knowledge of heats of atomisatiori of the elements concerned and the former also involves ionisation energies and electron affinities. 4. Experimental Determination of Heats of Formation Except in the case of certain oxides it is only rarely possible to determine heats of formation of inorganic compounds by direct measurement Conse- quently indirect paths usually have to be employed and the heats of formation computed by means of Hess’s law. Therinochemical data of the most varied kind niay be utilisecl. The four principal methods of gaining thermochemical information have already been mentioned and may be sunimarised thus (i) Calorimetric measurement from which heats of reactions and specific heats can be directly obtained ; (ii) study of the temperature-dependence of equilibrium constants from which AH can be calculated by means of van’t Hoff’s equation (reaction isochore) ; (iii) study of the temperature-dependence of e.1n.f.data of electrochemical processes at strictly reversible electrodes whereby AH can be calculated by means of the Gibbs-Helmholtz equation ; (iv) infra-red spectroscopy from which specific heats of gaseous substances limy be computed. 18 J . Chem. Educ. 1949 26 262. LONG HEATS OF FORMATION OF SIMPLE INORGAKIC COMPOUNDS 139 In addition thermochemical data have been obtained by means of ultra- violet spectroscopy from convergences of spectral series (and predissociation data) reaction-kinetic studies and electron-impact experiments. These methods are normally used to afford the heats of formation of free radicals since they concern processes in which chemical bonds are ruptured.By exception the heat of formation of a stable compound may be obtained by one of these methods. Thus the heat of formation of C10 can be cal- culated from a predissociation (attributed to the process C10 --+ C1 + O,).l9 Likewise heats of formation of the halides and oxyhalides of sulphur selenium and tellurium have been obtained from spectroscopic data in the ultra-violet. 2* Again ionisation energies and electron affinities have been utilised for calculating heats of formation? notably in the case of free ions both simple and complex. The inter-relationship between heats of forma- tion and certain ot'her physical properties and the extent to which the former may be derived from the latter will be discussed in later sections.Of the methods outlined above method (i) calls for further comment as being that which has received by far the widest application. In organic chemistry the matter is considerably simplified by the fact that the majority of organic compounds are combustible so that the determination of the heat of combustion in a bomb calorimeter-or in the case of very volatile substances in a gas calorimeter-is all that is required in order to be able to calculate the heat of formation. The only organic compound8 which will not yield to this type of Oreatment are those poor in hydrogen that simultaneously contain an unusually high proportion of oxygen nitrogen or halogen. I n inorganic chemistry on the other hand no such universal process is available since inorganic substances as a class cannot be made t o react with a single substance such as oxygen.Bomb calorimetry has consequently found only a very limited application in inorganic chemistry but it has been employed for determining the heats of combustion of numerous elements principally by Roth and his collaborators and more recently of a number of metal alkyls.2 1 The difficulties confronting the experimenter arc considerable and much greater than when organic com- pounds are being investigated. The bomb calorimeter has also been adapted on occasion for determining the heats of formation of sulphides chlorides,21a and intermetallic compounds and one important modification has been the development of high-temperature bomb calorimeters for studying inorganic compounds.22 By way of example the heats of formation of a number of metal phosphides have been determined in a bomb operating at 630" ; 2 3 and an evacuated bomb has been employed for determining the heat of formation of chromium trifluoride by double decomposition.24 Occasion- ally it has proved possible t o determine the heat of formation of an Is Mayer Z . physikul. Chewa. 1924 113 220. 2o Hussain and Samuel Currcnt Sci. 1936 4 734. 21Long and Norrish Phil. Trans. 1949 A 241 587. 'la See c.v. Ricmoiisen Z. Elektrochem. 1951 55 327. 2 2 See e.g. Riltz Rohlffs and x-on Vogel 2. anoTg. Chem. 1934 220 113. 23 Weibke and Schrag 2. Elektrochem. 1941 47 222. 24von Wartenberg 2. anorg. Chern. 1942 249 100. 140 QUARTERLY REVIEWS endothermic compound in a bomb calorimeter by direct measurement of the heat of decomposition as in the case of copper n i l ~ i d e .2 ~ ~ Such instances are however comparatively rare and other types of calorimeter have been used to provide most of the data required. The thermochemistry of inorganic substances is less concerned with heats of combustion than with heats of hydration of solution of dilution of neutral- isation and of reaction of various kinds including direct combination decomposition and double decomposition. Of particular importance are reactions in solution which have provided probably more than half of the available thermochemical data relating to inorganic compounds. The variety of reactions which may be drawn upon to determine the heat of formation of an inorganic compound may be conveniently illustrated by selecting an example.The heat of formation of iodine pentoxide I,O, is determined by measuring its heat of solution in excess of water with which it forms iodic acid. The calculation of the required value demands a knowledge of the heat of formation of iodic acid. This in turn can be calculated in a number of ways one of them being from the reaction KI + 3HC10 -+ HIO + 2HC1 + KC1. The heat of formation of hypochlorous acid can be calculated from the heats of reaction of hypo- chlorous acid hydrochloric acid and gaseous chlorine respectively with aqueous sodium hydroxide and the heat of reaction of chlorine with aqueous potassium iodide dispenses with the difference in the heats of formation of potassium iodide and potassium chloride. Also required to complete the calculation are the heat of formation of water from its elements and the heat of formation of aqueous hydrochloric acid which is equal to the sum of the heat of formation of gaseous hydrogen chloride from its elements and the heat of solution of the gas in water.The processes involved may be summarised thus 1. 2. 3. 4. 5. 6. 7. 8. 9. -+ -+ + -+ --f -+ -+ -+ -+ On adding and subtracting the appropriate multiples of these equations one obta,ins the overall equation The overall heat of reaction Ql0 namely the heat of formation of iodine pentoxide is related to thc various heats of reaction in the following manner 10. I ( c ) I- 280 ( 9 ) - 12% (c) &lo = 24?2 + 6&5 + 5Q7 - &I - 6&3 - 6&4 - &6 - 104? - 10& 24a Juza and Hahn 2. unorg. Chenz. 1939 241 172. In this instance a special microcalorimeter was developed for the purpose.LONG HEATS OF FORMATION O F SIMPLE INORGANIC COMPOUNDS 141 Even this is not quite the whole story since small corrections for heats of dilution and mixing are also involved in the accurate computation of Ql0. 5. The Tabulation of Experimental Values In harmony with the foregoing example the heat of formation of a compound is defined as the heat liberated when one mole of the substance is formed froin its component elements a t constant pressure (1 atm.) and some specified' temperature. Whereas the older European workers for the most part chose 18" as their working temperature much of the more accurate recent work refers to 25" a temperature better suited to the climate of Washington and some other parts of America. Although this temperature is less convenient for temperate latitudes and the transition to it is by no means complete it seems highly probable that in the future-if only as an outcome of the disproportionately large amount of thermochemical research being carried out across the Atlantic-25" will be universally accepted as the "standard" working temperature to which the heats of reaction carried out a t other temperatures must be recomputed.In expressing heats of formation (and indeed heats o f reaction gener- ally) it is of course vital to define the state of every participant whether solid liquid or gaseous. For example the heat of formation of gaseous sulphur trioxide differs from that of liquid sulphur trioxide by an amount equal to the heat of vaporisation of this compound. Again where more than one solid modification of a compound exists or where an element exists in allotropic forms the variety under consideration must be stated.It is usual in the case of elements to select the form most stable a t 25" as the standard shte and to compute all heats of formation accordingly. As thus defined the heat of formation Q (or more precisely Q) assumes a positive value for an exothermic compound and a negative value for an endothermic compound. This convention has always been accepted in England and other European countries. Unfortunately a different con- vention has sprung up in America where the heat liberated on the formation of an exothermic compound is regarded as a decrease in internal energy so that the quantity quoted AH is negative for an exothermic compound and vice versa. Care must therefore be exercised regarding the correct sign when referring to different sources for thermochemical data.The unit of energy usually employed is the kilocalorie which is now defined in such a way as to be independent of the heat capacity of water.25 The most recent internally consistent sets of tables of heats of formation (and other thermodynamic data) are due to Rossini and his collaborators.2s In these tables all the available information regarding heats of formation has been critically compiled with respect to 25" and in some cases to absolute zero as well. Where only old discordant values are available some See e.g. Rossini Chem. Reviews 1936 18 233. 26 Rossini Wagman Evans Levine and Jaffe " Select,ed values of chemical thermo- dynamic properties " National Bureau of Standards Circular No.500 Washington 1952. ,These tables began to appear in 1947 and are brought up to date from time to time. 142 QUARTERLY REVIEWS arbitrariness of choice has doubtless been inevitable a'nd it is to be re- gretted that no indication is given as to whether any systematic corrections have been applied to the older data ( e . g . such as those recommended by Kharasch 27 for Thomsen's data). Except where otherwise stated all the values quoted in the present paper are taken from these tables. Older compilations are due to Washburn,28 Roth and Scheel 29 and Bichowsky and Rossini . 3O The great advantage offered by tables of heats of formation is that the heats of all conceivable reactions between the substances listed-whether such reactions are realisable or merely hypothetical-can be simply calcu- lated by algebraic treatment of the values tabulated.hIanifesDly it is not necessary to measure the heat of every possible reaction in order to construct the tables in the first place but merely those of a judicious selection em- bracing the maximum number of substances. In principle the number of such reactions need only be of the same order as the number of substances to be included in the tables. An illustration of the way in which the tabulated heats of formation may be employed to calculate heats of reaction may be furnished by con- sidering the hypothetical reaction 4S0 (9) + 6KP (c) -+ 3KZSOd (c) $- SF (9) The heat of reaction is equivalent to the difference between the combined heat of formation of the reactants and that of the products.Since the heats of formation of gaseous sulphur trioxide solid potassium fluoride solid potassium sulphate and gaseous sulphur hexafluoride are 94-45 134.46? 342.66 and 262 kcal./mole respectively it can be calculated that the foregoing reaction-if conditions could be found under which it could be made to proceed-would be exothermic to the extent of 105 kcal. a t 25". Hitherto sulphur hexafluoride has been prepared only by the use of element- ary fluorine. 6. Heats of Formation and the Periodic Table General Survey.-As is to be expected the heats of formattion of individual classes of compounds exhibit a periodicity similar in kind to that shown by many other properties of the same compounds. This periodic variation is most clearly seen in the case of binary compounds. If one element is kept the same and the other varied a " saw-tooth " curve can be obtained not unlike that observed for say atomic volumes.The con- nection between the heat of formation and atomic number has been studied on an empirical basis by a number of ii~vestigators.~~-~~ Because of certain 27 Bur. Stand. J . Res. 1929 2 359. 28 International Critical Tables Vol. 5 (Now York anti London 1929). 29 Landolt-Bomstein's " Tabellen " (Berlin). 30 " The Thermochemistry of the Chemical Substances " (New York 1936). 31Roth and Schwartz 2. physikal. Chem. 1928 134 456. 32 Roth Naturwim. 1931 19 860. 3 4 Trombe Compt. rend. 1944 218 457. 35 Sue J. Chim. phys. 1945 42 45. 3 3 Lautii. Bull. SOC. chirn. 1938 5 1321. LONG HEBTS OF FORMATION O F SIMPLE INORGANIC COMPOUNDS 143 stlriking regularities it has even been claimed 36 that a careful study of the heats of formation of simple compounds reveals the same regularity as that observed by MendeEef for the atomic weights.According to this statement the heat of formation of a corppound of one element with a second invariant element approximates to t'he arithmetic mean of those of the compounds its neighbours-whether situated vertically or horizontally in the Periodic Systcm-form with the same element (all the heats of formation being expressed per gram-atom of common element). This is however a gross overstatement. Although such a relationship can be shown to hold approx- imately in A large number of cases it was subscquently shown by R'oth and Becker 37 t'hat it broke down in several inst)ances among the chlorides and oxides and later by Kroger 3R that it also failed when applied to the nitrides.Indeed a close examination of the available values reveals numerous other exceptions and irregularities. One need only cite the hydrides which as a class are most erratic or the surprisingly low values for the alkali-metal oxides. Again the maximum values within the individual groups or periods for one particular class of compounds fall not infrequently at points erratically situated within the respective groups or periods as can be seen from a study of Tables 1 and 2. These tables have been completed as far as the available data allow but numerous gaps in present-day knowledge relating to heats of formation have made it impossible to complete all the columns. Where it is still possible that further measurements may reveal compounds with higher heats of formation this has been indicated by a query in parentheses while compounds for which experimental data are not available but whose heats of formation can be predicted with confidence to be supreme (e.g.chromous bromide) are themselves inserted between parentheses. In point of fact fluorine liberates the greatest heat when combining with lithium chlorine when combining with potassium bromine and iodine when combining with caesium oxygen-as far as is known-with lanthanum sulphur and selenium probably with lithium nitrogen with zirconium and carbon probably with tantalum. Also except for Groups I1 and 111 hydrogen liberates the greatest heat on Combining with the lightest element in each group. The heats of formation of the relevant compounds are cited for comparison in Table 3.Except for TaC,39 the figures are taken from Rossini et aLZ6 Information regarding the tellurides phosphides arsenides antimonides silicides and borides is either very incomplete or virtually non-existent. Several points of considerable general interest emerge from Tables 1-3. Of the non-metals oxygen is that which is able to liberate the greatest heat per gram-atom on combination while fluorine liberates the most per gram- equivalent. The change in positions of the maxima in the individual groups and periods demonstrates the futility of trying to find some all-Smbracing relationship governing the whole of t'he Periodic System. Nor are the 3G Berlsenheim 2. physiknl. {'hmn. 1928 136 231. 37 Ibid. 1932 A 159 1. 3Q Brewer Bromley Gilles and Lofgren National Nuclear Energy Series Div.IV 3 8 Z . anorg. Chem. 1934 218 396. 19B Chem. and Met'. of Misc. Materials p. 40 (1950). 144 QUARTERLY REVIEWS MnF MnCl MnBr MnI MnO F,S Mn,N F,C F6S0 TABLE 1. Binary compounds of F C1 Br I 0 S Se N and C with elements of the individual groups having the highest heats of formation per gram-atom of the former. compounds are included) (Only stoicheiometric FeF FeC1 FeBr FeI Fe,O RuS ? Fe,N Fe,C Combining element ? LaCI (LaBr,) LaI La,O ( ? ) La,S3 ( ? ) ? LaN ? F . . c1 . . Br. . I . . 0 . . s . . Se. . N . . c . . ZrF ( ? ) ZrCl ( ? ) ZrBr ( ? ) ZrI ( ? ) HfO ? ? ZrN ZrC ( ? ) Group I I I1 ? I ? ? ? ? ? NbN ? Ta2O5 LiF KC1 CsBr CSI Li,O (LI2f3) Li,Se ( ? Li,N L&C Heat of formation (hcal./g .-a t oin) CaF BaCI BaBr BaI CaO CaS Base Be,N ? Combining 64.2 146.3 104.18 94.3 80-5 O .. . s . . . Se . . . N . . . c . . . VI * CrF CrCl (CrBr,) CrI CI-20 03s O,C ? CrK * In drawing up this table Th Pa and U have not been included in Groups IV V and VI respectiveIy (cf. Tables 4 and 5 ) . TABLE 2 . Binary compounds of F C1 Br I 0 S Se N and C with elements of the individual periods having the highest heats of compounds are included) formtiorb per gram-atom of the former. (Only stoicheiometric Combining Period lst element 2nd 3rd 4th 5th F . . . c1 . . . B r . . . I . . . . 0 . . . s . . . . So . . . N . . . c . . . LiF LiCl LiBr LiI Be0 F6 I?& He3N2 F,C NaF NaCl NaBr N a I Na,S Na,Se A1N Cl,C MgO CaF KC1 KBr I< I CaO CaS K,Se TIN ? SrF R.bC1 RbBr R b I SrS SrSe ( ? ) XrN ( Y 2 0 3 ) (?I ? BaF CSCl CsBr CSI La203 Bas Base ( ? ) HfN TaC ( ? ) TABLE 3.Heats of forwmtion of binary compounds with the maximurn values per gram-atom of H F C1 Br I 0 S Se N and C Combining element H . . . F . . . C1 . . . B r . . . I . . . . Compound with max. heat of formation Hy (9) ( c ) CSI ( c ) KC1 ( c ) CsBr ( c ) Compound with max. heat of formation &a203 ( c ) (?) L12S ( c ) ( ? ) Li,Se (c) (?) ZrN (c) TaC (c) Heat of formation (hcal./g.-atom) 152.7 82.2 63.8 LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 145 maxima situated a t the same positions for fluorine and oxygen. From Table 2 it is seen that fluorine forms the most stable compounds with the elements of groups I and 11 while with oxygen the maxima have shifted to the right namely to groups I1 and 111. With nitrogen and carbon the maxima move successively further to the right.This corresponds to a progressive decrease in the ionic character of the most stable compounds. The crystal structures with their differing energies also play a part in deciding where the maxima fall. This also applies to the vertical groups (Table l) where the relative sizes of the cationic and anionic particles constitute a criterion for the lattice energy. Thus chlorine finds the optimum energetic conditions when combining with potassium in group I and barium in group 11 while fluorine which has a smaller anion finds them respectively with lithium and calcium with their smaller cations the crystal types remaining unchanged. This accounts for the widespread immiscibility of the solid alkali halides and the observed reaction direc- tions.40 Another case in point is exhibited by the alkaline-earth metals barium forming the most stable selenide and calcium the most stable oxide and sulphide .It is to be observed in passing that electronegativities do not always prove to be the deciding factor in determining relative chemical reactivities. For example the hydride fluoride oxide and nitride of lithium have heats of formation which are respectively higher than those of the other alkali metals so that chemical replacement with the latter would be effected by metallic lithium. On this basis lithium might be said to be the most reactive alkali metal notwithstanding the fact that it is the least electro- positive. Heats of formation have been discussed in connection with the electronegativity scale by Hai’s~insky,~~ who comments on the anomalous values.However by confining attention essentially to the chlorides bromides and iodides he succeeds by means of a semi-empirical relationship in drawing up a revised electronegativity scale embracing the whole of the Periodic System. Fluorides and oxides are observed to conform to the relationship in a far less satisfactory manner while the order of the elements on the new scale is not invariably found to coincide with the order of their electrode potentials in solution. Apart from its approximate character the electronegativity scale is constructed from values for anhydrous compounds and is not concerned with solvent effects-notably heats of solvation-which will affect the observed potentials to varying extents. The reason for the anomalous position of a number of fluorides is not far to seek.The increase in lattice energy on passing from the iodide of an element to its bromide is comparatively small and the furthcr increase observed on passing to the chloride is only of the same order The step from the chloride to the fluoride however involves a jump in lattice energy about four times as big with a correspondingly wide variation (in terms of kilocalories) from metal to metal and it is this wider variation which is a t This is of course not surprising. 40Thomas and Wood J . Arner. Chem. SOC. 1935 57 822; 1936 58 1341. 41 J . Phys. Radium 1946 7 7. 146 QUARTERLY REVIEWS least partly responsible for the seemingly.erratic behaviour of the fluorides. The jumps in lattice energy referred to are listed for a number of elements by Sue.35 Having dispensed with the possibility of finding any over-all regularity governing the whole of the Periodic System it would be profitable to glance a t the sort of regularities that are observed among certain types of compound in certain parts of the Periodic System.By confining attention to one group a t a time Roth and Schwartz 31 have shown that when plotted against the atomic number the heats of formation of the chlorides or oxides frequently lie on smooth curves the curves for the two sub-groups being distinct from one another. The types of curves obtained are reproduced here for compounds of t'he Group I1 elements for which inforination regarding the heats of formation is relatively complete. In Fig. 1 the Aiomic number FIG. 1 Heats of formation of the chlorides and bromides of Group II elemerzts plottcd against tlheir atomic numbers.curves for the chlorides and bromides are shown those for the fluorides and iodides (which are similar) having been omitted for the sake of clarity. I t will be noted that the halides of the typical elements beryllium and mag- nesium do not lie on the same curves as those of the elements of either sub-group although they lie nearer to the curves for the A sub-group. Indeed by regarding the calcium halides as " anomalous " it is possible to draw smooth curves passing through the points for the respective halides of beryllium) magnesium strontium and barium. Such a procedure is however) misleading. The uniformly " high " values for the calcium halides could then only be accounted for on the supposition that the heat of subli- mation of calcium wits anomalously low.In point of fact it is rather on the high side. Again the construction of such a curve to include beryllium and magnesium is impossible in the case of the oxides. The curves for the oxides and sulphides are shown in Pig. 2 and those for the nitrides in Fig. 3. By exception the nitrides of all five elements lie on a single curve. By restricting attention to compounds in which the maximum group LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 147 - ' 150- 5 F 2 700 *3 'c '"0 x cad Be0 MgO SrO \ -0 0 I' . I I RaO BaO Bas CaS - ZnO SrS - Atomic number FIG. 2 Heats of formation of th,e oxirks ai-rtl sulphides of Group II elemetits plotted ngainst their atontic ?izinzherts. 4? k3 $ 50- BeS z f l z s o -. I ngs I FIG.3 JIeats of formation of the nitricles of Group I1 e l m i e n t s plotted crgnir-rst their atomic numbers. Atomic number F I G . 4 Heats of forinatioiz vf the chlorides (per g.-utom oj chlorine) oj second-period eleme7its plotted against their atomic numbers. 148 QUARTERLY REVIEWS valency is achieved and plotting heats’of formation per gram-atom of common element smooth curves are also frequently obtained for the hori- zontal periods. Thus the chlorides of the elements of the second period lie particularly well on a curve notwithstanding the fact that silicon tetra- chloride is exceptional in being a liquid a t room temperature. The curve is rpproduceti in Fig. 4. The cwvw for the oxitlcs have a differmtl shape Heats of Atomic number F I G . 5 nquiiist their atomic I I umbers.formotion 01 the oxides ( p e r g.-atom of oxygen) of seca7id-period elements plotted those for the second period and the fifth (excluding the rare earths) being given in Figs. 5 and 6 respectively. It has recently been observed by Kayustinskii 4 2 that if the heat of formation is plotted not against the atomic number but against the logarithm of the latter the curves already referred to are frequently replaced by straight lines. This is perhaps best illustrated in the case of the chlorides 4 2 Izvcst. Alcud. Nauk S.S.S.R. Otdel. Khim. Nauk 1948 568 581. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 149 of Groups I-IV. The heats of formation are plotted against the atomic number in Fig. 7 and against the logarithm of the atomic number in Fig. 8. Some of the values for the heats of formation are seen not to lie exactly at the positions to be expected for them according to this treatment the I I J 25 50 Atomic number FIG.7 Heats oj formntio)i of chlorides (per g.-atom of chlorine) of elements o j the Jirst four groups plotted a yairi st their utomic 71 umbers. 7 100 3 2 ? 8 s s g 50 F e % L Q 8 '0.4 0-6 0.8 I.0 7-2 f 4 1.6 7.8 FIG. 8 Heats of formation of chlorides (per g.-atom of chlorine) of elements of the first four groups zog z plotted against the logarithms of their atomic numbers. " anomalous " position of calcium chloride referred to earlier being particu- larly apparent. The conformity of the fluorides to this linear rule is rather less impressive and of the oxides and nitrides very much less so. In par- ticular some of the sub-groups fail to conform.Thus the heat of formation 150 QUARTERLY REVIEWS of indium trichloride is anomalously high and higher than that of the trichloride of either gallium or thallium indeed the anomalous positions of the compounds of tervalent indium are not confined to the halides nor for that matter to the heats of f0rmation.4~ Nevertheless the logarithmic rule referred to may be of some service in predicting unknown heats of forma- tion. Thus from the known heats of formation of gaseous silicon tetra- fluoride (370 kcal./mole) and gaseous sulphur hexafluoride (262 kcal. /mole) the heat of formation of phosphorus pentafluoride may in this way be predicted by interpolation to be 338 kcal./mole. Hydrides.-It is now profitable to make a brief survey of the numerical values of the heats of formation of somc of the more important classes of compound.The values for the hydrides of &he various elements are set out in Table 4 in such a way as to facilitate comparison between the values for the various groups and periods. The arrangement chosen is based on the electronic structure of the free elements so that the transition series from scandium to zinc from yttrium to cadmium and from lanthanum to mercury are separated out from the main groups. For the hydrides this arrangement-in which boron and aluminium are situated above gallium- is fully appropriate and justifiable though i t is less so for the halides and oxides. In the case of elements which form more than one hydride only the simplest or most stable has been included. Non-stoicheiometric com- pounds have been omitted.In general the heats of formation of the non-stoicheiometric hydrides are low but comparable with those of the stoicheiometric hydrides of the transition elements where such exist. The values given are all taken from Rossini et ~ 1 . ~ ~ (the figure for La3Hs which is obviously an error has been corrected here) except those for the hydrides of sodium potassium rubidium and caesium.44 To facilitate the calculation of atomic heats of formation (see later) the heat of atomisation (La) of each element is included for convenience and placed immediately after the symbol for the element concerned. The distribution within the Periodic System of those elements which form stable hydrides is comparatively simple. I n this connection the recent discovery of BeH2,45 MgH,,46 ZnH2,47 CdH2,45 and HgH2477a is particularly interesting.It thus transpires that all the typical elements form stablt. hydrides. As is well known the hydridos of the alkali and the alkaline- earth metals are essentially ionic in nature while those of the elements of Group 111-VII are covalent compounds. Where the transition eleinents forin hydrides those do not belong to either type except that the hydritlt.5 of lanthanum cerium praseodymium and neodymium are probably ionic in nature. Viewed horizontally in periods the hydrides show little regularity in 4 3 Juza Die Chemie 1942 55 45. 44 Herold Compt. rend. 1949 228 686. 45 Barbaras Dillard Finholt Wartik Wilzbach and Schlesinger J . A ~ e r . Chem. 46 Wiberg arid Bauer 2. Naturforsch. 1950 56 396. 47 Finholt Bond and Schlesinger J .Amer. Chem. SOC. 1947 69 1199. 4 7 a W i b e r g and Henle 2. Naturforsch. 1951 66 461. SOC. 1951 '73 4585. LONG HEATS OF FORMATION OF SIMFLE INORGANIC COMPOUNDS 151 their heats of formation. Viewed vertically in groups the tendency is for the first member in each group to form the hydride with the highest heat of formation. However in Group I11 the heat of formation of the hydrides of boron fall far below that of lanthanum and the Group I1 elements also fail to comply with this rule. True the heats of formation of the hydrides of beryllium and magnesium are not known but there can be no doubt from their rather low thermal stabilities that they will be smaller than the value for calcium hydride. In view of the high ionisation poten- tials of magnesium and beryllium and of the latter in particular these hydrides may not be truly ionic but highly polymerised covalent compounds containing chains of metal atoms linked by hydrogen bridges thus resem- bling aluminium hydride rather than calcium hydride.The position with regard to the unstable liydrides of zinc cadmium and mercury also remains to be clarified. Particularly noteworthy is the fact that the hydrides of the alkaline- earth metals have much higher heats of formation per gram-atom of hydrogen than the hydrides of the alkali metals. It may be remarked that the heats of formation of the latter compounds do not decrease systeniatic- ally the order being LiH KH NaH CsH RbH. The cause of this is that on passing down the group from one element to the next the decrease in lattice energy is purely accidentally rather finely counterbalanced against the combined effects of the decreases in heat of atoniisation and ionisation potential of the alkali metal being sometimes slightly greater and sometimes slightly less.Of the covalent hydrides there is no doubt from the relative thermal stabilities that the heats of formation of the hydrides of the elements of Groups IV-VII decrease systematically on passing down each group not- withstanding the fact that some of the values are lacking. The marked endothermicity of many of the hydrides (and indeed the low values for the heats of formation generally) is to be ascribed largely to the high heat of dissociation of hydrogen and its low electron affinity relative to other univalent non-metals. Probably all the hydrides of the Group I11 elements with the exception of La3H8 are endothermic the covalent members con- stituting electron-deficient compounds of unusual interest.48~ 49 The crystal- line hydrides ThH, UH, and PuH have comparatively high heats of formation and constitute a class of their own.(Conflicting statements appear in the literature concerning the formula of the last-named compound.) The heats of formation of the paraffins increase with molecular weight the increment per CH group tending to a constant value.50 Of the boranes the heats of formation of two of the more stable members B,H (E) and B,,H, (c) are - 7.8 and - 8 kcal./mole respectively so that there is scarcely room to doubt that all the members of this class are endothermic compounds. Hydrazine N,H (I) is endothermic with - 12 kcal./mole Values for the higher hydrides have not been inserted in Table 4.48 Bell and EmelBus Quart. Reviews 1948 2 132. 49 Hodgkin Ann. Reports 1949 46 64. 5a Prosen and Rossini J . Res. Nut. Bur. Stand. 1945 34 263. TABLE 4. Heats of formation (in kcal./mole) of the principal hydrides and oxides of the various ele?rwnts at 25". The heats of atornisation of the elements (see Section 7) are given in parentheses after the symbols for the elements. The figures refer to the crystalline state unless otherwise indicated by a superscript g or I (gas or liquid respectively) H (52.09) HH 0.00 H,O ( I ) 68.32 ; (9) 57.80 s c (93) Ti (1126) {Ti 1:3*91 Sc20 - rutile) 225.52 Y (103) Zr (142.5) yzo3 - ZrO (111) 258.2 Li (37.07) LiH 21.61 Li80 142.4 Na (25.98) NaH 13.94 Na,O 99.4 K (21.51) KH 14.11 K,O 86.4 ~ _ _ _ Rb (20.51) RbH 12.98 Rb,O 78.9 V (122.7) V,O 373 Nb (184.5) NbzO 463.2 CS (18.83) CSH 13-48 cs,o 75.9 Ac Th Pa ~ U(125) Np Pu i Am ; PuH 31.7 ; T h H 4 3 j i UH 30.4 j i Tho 293-2 / 1 UO 302 i NpO - j PuO 251 AmOz 239.9 Be (76.63) BeH - Be0 146.0 Ce (85) Pr (87) Nd (87) Co,O - PrZO 444.5 Nd,O 442.0 Ce,H 170 {CeO 233 {Pro 234.0 ; Mg (35.9) MgHz - MgO 143.70 ~~ Ca (46.04) CaH 45.1 CaO 151.9 Sr (39.2) SrH 42.3 SrO 141.1 Ba (41.961 BaH 40.9 BaO 133.4 La (88) La,H 160 Hf (170) T a (185.6) La,O 458 HfOs 271.5 1 Ta,O 499.9 Cr (94.0) CrO 138.4 MO (155.5) MOO 180.33 W (20 1.6) wo 200.84 Mn (68.32) MnO (I) 92-0 Mn,O - Tc Re (189) Re,O 297.5 Fr Ra (31) RaO 125 Fe (99.8) Fe,O 196.5 Ru (160) RuO 52.5 0 s (174) co (102.0) CoH 10.2 COO 57.2 Rh (138) Rho 21.7 Ir (165) OsO (11) 93.4 1 IrOz 40.1 H (52.09) HH (9) 0.00 H,O (I) 68.32 ; (9) 57.80 Ni (101.61) Cu (81.52) Zn (31.19) ZnH - I :??588:2q I {g: 39.84 ZnO 83.17 CUO 37 1 B (97.3) B,Os 302.0 ' B S H - 7.5 Ga (66.0) Ga,H - Ga,O 258 A1 (75.0) AlH - A1,0 ( a cor.) 400.29 Pd (93) Pd,H 8-9 PdO 20.4 Ag (67.5) Cd (26.97) In (58-2) Ag.0 7.31 CdO 60.86 In,O 222.5 CdH - In,H - {Ago 3.15 Pt (121.6) PtO - Au (84.6) Hg (14.54) TI (43.34) HgH - A u O - HgO (11) T120 - {AuiO - 19-3 21.68 i Pm / Sm (87) Eu (87) i Gd (87) Tb (87) ~ Pm,O - j Sm,O 430 i Eu,O - [ Gd,O - Tb,O - C (125.0) uCH 17.89 rCO 94.05 Si (88.04) VSiH 14.8 SiO ( a quartz) 210.26 Ge (84.0) GeH - GeO 129.2 Sn (72) SnH - SnO 138.8 N (85.57) B N H 11.04 ~ ~ ~ 3 1 ~ 0 2 0 m 0 P (75.18) P,O (11) 360.0 As (60.64) H F i 1 i 6 .9 ' Sh (60.S) p 3 + I ) 168.4 Sb,Oa 234.4 0 (59-16) ZOH 68.32 00 0.00 Se (48.37) BSeO - 9-48 i:; 1 2 0 .5 TC (47.6) iQoz; 1 3 6 . 9 gTeO - 43.0 P b (46.34) PbH4 - PbO 66-13 Bi (49.7) BiH - Po F (18.3) BFH 64.2 QFSO - 5.5 c1 (29.01) @l~022.0 6 - 18.20 C1,0 - 63.4 Br (26.71) QBrH 8.66 B r O - { B k l - 12.5 I (25.48) g I H - 6.20 I,O 43-34 At Dy (87) i Ho i Er i Tm Yb (87) i Lu (87) Dy,O - i Ho,O - Er,O - i Tm,O - Yb,O - Lu,O - TABLE 5. Heats of formation (in kml./mole) of the primipal Jrluorides and chlorides of the various elomnts at 25". The heats of atomisation of the elements (see Section 7 ) are given in parentheses after the symbols for the elements. The Jigures refer to the crystalline state unless otherwise indicated by a superscript g or 1 (gas or liquid respectively) V (122.7) Sc (93) Ti (112.6) TiF 198 SCF - SCCl "0.8 ~ Li (37.07) LiF 146.3 LiCl 97.70 N a (25.98) NaF 136.0 NaCl 98.23 (h' (94.0) 3171 (88,34) CrF 181.0 AlnF (I) 189 CrC'I 94.56 JPnC1 115.3 K (21.51) K F 134.46 KCl 104.18 Y (103) YF - YCI 234.8 Rb (20.51) KbF 131.28 RbCl 102.91 Zr (142.5) Nb (184.5) 110 (156.5) TC ZrF 230 NbF - ZrC1 230 NbCI - ('s (18.83) 2sF 126.9 3 8 1 (11) 103.5 Fr H (52.09) gHF 64.2 QYCI 22.06 LaF - LaCl (CI) 263.6 Be (76.63) BeF - BeC1 122.3 HfF4 - WF6 - gReF 273 VI-c1 38 HfCl - li WCl 98.7 RHCI - Mg (35.9) MgF 263.5 MgCl 153.40 Ac Th \ Pa j U (125) Np Pu i Am ' UF 357 j NpF 360 ~ Pulr' 373 j i (UP6 517 j {?CIS 213.0 NpCI 216 iPuC1 280.0; AmCl 251.3 ThF 477 i ThCl 284.5 j j LCl 272.41 i Ca (4604) ('aF 290.3 CSCI 190.0 ~ Ce (85) i Pr ( 8 i ) CeF - jPrF - CUF 442 C C ~ Y 260.3; PI.CI 257.8 Sr (39.2) SrF 290.3 SrCl 198.0 Ba (41.96) Bd? 286.9 BnC1 205.56 R a (31) RaF - RaCl - La (88) 1 H f (170) 1 Ta (185.6) 1 W (201.6) 1 Re (189) Fe (99.8) FeF 168 FeC1 81.5 RU (160) RuF - RuCl 63 ~~ 0 s (174) OSF - OSC1 - c-0 (102 0) CoF 159 CoC1 77.8 Rh (138) RhF - RhC1 36 I r (165) IIrF 130 lrC1 42.8 i Nd (87) j j XdF - j SclCl 254.3 / H (52 09) OHF 64.2 OHCl 22.06 0 (59.16) *OF - 5.5 *OC1 - 18.2 F (18.3) 'JFF 0.00 QFCL 11.6 B (97.2) gBF 265.4 gBC13 94.5 c (125.0) WF 231 ZCCI 33.3 N (85.57) WCl - - 55 QNF 27.2 S (53.25) ISF - ' X I 28 !QSF 262 A1 (75.0) AlF 311 AICI 166.2 Si (88.04) gSiF 370 zSiCI 153.0 C1 (2941) QClF 11.6 P (76.18) PI? - PCI 110.7 AS (60.64) EAsF 226.8 'AsCl 80.2 Ki (101.61) NiF 159.5 NiCI 75.5 Zn (31.19) ZnF 176 ZIICI 99.40 GEL (66.0) GaP - GaC'1 125.4 CU (81.52) CuCl 32.2 ChCl 49.2 Se (48.37) gSeF 246 q8ec1 9.7 Te (47.6) PTeF 315 TeCI - Br (26.71) RrF - OUrCl - 3.51 I(25.48) 1F - 9 ' 1 ~ 1 - 4.20 Ge (84.0) GeF - zGeC'I 130 Sn (72) SnF - ISnCl 130.3 Pd (93) PdF - PdCl 45.4 Cd (26.97) CdF 164.9 CdCl 93.00 In (58.2) InF 250 InCI 128.4 Ag (b7.8) AgF 48.5 AgF 88.5 AgCl 30.36 Pt (121.6) PtF - PtCI 35.5 Hg (14.54) HgF2 95 HgCl 55.0 T1 (43.34) TIF - TlCI 83.9 At Bi (49.7) BiF - BiC1 90.61 Y O P b (46.34) PbF 222.3 PbC1 - AU (84.6) AuF 18 AuCl 28.3 \ I Pm i Sm (87) i E u (87) Gd (87) [ Tb (87) Dy (87) i Ho PmF - jSmF - i EuF - GdF - i T b F - ; DyF - [ HoF - ErF - ! TmF - :YbF - i LuF - 'mC1 251.9 SmCI 249.8 EuCI 347.1 GdCI 245.TbCI 241-6 DyCI 237.8 j HoCI 23243 ErC1 231.5 TmCl 229.5 YbC1 228.7 gLLuCI 227"9 156 QUARTERLY REVIEWS which accounts for its explosive nature.Hydrogen peroxide H,O (Z) is not endothermic with respect to its elements (heat of formation 44.84 kcal./mole) but is endothermic with respect to water and oxygen so is nevertheless capable of detonating. Halides.-Heats of formation of the fluorides and chlorides of the various elements are set out in a similar way in Table 5. In the case of elements of variable valency for the sake of space and clarity never more than two halides of each class are shown. On the right-hand side of the Periodic System the valencies selected are that exhibited towards hydrogen and the normal group valency namely 3 and 5 for Group V 2 and 6 for Group VI and 1 and 7 for Group VII. For the transition elements in addition to the group valency the valency 2 has been selected as being one of the more pronounced common valencies.Where neither valency is observed the most stable halide or one for which the heat of formation happens to be known is cited. The valency 3 has been selected for the trans-uranic elements as well as for the rare earths. Except for CF4,51 SC12,52 ClF,53 FeF2,52 C U F ~ ~ ZnF2,52 InF3,52 CeF4,52 A u F ~ ~ HgF,,52 ThC14,53a P u F ~ ~ ~ and AmC13,54" the values are all taken from Rossini et aZ.26 The heats of formation of the fluorides have been the subject of a special discu~sion.~~ As is to be expected the fluorides exhibit values which are everywhere the highest while those of the iodides are everywhere the lowest. The general trend of the values is similar for the fluorides chlorides bromides and iodides respectively except that the fluorides of the first two groups are anomalous.In Group I (excluding Group IB) lithium fluoride has the highest and caxiuni fluoride the lowest heat of formation while in Group I1 calcium fluoride has the highest value. This is essentially a question of lattice energy and it is of interest that lithium and calcium have the least soluble fluorides in their respective groups. On the other hand the chlorides -and likewise the bromides and iodides-show uninterrupted increases in their heats of formation on passing down Groups I and 11. Among the transition elements the same behaviour is observed for all the halides in Groups IIIA IVA and possibly VA. Elsewhere in the Periodic System the general tendency is for the heats of formation to decrease on passing down the groups but there are some irregularities.In particular those of the halides of the second period are mostly higher than those of the first. Again from indium onwards the values for the elements of the fourth period mostly exceed those of the elements situated immediately above them. In par- ticular tellurium hexafluoride has a surprisingly high heat of formation exceeding not only that for selenium hexafluoride but even that for sulphur hexafluoride by a wide margin. It seems that fluorine is able to form extra 5 1 von Wartenberg 2. anorg. Chem. 1949 258 356. 5 2 Brewer Bromley Gilles and Lofgren op. cit. (ref. 39) p. 76. S 3 Wicke Nachr. Akad. Wiss. Gottingen Math.-physilc. Klasse 1946 89. 53aEyring and Westrum J . Amer. Ghem. Soc. 1950 72 5555. 5 4 Westrwn and Eyring National Nuclear Energy Series Div.IV 14B Transur- 54aLohr and Cunningham J . Arner. Ghem. ~Soc. 1951 73 2025. 5 5 Wicke Naturwiss 1946 33 132. anium Elements Part 11 p. 90s. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 157 strong bonds with elements which have vacant orbitals available for bonding which suggests that with tellurium the unfilled 4f orbitals may offer them- selves as such in much the same way as the unfilled 3d orbitals do with silicon-TeF and Sip are hydrolysed by water SeF and CF with their lower heats of formation are not. For the trichlorides of the rare earths there is a remarkably steady drift in the values. Where variable valency occurs the heat of formation per gram-atom of halogen increases with decreasing valency. This is one of the conditions for stability (cf.Section 10). The difference between the heats of formation of the fluoride and chloride varies considerably from element to element. It reaches a maximum a t boron with 57 kcal. per gram-atom of halogen and drops to about 10 for univalent gold. The difference is also small for the silver and mercuric halides which accounts for the especially good fluorinating powers of AgF and HgF,. The heats of formation of the halides are greatest in the case o f the purely ionic compounds i.~. for the alkali-metal halides. The values for the halides where the bonding is neither ionic nor covalent but transitional in type are particularly interesting since these compounds frequently show features of unusual interest in their crystal structures. 49 Oxides and Sulphides.-To economise in space the values for the heats of formation of the oxides have been inserted in Table 4.Where an element forms a number of oxides the scheme adopted has been the same as in Table 5. Oxides such as VO CrO and FeO which in contrast to MnO are not stable as stoicheiometric compounds at 25" are not included. Except for Mg0,55a A1,03,55a Si0,,56 P203,56a Ti0,56b Ti0,,56b Ge02,56C Br02,56d Sm203,30 and A I ~ O ~ ~ ~ the values have been taken from Rossini et aE.26 The heats of formation of the oxides are mostly known and are more complete than for any other class of compounds but experi- mental values are still lacking for the oxides of scandium yttrium several rare earths and platinum although values have been predicted for Sc203 and Y,03.37 However especially in view of the opposite trends in the values for Groups IIA and IVA overmuch confidence cannot be placed on such predictions.The general trends in the values for the oxides within the groups resemble those for the fluorides. That this is less true when the Periodic System is viewed horizontally in periods is due to the different crystal structures of the oxides.57 The decrease in values from lithium to cssium is again en- countered in Group I as is the maximum at calcium in Group 11. For 55a Holley and Huber J . Amer. C'hem. SOC. 1951 73 5577. 5 6 Humphrey and King ibid. 1952 74 2041. 56a Koerner and Dmiels J . Chem. Phys. 1952 20 113. 5'jbHurnphrey J . Amer. Chem. SOC. 1951 73 1587. 56c Jolly and Latimer ibid. 1952 74 5757. 56dPflugmacher Schwarz and Rabben 2. anorg. Chem. 1951 264 204. 56eHuber Holley and Meierkord J .Amer. Chem. SOC. 1952 74 3406. 5~ Eyring Lohr and Cunningham ibid. p. 1186. j7 Wells Quart. Reviews 1948 2 185. 158 QUARTERLY REVIEWS the transition elements the first few sub-groups again exhibit increasing va'lues on descending the group but this behaviour here extends as far as Group VIIA at which the d sub-shells are exactly half-filled. Again the second period from aluminium and the last few elements of the fourth period -in this case from tin onwards-contain oxides possessing higher heats of formation than the preceding periods although chlorine constitutes an exception. The heats of formation of the sulphides are lower than those of the oxides exceptions being K,S Rb,S Cs,S and Ag,S. The difference is very large for boron and aluminium. A few values which may be compared with those of the oxides are (in kcal./mole) BeS (c) 55.9 B2S3 (c) 57.0 CS ( I ) - 214 Al,S (c) 121.6 K,S (c) 100 CaS ( c ) 115.3 MnS (I) 48.8 As$ (c) 35 MoS3 ( c ) 61.2 Ag,S (IJ) 7.6 La,S (c) 306.8 HgS (11) 13.9.Nitrides Phosphides and Carbides.-The comparatively low heat's of formation of the nitrides are largely to be attributed t o the very high stability of the nitrogen molecule. Many nitrides are endothermic a'nd many elements form no stable nitrides at all. The most stable nitrides are formed by the elements of Groups I1 to V inclusive those of the A sub- groups having heats of formation far higher than those of the B sub-groups. A comparative study of the nitrides of the first long period has been Lithium is the only alkali metal to possess an exothermic nitride.The formulae of the nitrides of many elements do not correspond to the normal group valencies. The figures 26 for a few typical nitrides are (in kcal./mole) Li,N 47.2 Be,N2 135.7 BN 32.1 Ca,N 103.2 TiN 8 0 ~ 4 7 ~ ~ VN 41 CrN 29.8 Mn,N 57.8 Pe,N 2.55 Cu,N - 17.8 Zn,N 6.9 GaN 25 Ge,N 14.8. Information regarding the heats of formation of the phosphides is far less complete even than for the nitrides. It is however quite clear that the values are higher than for the corresponding nitrides this being the opposite to the changes observed on passing from the fluorides to the chlorides and from the oxides to the sulphides. The following are some typical values Z6 (in kcal./mole) Ca,P 120-5 Fe,Y 40 COP 35 Ni,P 53 Cu,P 38.4. Carbon has a higher heat of atomisation than any other element in the first period and this is partly responsible for the low values observed gener- ally for the heats of formation of the carbides.Furthermore very fre- quently the formulae of the carbides do not correspond to the group valencies. The most stable carbides are formed by some of the transition elements. Many are highly refractory substances and the negligible tendency for carbon to volatilise makes them stable at very high temperatures in spite of their low heats of formation. Knowledge concerning t'he heats of forma- tion is very incomplete but some of thc values 26 are as follows (in kcal./mole) Li2C2 14-2 CaC 15.0 Al,C 30.9 Tic 43.85,59 Cr,C 21.0 Mo,C - 4.3 Mn,C 1 Fe,C - 5.0 Ni,C - 11 Ag,C - 81.9. As is well known the last of these compounds is explosive. Apart from the silicides of inagiiesiuin and calciuim (Mg,Si 18.6 Ca,Si 50 58 Juza Die Chemie 1945 58 25.59Humphrey J . Amer. Chem. SOC. 1951 '73 2261. Iodine is the only halogen to possess an exothermic oxide. LONG HEATS O F FORMATION OF SIMPLE INORGANIC COMPOUNDS 159 CaSi 36 CaSi 36 kcal./mole 26) little is yet known concerning the heats of formation of silicides. Although many borides have been characterised and the crystal structures of a number determined,60 apparently nothing is known about the heats of formation of any of them except that as a class the t'ransition elements form the most stable borides. This constitutes one of the many gaps in our knowledge concerning heats of formation. Intermetallic Compounds.-The heats of formation of alloys and inter- metallic compounds are frequently comparatively low.However it may a t first sight appear surprising that the observed values are on occasion comparable in magnitude with those of other inorganic compounds. A study of the numerical data in connection with other physical properties has been undertaken by 8auerwald.61 The heats of formation of rather more than 100 intermetallic compounds are known but this is only a tiny fraction of tlhe realisabls compounds. Some of the values *6 are tabulated in Table 6. TABLE 6. Heats of forrnation (in EcaZ./rnoZe) of Some intermetallic compounds a.t 25" I compound I LiHg (c) LiTl (c) Li,Sn (c) LiSn (c) Li,Pb (c) LiPb (c) Li,Bi (c) NaK (I) NaCd (c) Li3SbZ ( c ) NaHg ( c ) NaHg ( c ) Na,Sn (c) NaSn (c) Na,Pb (c) NaPb (c) Ka3Sb (c) Xa3Bi (c) KHg ( c ) KHg ( c ) Mg,Ca (c) Mg,A13 (c) MgLa ( c ) Qf 20.8 12.8 47.0 16.8 42 14.6 43.5 55.2 2-4 8.4 10.2 18.3 14.4 12 15.6 11.6 47-2 45-6 11.6 17.7 30-0 48.7 5.7 Compound MgCe ( c ) MgPr ( c ) MgZn2 ( c ) MgTl ( c ) MgzSn ( c ) Mg3B1 ( c ) MgCd (11) Mg3Sb2 ( c ) CaA1 (c) CaZn (c) CaZn (c) CaCd (c) CaTl (c) Ca2Sn (c) CaSn (c) Ca,Pb (c) CaPb (c) Ca,Bi (c) Ba,Sn (c) Ba,Pb ( c ) BaPb (c) Ha,Sb ( c ) Ca,Sb ( c ) Qf 13 8.2 12.6 9.2 11 17 68.1 36.5 52 17.4 22 30 35 75 38 47 25 155 112 9 0 89 36 175 Conlpoulld Ba,Bi (c) A1,La (c) A1,Ce (TI) AICe (c) A1,Pr (c) AlFe (c) AI,Co (c) AlCo (c) AlNi (c) AlCu (c) CeHg ( c ) FeSb (c) CoSb (c) NiSn (c) NiSb (c) Cu3Sn (c) AuSb (111) ZnSb (c) CdSb ( c ) A1,Coz ( c ) Cu2Zn3 ( c ) AgJn3 ( c ) Hg5T1 (c) 160 36.1 39 22 52-1 12 38 70 26 34 10.0 21.5 - 2.4 10 14.8 15.6 16 8 9.5 4.8 3.29 2.5 36 7.Heats of Formation and Crystal Energies The crystal energy of an ionic lattice is the energy liberated on its forina'tion from free ions a t infinite distance. Subject to certain simplifying assumptions this energy can be derived theoretically as has long been renlised.62-62 The tierivation will not be repeated here as it is given in (in Kiessling Actu Client. Scund. 2950 4 209 ; J. Electrochem. Xoc. 1951,98 166 518. 61 2. Metallk. 1943 35 105. 62L4ppell Acta Math. 1884 4 313. 63Madelung Physikal. Z. 1918 19 524. 6 4 Born 2. Physik 1921 7 124. 160 QUARTERLY REVIEWS numerous text-books. Suffice it to say that with rigid ions the crystal energy U, is given by U = NAx2e2/r where N is Avogadro’s number A is a constant dependent on the crystal type 65 and known as the Madelung constant x is an integer giving the multiple of the ionic charge with respect to that for which A has been derived for the respective crystal type e is the electronic charge and ro is the interionic distance.This energy arises from the Coulomb attractive forces which are counterbalanced at equilibrium distance by repulsive forces. Since the ions are not rigid the latter forces come into effect a t larger distances thus reducing the lattice energy. It can be shown that U is reduced by a factor equal to l/n where n is the exponent of the distance r in the expression reproducing the decrease of the repulsive forces with distance. The value of n can be determined for the crystal species from compressibility measurement,s. It varies from case to case according to the ionic species present but lies between 5 and 12.The above expression has been further refined by Born and Mayer 66 to allow for van der Waals forces and zero- point energy. Experimentally the crystal energy is related to the heat of formation and other thermochemical quantities by the well-known Born-Haber cycle;679 68 which for the special casc of an alkali halide MX can be repre- sented schematically in the following manner Thus Uo = (1 - l/n)NL4x2e2/r . (1) It is immediately apparent that U == Q + Lu(M) + I(M) + &D(X,) - E ( X ) - * (2) where Lu(M) is the heat of atomisation of the metal I ( M ) its ionisation potential D(X,) the dissociation energy of the halogen and E ( X ) its electron affinity [+D(X,) must be replaced by the heat of atomisation of the non-metal when the latter is not a diatomic gas a t ordinary temperatures].Some ionisation energies 69 are given in Table 7. The electron affinities 69 of hydrogen and the halogens are listed in Table 8. The accuracy of the figures is generally very high in the case of the ionisation energies derived from spectral series and except for the electron affinity of fluorine reason- ably so for the remaining figures. 6 5 Sherman Chem. Reviews 1932 11 93. 6 6 2. Physik 1932 75 1 . 67 Born Verh. deut. physikal. Ges. 1919 21 13. 69 Herzberg “ Atomic Spectra and Atomic Structure ” (2nd edn. New York 1944). 68 Haber ibid. p . 750. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS TABLE 7. 161 Iomktion energies (in kcal./q.-adom) of hydrogen and Element H . . Li . . Na . . 2 K . . Ca . . Mn. . some metals Ionisation energy 1st electron 313.4 124.3 118-4 176.2 138.0 100.1 140-9 171.3 2nd electron 346.5 433.9 273.6 358.5 3rd electron 655.7 Mement Fe .. co . . Ni . . c u . . Zn . . Ag . . Cd . . Ionisation energy 1st electron 181.2 181.6 176.0 178.0 2 17.5 174.6 207.3 2nd elwtron 374-4 401 420 466.6 414.0 389.7 3rd electron 705 TABLE 8. Electrcm afinities (in Ecal./g.-atom) of hydrogen and the halogens Element . . . . . . Electron affinity . . . . H 16.5 F 95.3* c1 85.8 Br I 80.5 ~ 72.4 ~ * This figure must be regarded as highly uncertain. I f the lower value (30-40 kcal./mole) for the energy of dissociation of the fluorine molecule should become fhally establishsd-and considerable evidence for it has accumulated latterly -application of the Born-Haber cycle to the alkali-metal fluoride lattices leads to an electron affinity for fluorine which is lower than that for chlorine.See also Johnston J . Chem. Phys. 1951 19 1391. The same is not always true of heats of atomisation many of which in the face of sparse and discordant vapour-pressure data are little more than judicious guesses. Although a number of heats of atomisation particularly for the more volatile elements are known with fair precision the values for nitrogen fluorine and many of the less volatile elements are still subject to considerable uncertainty. The values derived may only be considered reasonably reliable when' the figures obtained by application of the second and third laws of thermodynamics respectively are in good agreement. Frequently as e.g. in the case of tin,21 this is far from being the case.Values for most of the elements are listed by Rossini et a1.26 and by Brewer.70 Their respective values differ appreciably in the cases of beryllium boron calcium arsenic niobium antimony tellurium platinum and thallium. More recent values are available for titanium,71 vanadium,'la chromium ,7lb iron77lc c0balt,7~c germanium,'lCE silver,y2 tantal~m,7~a and 70 Brewer National Nuclear Energy Series Div. IVY 19B Chem. and Met. of Misc. Materials p. 13 (1950). 7 1 Carpenter and Mair Proc. Phys. SOC. 1951 64B 57. 71uEdwards Johnston and Blackburn J . Amer. Chem. Soc. 1951 73 4727. Speiser Johnston and Blackburn ibid. 1950 72 4142. ' l o Edwards Johnston and Ditmars ibid. 1951 73 4729. 71aSearcy ibid. 1952 74 4789. 71sSkinner Edwards and Johnston ibid. 1951 73 174. 7 2 Schadel and Birchenall J .Metals Trans. 1950 188 1134. 72uEdwards Johnston and Blackburn J . Amer. Chem. SOC. 1951 73 172. 162 QUARTERLY REVIEWS and these (adjusted where necessary to 25') have been included in Tables 4 and 5. Otherwise except in the case of carbon Rossini's values have been inserted uncritically in Tables 4 and 5 although this is not to be interpreted that they are favoured to Brewer's. The value for hafnium is due to Brewer. The figure these authors quote for carbon is based on calculations assuming an accommodation coefficient of approximately unity for this element and conflicts with much other evidence reviewed else- where.73 Recently Goldfinger and his co-workers 74 have found that the accommodation coefficient of carbon is of the order 10-3 to 10-4 and obtain a much lower experimental value (-146 kcal./g.-atom) for the heat of atomisation.Electron-impact studies on CO 75 have yielded the figure -136 and those on CH476 and CH,*CN76 -120-125 with an upper limit of 140. Electron-impact work on other molecules 76.z-c is in general harmony with these results. There is therefore no difficulty in accepting the upper limit of 135 kcal./g.-atom for the heat of atomisation of carbon as fixed by t'he photodissociation of C0.77 Accordingly it seems that the most probable value is 125.0 kcal./g.-atom obtained from a predissociation observed in the CO and this figure has been entered in Tables 4 and 5 though any value between 125 and 135 kcal./g.-atom could be harmonised with the evidence. There are thus two principal methods of determining the lattice energies of purely ionic compounds.For any crystal type the lattice energy obviously decreases as the ionic radii increase. From a study of the inter- relationship between heats of formation and crystal energies it was early realised 79 that salts of cations with 18 electrons in their outer shells possess higher lattice energies than those of cations with the $are-gas electronic structure. The difference is due to the higher polarisabilities of the former which have the effect of increasing the heats of formation.80 Departure from strict heteropolarity is in this way revealed for a number of halides of the heavy metals.81 This method has been utilised by Sherman 65 for a wide range of com- pounds including not only halides but also oxides sulphides and selenides. For typically ionic compounds such as the alkali halides the theoretical value of ?Yo may be used for calculating the electron affinity of the halogen by means of equation (a) and consistent values are obtained thereby.Thus the electron affinit)y of fluorinc-i.e. the heat of formation of the 7 2 b Hall J . Amer. Chem. ~S'oc. 1951 73 757. 73 Long Proc. Roy. SOC. 1949 A 198 62. 7 4 Doechaerd Goldfinger and Waelbroeck J. Chem. Phys. 1952 20 757. 7 5 Hagstrum Rev. Mod. Physics 1951 23 185. 76McDowell and Warren Discuss. Farnrlcsy SOC. 1951 10 53. ibaRranson and Smith J. Chem. Phys. 1952 20 1047. i6bField ibid. 1951 19 793. 76c McDowell anti Warren 1'rCois. Paraday SOC. 1952 48 1084. i7 Faltings Groth aiid Harteck Z. physikcrl. Chem. 1938 B 41 15. 7 8 Herzbcrg J. Phys. Phem. 1942 10 306. i9 Grimm 2.physikal. Chem. 1922 102 113 141 50-2. 8o Born and Heisenberg 2. Physik 1924 23 388. 61 Rabinowitsch and Thilo 2. physikal. Chem. 1930 B 6 284. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 163 fluoride ion from a fluorine atom plus an electron-as calculated from the lattice energies of LiF NaF KF RbE’ and CsF is constant to within about 2 kcal. This mctliod being applied to the oxides of the alkaline-earth metals the heat of formation of the oxide ion from an oxygen atom and two electrons can be likewise calculated. The values are however not consistent and show a steady drift from BaO to MgO amounting to about 20 kcal. This may in part be attributable to the heat of formation of the oxide ion varying somewhat according to its surroundings but the effect is doubtless also brought about by departure of these oxides from strict heteropolarity .Thus X-ray studies of MgO have revealed that the ions in this compound in contrast to those in NaCl for example are not truly discrete which is not difficult to understand in view of the fact that the heat of formation of the oxide ion is strongly negative whereas for a halide ion it is positive. Sherman then proceeds to use the mean values thus obtained for the halide and oxide ions to calculate the lattice energies of numerous other halides and oxides by means of equation ( 2 ) . Some of these experimental values are reproduced uncorrected in Table 9 along with the theoretical values calculated for strict heteropolarity by means of equation (1). TABLE 9. Comparison of crystal energies (in Iccal./mole) derived experimentally by means of the Born-Haber cycle with the theoretical values for strict heteropolarity (after Xherman Compound MgF .. . CaF . . . Mid’ . . . NiF . . . CdF . . . CUCl . . . SrCI . . . A g I . . . . CdI . . . Li,O . . MnO . . . NiO. . . . Cu,O . * . ZriO . . . Ag,O . . . CdO . . . PbO . . . Y t i ucture type ltutile Fluorite Rutile Rutile Fluorihe Sphalerite Fluorite Lead iodide Ant ifluorit)e Rock-salt Rock-salt Cuprite Wurtzite Cuprite Rock-salt Rutile 688.8 617-2 645.0 733.5 661.9 228.1 494.0 201.9 563.1 693 959 966 786 970 716 91 1 2832 696.8 617.7 656.3 697.1 628.7 206-1 493.6 175.9 477.0 696 912 968 682 877 685 867 2620 Diffrrence 8.0 - 0.5 - 11.3 + 36.4 + 33.2 + 22.0 + 0.4 + 26.0 + 86.1 - 2 - - + 4; + 10.1 7 $- 130 + 44 + 212 - Although the utilisation of more recent thermochemical and crystallo- graphical data would change some of the individual values somewhat the general trend is unmistakable.Agreement is excellent for many compounds such as CaF, SrCl, or Li,O suggesting (but not proving) that they are truly ionic. For others such as CuC1 AgI CdI, Ag,O and PbO, ( Uexp. - Ucalc.) is strongly positive implying considerable departure from strict heteropolarity . Heats of formation are thus not only serviceable for deriving lattice energies important quantities not in the ordinary way 164 QUARTERLY REVIEWS directly measurable buti also for deriving information concerning the state of bonding in crystals . 8. Heats of Formation and Bond Energies Apart from the special cases of molecules of elements and of certain other diatomic molecules suitable for spectroscopic electron-impact kinetic or equilibrium studies the evaluation of bond energies cannot be made without a knowledge of heats of formation.In this section we are concerned with compounds which are essentially covalent in nature the molecules of which are therefore more appropriately regarded as built up from free atoms than from ions since the forces holding them together are decidedly not those of Coulomb attraction. Consequently the energy which is of fundamental importance here is the atomic heat of formation. The atomic heats of formation of molecules are simply calculated from the experimental heats of formation of the gaseous compounds by the addition of the appro- priate heats of atomisation of the elements concerned (cf. Tables 4 and 5).It was early realised that the energy of a molecule obtained in this way could be divided up either among the atoms participating 82 or among the chemical bonds present.83 The values obtained by either method are with certain restrictions approximately additive. Although both are equally justifiable empirically it is the latter method which has received by far the greater attention. The energy which is assigned to a particular bond is known as the (( bond energy ”. An illustration of the way in which bond energies are calculated is pro- vided for the case of the N-H bond in ammonia kcal./mole 4N2 + iH2 -+ NH ( 9 ) + 11.04 N -+ +N + 85.57 3H + QH + 156.27 (by addition) N + 3H -+ NH ( 9 ) -k 252.88 The figure 252.88 kcal. represents the heat liberated on the formation of three N-H bonds so that the (average) N-H bond energy is stated to be 84.3 kcal.Where a compound is liquid or solid at ordinary temperatures the heat of formation includes van der Waals forces and these must be allowed for by subtracting the heat of volatilisation. Some bond energies calculated in this way are listed in Table 10. For molecules containing more than one kind of bond a certain arbi- trariness in partitioning the energy is unavoidable. The usual method is to assume the strict validity of the postulate of additivity in bond energies and insert values for bond energies obtained from other molecules. By way of example the N-N bond energy in hydrazinc may be calculated by assuming that the N-H bond energy is the same as in ammonia. Since however it can be demonstrated that bond energies vary from compound to compound this procedure is inaccurate.Thus a variation of 2 kcal. 8 2 Swietoslawski Bull. SOC. chim. 1921 29 496. 83 Fajans 2. Physik 1920 1 101 ; Ber. 1920 53 643. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 165 in the N-H bond energy would lead to an error of 8 kcal. in the N-N bond energy in the example cited. In compounds containing multiple bonds the departure from strict additivity of bond energies is likely to be particu- larly large. A well-known example is that provided by conjugated hydrocarbons. TABLE 10. Net bond energies and bond lengths for Some volatile binary inorganic compounds Bond F-H Cl-H C1-F Br-H Br-C1 I-H I-F I-c1 I-Br O-H O-F 0-c1 S-H S-F X=O Se-H Se-F Se-C1 Te-H Te-F N-H N-F P-H P-c1 P-Br AS-H AS-F Compound HF HCl C1F HBr BrCl HI IF6 IC1 IBr H2O F,O c1,o H2S 803 H2Se SeCl H2Te TeF SF SeF NH NF PH3 PCI PBr ASH AsF Net energy (kcal.) 148-5 103.2 72.9 87.5 52.2 71.4 76*3* 50.4 42.4 110.6 56.1 44.5 81.1 84.8 108.4 66.0 81.3 58.0 57.4 92.7 84.3 69.8 73.4 78-5 63.7 58.6 125.6 Length (A) Bond 0.92 1.32 1.63 1.41 2.14 1-60 1.75 2.32 2.48 0.96 1.41 1.68 1-33 1.58 1.43 1.50 1.68 2-00 1.69 1.82 1.01 1-37 1.46 2.02 2.2 1.56 1.72 As-C1 Bi-Cl Xb-C1 C-H C-F c-c1 C-0 c-S C=Se Si-H Si-F Si-C1 Si-Br Ge-C1 Sn-C1 B-F B-Ci B-Br Hg-F Hg-Cl Hg-Br Hg-I Ir-I? 0s-0 Re-F Ti-C1 U-F __ ._ ~ Compound AsCl SbC1 BiC1 CH CF4 CCl co2 CS CSe SiH SiF SiBr GeC1 SnC1 BF3 BCl BBr HgF2 HgC1 HgBr2 HgI oso SiCI Irk’ RoF TiCl UE’6 Net energy (kcal.) 73-1 74.3 67.1 87-8 121.3 66.6 168.7 102.0 87.9 77.8 146.8 87.4 70-3 79.1 77.5 153.1 92.9 74.0 79.0 54.5 44.8 35.1 80.0 122.6 109.3 99-7 137.3 Length 2-16 2.37 2-48 1.09 1.36 1.76 1.16 1-55 1.46 1.54 2.02 2.15 2.08 2.30 1.29 1.74 1.87 2.3 2-4 2.6 1.66 2.2 -2.0 * Heat of formation of IF from Woolf J.1951 231. Two-points need specific mention. The first-which will be dealt with in greater detail in Section 11-is that the values listed in Table 10 are net quantities and are not suitable for directly relating them t o other bond proper tie^,^^ since they do not represent the absolute or intrinsic energies of the respective bonds. The reason for this is that the internal energy of an atom in combination is not identical with that of the free atom (as is tacitly assumed in deriving bond energies thermochemically) but is increased by an amount equivalent t o the respective “ valency-state energy ”.The second point is that with multivalent elements the energy required to rupture one bond of a molecule is not equivalent to the average bond energy for the respective molecule; e.g. the energy required to dissociate one 8 4 Cottrell and Sutton Quart. Reviews 1948 2 260. 166 QUARTERLY REVIEWS N-H bond in ammonia D(NH,-H) is 104 2 k ~ a l . / m o l e ~ ~ whereas the net N-H bond energy is 84.3 kcal. The difference is in part caused by the valency-state energy of nitrogen which is considerable and in part by the “ energy of reorganisation ” 86 of the NH radical. The subject of dissociation energies has been reviewed elsewhere.87 9. Heats of Formation and Other Physical Properties From the foregoing i t is clear that heats of formation are composite quantities related to other energetic terms namely crystal energies heats of dissociation and atomisation ionisation potentials electron affinities bond energies and valency-state energies.Consequently such regularities as have been observed in the trends of the heats of formation must be reflections of like regularit’ies in the trends of the other energetic terms in- volved. It follows also that any attempt to derive a means for calculating heats of formation empirically is likely to become involved,s8 and that simple relationships with other physical properties are not in general to be expected. Nevertheless where such physical properties are themselves connected with the factors governing heats of formation relationships may be discoverable. Two which have been the object of considerable study in this connection are molecular volumes (including the closely connected coefficients of expansion) and vibrational frequencies and it would be profitable to glance at the outcome of these investigations.that there is a connection between the heat liberated and the contraction undergone by a compound on forma- tion from its component elements serious attempts to interrelate them on a quantitative basis were only undertaken during the second and the third decade of the present century. For condensed (solid or liquid) compounds Bousfield 91 observed that the heat of formation Q approximately obeyed a relationship of the type Q = H + H2 + k dv where H and H are heat components characteristic of the elements or radicals participating in the compound Ic is a constant and 6v is the molecular contraction on formation.Collins 9 2 likewise started from the thesis that the contribution to both the molecular volume and the heat of formation is specific for each element and attempted to demonstrate from a large number of compounds tjhztt for un element the contribution to the heat of formation is proportional to the product of its atomic weight and volume contraction with respect to the element in the solid state. Another linear relationship obtained by Balandin 93 has the form C = Ic - Q/Qo. Here C is the “contraction constant ” (namely the volume of the compound divided by that of the uncombined elements) Although it was early recognised 8 9 3 85 Szwarc Proc. Roy. SOC. 1949 A 198 267. 86 Norrish Trans. Farcaday SOC. 1934 30 103. 88 See e.g.Fehrle Physikab. Z. 1918 19 281 ; 1919 20 330. 89 Muller-Erzbach Ber. 1881 14 217. 91 PTOC. Roy. SOC. 1913 A 88 147. 9 2 Chem. News 1922 125 81 97. 9 3 Balandm 2. physikal. Chem. 1925 116 123. Szwarc Chem. Reviews 1950 47 75 ; Quart. Reviews 1951 5 22. Richards 2. physilcal. Chem. 1902 40 169 597. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 167 k an empirical constant of the order of unity and Qo an empirical energy dimension related to the heat of atomisation of the anionic component (both k and Qo are affected by the valency of the cation). For a large number of halides hydroxides and sulphates the normal deviation was observed to be of the order of 1% but for some others (e.g. silver compounds) was about ten times as much. Possibly a more satisfactory relationship is that due to Beck,94 k& = RT(1og v - log up) where lc is an empirical constant (equal to 1.31 for the alkali halides) and v and vp are the total volumes of the reactants and pro- ducts respectively.Another relati~nship,~~ namely Q = 1 . 3 3 ~ x 105(6v)1’3 ( x being the valency of the cation) has been tested only for the halides of the alkali and alkaline-earth metals. It receives qualitative confirmation in the work of Thomas and WOO^,^^ who find that the reactions between alkali halides invariably proceed in such a direction that the average of the cube edges of the stable pair assumes the least possible value. In addition to the foregoing evidence has recently been put forward suggesting that a quantitative relation exists between the heat of formation and the ionic potential of the cationic component that is to say the ratio of the charge on the cation to its crystal The different mathematical expressions for the relationship and the fact that each contains one or more empirical constants or has limited applica- bility suggests that the last word has not yet been said concerning the connection between contraction and heats of formation.That there is a connection is indisputable since large contractions are associated with high heats of formation and vice versa. From general considerations this is not surprising since for ionic compounds high lattice energies and for covalent compounds high bond energies are to be associated with small internuclear distances. Another related property which might similarly be expected to be connected with the heat of formation is the coefficient of thermal expan- sion and indeed for the alkali halides at the one is observed to be inversely proportional to the other.On turning to consider the relationship between heats of formation and infra-red frequencies of crystalline compounds one again finds a number of relationships. Possibly the most satisfying is that due to Lewis,97 viz. Q = Nh(Zvresultants - XY,,,,tants). Here N is Avogadro’s number h is Planck’s constant and the Y values are the frequencies of the chemical species concerned. Lewis’s equation is a logical extension of the pioneer work of Lindemann 98 and Haber,99 which in turn followed on the still earlier studies of Stark and Nernst on specific heats. The importance of the expression has perhaps not been generally recognised and it would merit re-examination in the light of modern knowledge.One interesting side- light on its applicability is the fact that Lewis was able therefrom to deduce 9 4 2. anorg. Chem. 1926 156 288 ; 1927 161 76 ; 1928 174 31 ; 1929 182 332. g 5 Balce Univ. Philippines Nat. and Appl. Sci. Bull. 1934 4 119. g5a Cartledge J. Phys. Colloid Chem. 1951 55 248. g6 Henglein 2. Elektrochem. 1925 31 424. g7 J. 1917 111 1086. 98 Verh. deut. physikal. Ges. 1911 13 1107. gg Ibid. p. 1117. M 168 QUARTERLY REVIEWS the energy required to rupture the carbon-carbon link in cyanogen that is the dimension of D(NC-CN). The value he obtained (115.2 kcal./mole) agrees quite well with that which now appears to be 7 6 c 3 99-101 but not with other highly discordant values proposed in the interim.An alternative expression due to Henry lo2? l o 3 assumes the form Q = SNMhc/&J where M is the molecular weight c the velocity of light J the mechanical equivalent of heat and lo the average extinction wave- length of the conipound in the infra-red. Since this takes no account of the frequencies of the elements concerned this expression is probably less reliable. The same is true of the expression of the form Q = /c - E’( v1 - v2) deduced by Balandin,lo4 in which v1 and v2 are the frequencies of the two residual rays (” Iteststrahlen ”) of thc compound in the infra-red. An additional disadvantage here is that the constants lc and E‘ must be deter- mined empirically for a few known compounds but the relationship is also found to hold for certain gaseous compounds even though the assumptions involved are not wholly valid for the latter.A relation linking the ultra-violet radiat,ion frequency to the heat of formation has also been derived.lOj 10. Variable Valency and Stability The question of stability in relation to valency is one of such great interest in inorganic chemistry that this Review could scarcely be regarded as complete without reference to it. Grimm and Herzfeld Io6 have devised a method for estimating the heats of formation of ionic compounds in which the metal shows an unusual valency. The method makes use of known heats of formation and the Born-Haber cycle (see Section 7) and it is immaterial whether the compounds are preparable or merely hypothetical. The Born-Haber cycle is equally valid for the real compound Na+Cl- and the hypothetical compound Ne+Cl- Q(NaC1) = U(NaC1) - L,(Na) - I(Na) - +D(Cl,) + E(C1) Q(NeC1) = U(NeC1) - LJNe) - I(Ne) - iD(C1,) + E(C1) If it is now assumed that NeCl would have approximately the same lattice energy as NaCl then by subtraction Q(NeC1) w Q(NaC1) - L,(Ne) + LJNa) - I(Ne) + I(Na) Since all the terms on the right-hand side of the equation are known Q(NeC1) can be estimated.Tn point of fact the Ne+ ion with its small nuclear charge would probably be slightly larger than the Na+ ion and the Mg+ ion with an odd electron in the M shell certainly would be. The lattice energies of NeCl and MgCl would accord- ingly be reduced below that of NaCl SO that the estimates obtained in this In like manner Q(MgC1) can be deduced. OSa Stevenson J . Chem. Phys. 1950 18 1347. lOOBrewer Templeton and Jenkins J .Amer. Chem. Xoc. 1951 73 1462. lol Szwarc and Taylor Trans. Faraday SOC. 1951 47 1293. l o 2 Mem. Real Acad. Ciencas Barcelona 1921 17 No. 7. Io3 Compt. Tend. 1924 178 2248. I o 4 Z . Phylsik 1924 26 145. Bernoulli li’e2v. Chim. Actu 1920 2 720. Io6 %. PhJszk 1023 19 141. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUXDS 169 way may be regarded as upper limits. Energies of transformation due to possible changes in lattice type would be negligible in comparison with the large differences observed. For multivalent cations the total ionisation energy must be included in the calculation. Figures for the total ionisation energies of the first four elements of the second short period are listed in Table 11 and values calculated in the foregoing manner for the heats of formation of the various fluorine compounds in Table 12.(The value for AlF has been calculated for a molecular model with the same bond energy as SiF,.) The line in Table 12 separates the unstable endothermic compounds from the exothermic and corresponds to a particularly high jump in ionisation energy in Table 11. TABLE 11. Total ionisation TABLE 12. Heuts of formation of energy ( i i z Ecal./g.-atom) $fluorides (in kcaE./mole) A1 + 138 Na++ Mg++ Al++ 1209 1 523 572 Mg+++ Al+++ 2370 1 1228 3993 Al++++ NgF AlF NaF I MgF AIF2 < 68 < 67 < - 413 263 < 175 < - 792 AlF N - 1383 The question now arises whether any of the subhalides will be stable. Since the reaction 2MgF +- MgF + Mg will according to the data in Table 12 liberate a large amount of energy MgP will not be stable-or a t the most will be metastable-and tend to disproportionate spontaneously ; i.e.the criterion of stability is that the heat of formation (or more strictly the free energy of formation) of MgF exceeds one-half that of MgF,. Like- wise AlF will not be stable in the solid state since its heat of formation is less than one-third that of AlF,. This is not to say that molecules such as A1P will not exist in the vapour phase. Indeed the heat of formation of gaseous A1F has been estimated from equilibrium data to be 49 kcal./mole.107 Since the latent heats of fusion and vaporisation of A1F have respectively been estimated to be 5 and 38 kcal./mole,l0* the discrepancy with the value obtained by Grimm and Herzfeld’s very approximate method is only of the order of 25 kcal./mole. Whereas this procedure clearly indicates that the subhalides of magnesium will be unstable in the solid state yet for the subhalides of the alkaline-earth metals it yields values for the heats of formation high enough to suggest that in view of the inaccuracies involved these compounds may be on the verge of stability.Experience teaches that this is indeed the case. Values for the heats of formation of the alkaline-earth subhalides have been estimated by Hush,lo9 and for those of the subhalides of aluminium by Irmann.loga Gross Campbell Kent and Levi Discuss. Fnraduy SIoc. 1948 4 206. lo8 Brewer op. cit. (ref. 39) p. 193. lo9 J . Proc. Roy. SOC. N.S. ITT. 1949 82 229. loQa IIeEv. C’him. Acta 1950 33 1449. 170 QUARTERLY REVIEWS From a comparison of the figures cited for sodium and magnesium in Tables 11 and 12 it will be apparent that if the jump in the ionisation energy on passing from one valency to another is too high then the higher valency (here 2) corresponds to an unstable compound if on the other hand it is too low then the compound corresponding to the lower valency (here 1) becomes metastable or totally unstable and liable to disproportionate.Intermediate magnitudes in ionisation energy appear with many of the transition elements so that these elements commonly form whole series of stable compounds in which successive steps in valency are realised. As an example the heats of formation of the solid halides of molybdenum 26 (those of the fluorides are unfortunately not known) are given in Table 13. TABLE 13. Heats of formation of the molybdenum halides Chlorides MoCl MoC1 MoC1 MoCl MoC1 Qf (kcal./mole) 44 65 70 90.8 90 Bromides MoBr MolJr MoBr MoBr - Qf (hcal /mole) 29 41 45 51 Iodides MoI M O I M O I MoI - 1,” 15 18 18 The figures for each column of halides lie almost on smooth curves.Van Arkel 110 has recently discussed the various possible types of curves that may in theory be obtained for the halides of an element of va’riable valency. The iodides and bromides frequently give curves belonging to type C (see Fig. 9) in which a maximum is observed rendering the highest halides unstable. The increment in the heats of formation on passing from the bromide to the’chloride (or from the chloride to the fluoride) varies according to simple theory in proportion to the square of the valency so that the chlorides of higher valency are further stabilised with respect to those of lower valency and a curve of type 112 (Fig.9) may be realised for the chlorides whereupon the highest chlorides are stable. (A glance at the values in Table 13 will show that the increments for the molybdenum halides are qualitatively but not qua,ntitatively in agreement with the simple theory.) If now on passing to the fluorides the further enhancement of stability of the compounds of higher valency is such as t o make the curve for the fluorides convex towards the valency axis (type A Fig. 9) then the lower fluorides become metastable since they liberate heat on dispropor- tionation. This explains in principle why frequently the maximum valency is realised only in the case of the fluorides. Thus VF exists but the highest chloride of vanadium is VC1 and the highest bromide VBr,.For molyb- denum (Table 13) the hexachloride and pentaiodide are on the verge of stability while the hexabromide and hexaiodide apparently do not exist and would a t least be thermochemically unstable with respect to the penta- halides. That a higher compound may have a smaller heat of formation than a lower compound need not imply that the former is incapable of 110 Research 1949 2 307. LONG HEATS OF FORMATION OF SIMPLE INORGANIC COMPOUNDS 171 existence if it can be prepared indirectly. Thus rhenium heptasulphide Re,S, decomposes into ReS and sulphur with the liberation of heat so that it cannot be prepared from the elements ; but it can be prepared indirectly and is metastable at ordinary temperatures. ll1 Where a change in valency of a non-metal is involved the picture is rather different in that now bonding pairs of electrons have to be unpaired and the valency increases by steps of two.The promotion involved at each step involves absorption of energy the atom thereby becoming excited to a new valency state (see next section). An increase in valency usually decreases the- bond length and in- creases the stretching force constant of the bonds. It may further be inferred that the bond polarity de- creases. These factors are to be t associated with an increase in the ,s absolute or intrinsic energy of each 2 bond. Nevertheless when the above- 2 mentioned promotional energy i s taken into account the net (or a thermochemical) bond energy is The chlorides of iodine may serve as an example. The heat of formation of gaseous IC1 from gaseous I and C1 is 3-24 kcal./mole from which the bond energy may be estimated to be 50-3 kcal.from the dissociation t usually decreased. P o Stable ha//& x Unstable halide / /; 1 7 2 3 4 5 Valency FIG. 9 energies of iodine and chlorine. trichloride ICl, is stable as a solid 'Ln the but the vapour breaks down into ull valencies from. 1 to 5. IC1 + Cl, from which it appears that the net I-Cl bond energy in ICl is depressed considerably below that in IC1. For the reaction ICl ( g ) -+ ICl (9) + Cl (9) to be exothermic the net bond energy in ICl must be less than 36-1 kcal. Thus if both compounds are to be stable in the vapour phase the depression in the net bond energy must not exceed a certain upper limit nor must it fall below a certain lower limit or the lower compound will become unstable.It can be shown that if the net bond energy exceeded 38.3 kcal. the reaction 3IC1 (9) + ICl (9) + 1Q1 ( g ) would become exothermic. The margin tends therefore to be narrow especially where compounds with small heats of formation are being dealt with. In the case of the fluorides of iodine the depression in the net bond energy is too small for IF to exist. Indeed IF is likewise unstable with respect to IF, this and IF being the only known fluorides. Fluorine is the only halogen to form bonds with iodine strong enough to provide enough energy for raising the latter to the quinque- and septa-valent states. ll1 Biltz and Weibke 2. anorg. Chem. 1931 203 3. The H ~ ~ O t h e t i c ~ l C U ~ V ~ S illustrating the trends a d unstable halides of a n element exhibiting O f formation Of 172 QUARTERLY REVIEWS The question of critical bond energies has been discussed recently from a rather different aspect.l12 A discussion of the conditions under which disproportionation may occur among inorganic compounds will not be entered into here as the matter has been reviewed in detail elsewhere.ll3 11.Heats of Formation and Modern Chemical Theories It is not the present purpose to review the various attempts to gain a theoretical understanding of the energetic structure of inorganic compounds since the earliest application of the quantum theory to this p r ~ b l e m . ~ l ~ ~ llj It will suffice to make some general observations. The wave function of each elecfron in a molecule-whether involved in chemical bonding or not-is to be associated with a particular energy.In theory the difference in the sum of the energies for the free atoms which make up the molecule and those of the molecule itself will provide an estimate of the atomic heat of formation. The mathematical difficulties in solving the Xchrijdinger wave equations for any except the simplest mole- cules Eiavc however compelled the introduction of certain approximations. The valency-bond method and inolecular-orbital method are two alterna- tive ways of approaching this intricate problem. Whereas the former has roved itself to be reliable in certain simple cases of molecules with single bonds tlic latter has proved the more adaptable for systems with n electrons a i d has received the greater attention. The interested reader is referred to Coulson’s excellent review on this subject.lls Both methods have their limitations.Whereas the original valency-bond method is unsuited for inolccules in which delocalisation of bonding electrons is important yet for molecules containing only cr bonds the molecular-orbital approach tends to over-estimate the probability of both electrons of such a bond being found simultaneously round one atom especially a t large internuclear distances this arising through the inadequate recognition of repulsive factors operative. I n emphasising these facts Lennard- Jones and his collaborators have in the past four years made an important advance. Many of the weaknesses in the approximate treatment of earlier theories have been partly overcome by replacing molecular orbitals by equivalent orbitals in which the respec- tive pairs of electrons are assumed to interact according to the ordinary laws governing electrostatic forces.In this way due account is taken of the Coulomb forces operating between the electrons without losing sight of their exchange energy. The various methods have been compared in a recent summary 1179 11* where reference to detailed treatment of specific molecules by the new procedure will be found. I n this procedure it is of importance 112 Ormont Acta Physicochim. U.R.S?S. 1946 21 409. 113 Wilson and Bremner Quart. Rewiews 1948 2 1. 114 Born Nuturu&s. 1924 12 1199. 115 Wilsdon Phil. Mag. 1925 49 354 900. 116 Quart. hhieuw 1947 1 144. 117 Lennard-Jones and Pople Disciiss. Faraduy SOC. 1951 10 9. 11* Lennard-Jones and Hall ibid. p. 18. LONG HEATS OF F O R ~ T I O N OF SIMPLE INORGANIC COB.IPOVCTNDS 173 to note that part of the total energy of a moleciile becomes associated with the bonds and part with the atoms themselves.Qualitatively at least' this is in accord h t h with expectation and wit'h experimental evidence provided by dissociation energies and bond properties (here come into consideration inore partirularly force constants l9 and bond lengths 120? 121). Since the difference in the sums of the energies of the indivictiial electrons in the molecule and in the free atoms respectively provides a measure of the energy of formation of a molecule changes in the wave functions of the non-bonding electrons as well as those of the bonding electrons must be considered in the complete picture ; i.e. the energy of the bonds alone as provided by the wave functions cannot in general be cquated with the atomic heat of formation of the molecule in question.A term must be included to take account of change in internal energy of the atoms themselves in bringing ea'ch to the appropriate valency state in which it finds itsclf in the compound. This will cover the energy required to promote one or more electrons to higher orbitals when the ground state of the atom has an insufficiency of unpaired electrons and also hybridisation effects which may affect non-bonding as well as bonding electrons. According to this viewpoint the usual equation Qa = CE, where Qa is the atomic heat of formation and E the net or thermochemical bond energy is replaced by Qa = CEi - C V where Ei is the gross or intrinsic bond energy and V represents the valency-state energy.I n the improved picture therefore the interatomic energy is enhanced a t the expense of intra-atomic energy. Logically it is the Ei values and not the E values which are to be related to other bond properties. (The energies listed in Table 10 are E values.) The derivation of Ei values from heats of formation requires a knowledge of valency-state energies. Clearly the calculation of resonance energy from atomic heats of forma- tion by equating it to the deviation in the sum of the E values as derived from other molecules is a very risky procedure since it takes no account of the variation in Ei values (as reflected in other bond properties) or in valency-state energies brought about by such effects as conjugation. Jndeed no conclusions regarding resonance can logically be drawn from heats of formation nor do the latter enable a decision to be made between alternative structures,122 as has frequently been supposed.Other objections to certain common assumptions regarding resonance have been referred to It is o n l ~ in recent years that attempts have been made to derive valency-state energies from experimental data and so far estimates are available only for quadrivalent carbon,126 127 the alkali nietrals (in their 119 Liiinett .&wort. Reviews 1947 1 73. Wells J. 1049 55. lZ1 Allen and Sutton ,4ctn Oryst. 1050 3 46. 12* Samuel J . Chem. Phys. 1944 12 180. lZ3 Hiiclrel '. Structural Chemistry of Inorganic Compuiinds " Vol. I (English translation by I,. H. Long Xlsevier Amsterdam 1950) translator's note pp. 434 ff.12* Longuet-Higgins Xature 1950 165 908. 126 Qillespie J . 1952 100'7. 126 Long and Kiorrish Proc. Roy. SOC. 1946 9 187 337. 1 2 7 Long Esp~'.i~?7tin 1951 7 195. elsewhere. 1 2 3- 13 5 1 74 QUARTERLY REVIEWS diatomic molecules),128 oxygen,12g nitrogen,130 and bivalent carbon. 130 Earlier theoretical attempts to calculate valency-state energies were not wholly successful in view of the inadequate nature of the theories involved and they sometimes provided values which experimentally are now known to be unacceptable. The observational data utilised in the experimental estimations are dissociation energies in conjunction with other bond properties for polyatomic molecules and extrapolation of spectroscopically observed vibrational levels for diatomic molecules. Because of the approx- imating assumptions involved neither method is very accurate and it is doubtful if valency-state energies can be estimated with an accuracy better than 5 loo/ (if as good) a t present.However the values derived by different methods exhibit reasonable agreement. In the case of quadrivalent carbon for example six different procedures 127 have yielded the values 58.6 (lower limit) 70.2 (upper limit) 66 57 65 and 67 kcal. for the valency-state energy. Clearly what is ne?ded is a reliable and accurate method for deriving valency-state energies along theoretical lines and in this connection a step forward has recently been made by Moffitt.131 Given the valency-state energies it will be possible to calculate intrinsic bond energies from atomic heats of formation just as the reverse procedure is also possible.Like valency states intrinsic bond energies are not directly observable but it is to be expected that they are related to other bond properties. Thus attempts such as those of Cook 132 and W a l ~ h l ~ ~ to interrelate bond energies with stretching force constants bond lengths bond polarities and ionisation potentials all of which can be directly observed or calculated may ultimately develop into a reliable method of assessing intrinsic bond energies. At all events the near future should witness an increasing interest in determining the individual contributions of valency-state energies and intrinsic bond energies to atomic heat,s of formation. 128 Pauling Proc. Roy. Roc. 1949 A 196 343. 12* Idem Proc. Nat. Acad. Sci. 1949 35 239. 130 Pauling and Sheehan ibid p 359.131 Proc. Roy. Soc. 1950 A 202 634. 132 J . Phys. Colloid Chem. 1947 51 407. 133 Discuss. Faraday SOC. 1947 2 18 ; J . 1948 398 ; Quart. Revzews 1948 2 73.

ISSN:0009-2681    

DOI:10.1039/QR9530700134

出版商:RSC    

年代:1953

数据来源: RSC

摘要:

RECENT DEVELOPMENTS IN THE PREPARATION OF NATURAL AND SyNTaETIC STRAIGHT-CHAIN FATTY ACIDS By F. D. GUNSTONE PH.D. A.R.I.C. (LECTURER IN CHEMISTRY UNIVERSITY OF GLASGOW) MANY aliphatic carboxylic acids have been isolated from natural sources or prepared by synthetic methods. The number of normal saturated acids is relatively small whereas the number of possible normal unsaturated acids is much greater owing to variation in the number position and con- figuration of the unsaturated centres. Methods of synthesising saturated acids were developed many years ago but the synthesis of unsaturated acids is a more recent development oleic and linoleic acids being first synthesised only in 1934 and 1950 respectively. In the last decade many aliphatic acids have been prepared and several previously unknown acids have been isolated from natural sources.In this Review the methods of sumthesis of normal saturated and unsaturated acids containing not less than six carbon atoms are reviewed and recent contributions to our knowledge of naturally occurring fatty acids are discussed. Some aspects of this subject are included in the works of Hilditch,l Markley,2 R a l ~ t o n ~ and J ~ h n s o n ~ and in some more recent review^.^ The Geneva nomenclature (C0,H = 1) is used throughout this Review and systematic names are preferred to trivial names except in a few estab- lished cases. Trivial names are used for the following saturated acids lauric ( C12) myristic ( CI4) palmitic ( C16) stearic (C,,) and behenic ( C22) and for the unsaturated acids listed below. Sorbic CH,*CH:CH*CH:CH*CO ,H Hexa-2 4-dienoic acid Oleic * CH,fCH,] ,CH:CH-[CH J ,.CO,H Octadec -9-enoic acid Stearolic CH,*[CH J ,*CiC-[CH,] ,GO ,H Oc tadec - 9-ynoic acid Linoleic * CH,fCH ,],.CH:CH*CH,CH:CH.[CH ,] ,CO ,H Octadeca- 9 12 -dienoic acid Linolenic CH,-CH ,*CH:CH.CH,*CH:CH-CH,CH:CH*[CH J ,*CO ,H Octadeca-9 12 15-trienoic acid * Elaidic linelaidic and brassidic acids are the trans-isomers of the naturally occurring cis-acids.1 Hilditch " The Chemical Constitution of Natural Fats " Chapman and Hall Markley " Fatty Acids their Chemistry and Physical Properties " Interscience Salston " Fatty Acids and their Derivatives " John Wiley and Sons Inc. New Johnson " Acetylene Compounds " Vol. 11 " Acetylenic Acids " Edward Arnold Lennartz Angew. Chem. 1947 59 A 10; Breusch Fortschr. Chem. Forsch.Ltd. London 1947. Publ. Inc. New York 1947. York 1948. and Co. London 1950. 1950 1 667 ; Seher Fette u. Seifen 1951 53 692. 175 176 QUARTERLY REVIEWS Elaeostearic CH,*[CH2],*CH:CHCH:CHCH:CH,I,.C0,H Ricinoleic Arac hidonic Octadeca-9 11 13-trienoic acid 12 -Hydroxyoctadec - 9-enoic acid CH3*[CH2 ],.CH:CH*CH ,.CH:CH.CH,.CH:CH*CH,*CH:CH.[CH ,],.CO ,H Eicosa-5 8 11 14-tetraenoic acid Erucic * CH3*[CH2],*CH:CH*[CH2]llC02H Docos- 13-enoic acid * Elnidic linelaidic and brassidic acids are the trans-isomers of the naturally occurring cis-acids. CH,*[CH,],*CH( 0H)CH ,*CH:CH-[CH,] ,*CO ,H 1. Synthesis of Saturated Fatty Acids Methods of synthesising saturated acids may be divided into three groups depending on whether the reaction leaves the chain length unchanged or whether there is chain extension or chain degradation.Methods involving no Change in Chain Length.-Saturated fatty acids arc often prepared from closely related compounds possessing the required carbon chain. Included under this head are reduction of the unsaturated acids and oxidation of alcohols and aldehydes. These are general methods applicable to a wide range of compounds but limited for practical purposes to starting materials either more readily accessible or available in a purer condition than is the saturated acid. Hydrogenation of unsaturated acids. Since it is sometimes possible to prepare unsaturated acids free from lower or higher homologues this method had been used to prepare pure saturated acids especially undecanoic stearic and behenic acids from one or other of their unsaturated analogues.Catalytic reduction is preferred though chemical methods have been used. Because of the proviso already stated concerning the relative availability of alcohols aldehydes and acids this method has been used mainly for the preparation of heptanoic acid (from heptaldehyde obtained by pyrolysis of ricinoleic acid) and the higher members of the series (above C2J. There has been much confusion among the higher naturally occurring alcohols. The alcohols and consequently trhe resulting acids also have often been homologous mixtures whilst some- times wrong formulz have been assigned to both alcohol and acid. Piper Chibnall and Williams 6 in a summarising paper describe the C26 C28 and C, acids obtained by oxidation of the corresponding alcohols. Attempts to convert hydro- carbons into acids by oxidation or by interaction with carbon monoxide have yielded mixtures of acids used directly for the production of soap or edible fat.These processes are not designed primarily for the production of individual acids though they may become more important in this con- nection. Useful summaries arc given by Markley ' and in the Annual Reports on the Progress of Applied Chemistry.8 Methods involving Chain Extension.-These methods may be further Oxidation of alcohols and aldehydes. Production of fatty acids from hydrocarbons. Piper Chibnall and Williams Biochem. J . 1934 28 2175. Ref. 2 pp. 540-547. Ann. Reports Progr. of Applied Chem. 1950 35 239 ; 1951 36 119. GUNSTONE PREPARATION OF STRAIGHT-CHAIN FATTY ACIDS 177 divided according to the number of carbon atoms added to the starting material.Of the standard procedures used for increasing the length of a carbon chain by one unit that involving the reaction sequence given below has been used most extensively R.CO,H -+ R.CO,R' -+ R*CH,*OH --P R*CH,X + Reactions resulting in the addition of one carbon atom. R*CH,*CN + R*CH,*CO,H The starting material is generally a naturally occurring acid or (less fre- quently) alcohol and since these contain an even number of carbon atoms the acids so obtained are niainly those containing an odd number of carbon atoms. The starting material must be pure if pure products are to result indeed the main difficulty in these reactions is the separation of the products from impurities with very similar physical properties. For this reason pure stearic and behenic acid obtained by the reduction of oleic and erucic acid are useful starting materials.Many steps are involved but yields are good and pure products are claimed given the above safeguard. Almost every acid in the series between C, and C, has been prepared in this way.6 9 1 lo Other methods of increasing chain length by one unit wliicli have bccn used include the Arndt-Eistert reaction l1 and carboxylation of the Grignard reagent. Isotopically labelled acids have been prepared by the latter method. l2 By using malonio ester it is possible to add two carbon atoms to the appropriate alkyl halide and this method has been used mainly to prepare the higher acids contain- ing an even number of carbon atoms. Stearic and behenic acids are again the most important starting materials.The procedure is described by Bleyberg and Ulrich l 3 and by Francis et U Z . ~ ~ ~ 14 l5 who have prepared most of the acids between C, and CS8. Some standard condensation reactions have been successfully applied to the preparation of saturated acids. These methods being mainly of recent description have been developed largely for other reasons such as the preparation of branched-chain acids or of keto-acids but appropriate modifications lead to the normal saturated acids. In 1925 Robinson and Robinson l6 described a nzethod of preparing long-chain keto-acids involving Reactions resulting in the addition of two cccrbon atoms. Reactions resulting in the addition of several carbon atoms. (a) The use of acetoacetic ester as a coupling unit. 9 Levene and Taylor J. Biol. Chem. 1924 59 905.10 Francis Piper and Malkin Proc. Roy. SOC. 1930 .4 128 214. 11 Proitonik Arkiv Kerni 1946 18 1 ; Vandenheuvel and Yates C'u~iud. J . Res. l2 Harwood and Ralston J. Org. Chern. 1947 12 740 ; Dauben J. ArrLcr. Chent. 13 Bleyberg and Ulrich Ber. 1931 64 2504. 1 4 Francis King and Willis J. 1937 999. l5 Francis Collins and Piper Proc. Roy. SOC. 1937 A 158 691. l6 G. M. Robinson and R. Robinson J. 1985 127 175; 1950 28 B 556. Soc. 1948 70 1376. 1926 2204. 178 QUARTERLY REVIEWS condensation of (i) an alkyl halide and (ii) a carbethoxy-acyl ha,lide with acetoacetic ester. Subsequent stepwise hydrolysis afforded a keto-acid C0,Et C0,Et I CH,-[CH,],.Br I Cl-CO~[CH,],~CO,Et CH - CH,.[CH,],*CH + I I CO-CH COCH C0,Et I I CO-CH CH3*[CH2],.C.C0.[CH,]aoC02Et - CH,fCH,],*CO*[C'H,]a*CO,H which could be reduced by the Clemmensen procedure.Later one of these authors l7 drew attention to the rather low yields obtained. The main product appears to be a dibasic acid (111) produced by the alterizativc hydrolysis of the condensatmion production (I). Other work on the hydrolysis of diketones of the type R*CO*CH,*COR' shows that the stronger acid preponderates. The desired keto-acid (IV) ma,y result from either (I) or HO ,C.[CH,],,*CO ,H (111) / \ / \ C0,Et I CH3.[CH,]nL.G*COfC'H2],zC02Et I COCH (1) CH3*[CH2],,,+1CO.[CH2],,*C0,H (IV) I I (11) C0,Et CH ,fCH ,Inl + 1.CO.CfCH ,In - 1*CO ,E t COCH CH 3 *r CH ,In&+ 1.co ,H (V) (11) and since (111) is a stronger acid than (V) it was conceived t!hat (11) might give a better yield of the acid (IV). This was confirmed in practice and the improved procedure has been used for the preparation of several C0,Et C0,Et I CH2 I COCH COCH Br fCH,] C O ,E t 1 CH,.[CH,],,*COCl + CHfCH,],,*CO,Et + I C0,Et I I CO CH CH,*[C~,]1,*CO~Co[CH2]l~*~~ ,Et + CH,~[CH,],,*CO~[CH,]ll*CO ,H -+ CH,fCH,],,*CO,H acids.l49 l8 The method is limited only by the availability of the cu-bromo- esters ; the C1 and Cll compounds were however accessible when this work was described thus permitting the addition of eleven or twelve carbon atoms in one cycle of reactions.1' G. M. Robinson? J . 1930 745. Idem J . 1934 1543 ; Ashton Robinson and Smith J . 1936 283. GUNSTONE PREPARATION OF STRAIGHT-CHAIN FATTY ACIDS 179 Stallberg-Stenhagen Stenhagen et al. have developed an improved modification of this reaction by which they have synthesised many normal and branched- chain acids.The preparation of tetratriacontanoic acid is illustrative. l9 COCH CH,.CO.CH,*CO,Et I NaOMe CH,*[CH2] ,,*COCl + CH,*[CH,],,.CO*CH*CO,Et - I.[CH ,.CO ,Et CH,.[CHJ,O*CO*CH,.CO ,Me - CO ,Me I CH,*[CH,],,~CO~CH~[CH,]lo*CO ,Et ____+ CH,~[CH,],o~CO~[CH,]l~*CO,H - CH,-[CH,],,.CO,H Bowman and his col- leagues 2o have recently described methods similar t o those of Robinson lout using nialonic ester as the coupling unit. The novelty of the method is in the CO,Et I Br*[CH,];CO,Et CH - I CO,Et (b) The use of malonic ester as a coupling unit. C0,Et CO ,R I Na- I CH*[CH,],-CO,~t f CH*[CH,],.CO,R C0,Et C0,R CH,.[CH,],-COCl * I Ph*CH,*OH 1 - -1 (VI) - - - - - - - - - - - - - - - - - - - - - (70°L) I I V CO ,R I - co CO ,R I H 2-Pd CH,.[CH,],.C0.C.[CH2]60~OzR ---+ CH3*[CH2]4*CiO*[CH2]7COzH CH,fCH,],,.CO,H CO,Et CO,Et CO,R I CH,.[CH,],.Br I Na- I CH + CH,*[CH,],*CH + CH,*[CH,],*CH I Ph*CH,*OH I CO,Et CO ,R I C0,Et I I I I I I I ClCO*[CH,] ,CO ,E t (71%) I I CO ,R I I I 0 C02R Stallberg-Stenhagen and Stenhagen Arkiw Kerni Min.Geol. 1945 19 A No. 1 2O Ames Bowman and Mason J . 1950 174 ; Bowman and Mason J . 1951 2748. (and many later papers by t,hese authors). 180 QUARTERLY REVIEWS use of the benzyl esters since the benzyl group may be split off by hydrogena- tion thus avoiding the hydrolysis by which undesirable by-products are formed. The benzyl esters are prepared from the ethyl esters by trans- osterification. Yields are high and the desired intermediates are readily prepared. The reaction may be carried out in two ways (see reaction chart).In addition to these acids (C14 and C18) the C23 C39 and C, acids have been prepared. The preparation of w- bromoheptanoic acid from tetrahydropyrm (60%) is described also an alternative preparation of triesters of type (VI). Fatty acids result via the keto- esters from interaction of a carbethoxy-acyl halide with an orgaiio-metallic compound generally a zinc or cadmium compound. These methods which have found extensive use in the preparation of branched-chain compounds 21 are summarised thus (c) The use of organo-metallic compounds. I-+ RZnX-' ZnC1 R*CO*[CH,],*CO2Et + R*[CH~],,+I*CO~H The c,6-C35 straight-chain acids have been prepared in this way.22 hydroxy-ester. acids (see below) but Pieser ~ . t froin alicyclic ketones. Interaction of a Grignard compound with an aldehydo-ester affords a This reaction has been used mainly to prepare unsaturated have indicated how saturated acids result HO R.C'O.[C'H,],,-l'CO,H -+ R.[CH2],*C0,H The method was illustrated by the description of the C2,, C22 C2$ and c26 acids and has since been used for the preparation of some ucnteiso-acids.24 (d) Anodic syntheses.The Kolbe electrolytic synthesis has recently been adapted for the production of saturated fatty acids. A discussion of this method is included in a recent review.25 (e) Other condensations. Kuhn 2 6 has reported that acetaldehyde or crotonaldeliyde undergoes condensation in presence of piperidine acetate yielding polyene-aldehydes R*[CH :CH*],*CHO. These may be reduced to saturated alcohols and then oxidised to the acids or condensed with malonic acid before hydrogenation.21 Cason Taylor and Williams J . Org. Chem. 1951 16 1187 and earlier papers in this series. 2 2 Drake and Melamed J . Amer. Chem. SOC. 1948 70 364 ; Jones ibid. 1947 69 2350 ; Schuette Roth and Christenson Oil and Soap 1946 22 107 ; Schuette Maylott and Roth J . Amer. Oil (Ihem. h'oc. 1948 25 64. 23 Fieser anti Szmuszkovicz J . Anzer. C'hrm. ,SOP. 1948 70 3352. 2 4 Nunn ,I. 1951 1740. 2 5 Weedon Quart. Reviews 1952 6 390. 26 Kuhn J. 1938 605. GUNSTONE PREPARATION OF STRAIQHT-CHAIN FATTY ACIDS 181 A method of extending chain length by six carbon atoms involving C-alkylation of cyclbhexane- 1 3-dione and subsequent hydrolysis and reduc- tion has recently been reported. 27 Methods involving Chain Degradation.-There are many ways of degrad- ing saturated or unsaturated acids to lower homologues.Although mostl of these have been designed for determination of structure where yields are high and starting materials readily available they have also been used as preparative methods. An early method of degradation due to Krafft,28 involves oxidation of the methyl ketone which results from heating the barium salt of the acid with barium acetate Degradation of saturated acids. B,t(OAc) It*CH,.CO,Ba - R*CH,COCH - R.CO,H The modification of the Hofmann reaction in which an amide is converted into a nitrile containing one less carbon atom has yielded several acids.29 Another method involves decomposition of the a-hydroxy-acid by heat and subsequent oxidation or by direct oxidation ; 3* / RCH( OH)*CO,H KMnO or Pb(OAc) Degradation of unsaturated acids.Degradation of unsaturated acids is achieved by alkali fusion or by oxidation. Unsaturated acids whether naturally occurring or prepared from sat,ur- ated acids by bromination and subsequent dehydrobromination yield the saturated acid with two fewer carbon atoms when fused with potassium hydroxide. When the double bond is not in the ccg-position migration to this position probably precedes fission. Stearic and erucic acids have long been known to give palmitic 31 and eicosanoic acid 32 respectively by this means. Farmer 33 states that under appropriate conditions oleic acid affords isomeric octadecenoic acids. Hunter and Popjak 34 have described optimum conditions for the degradation of the a/3-unsaturated acid. Of the many oxidation procedures designed for fission of unsaturated acids the most satisfactory method particularly from the preparative view- point is oxidation by potassium permanganate in acetone or acetic acid solution.35 36 *’ Stetter and Dierichs Chem. Ber. 1952 85 61 290 1061. 28 Krafft Ber. 1879 12 1664 1668; 1882 15 1687. 29 Hofmann Ber. 1884 17 1406 ; Lutz Ber. 1886 19 1433 ; Wallis and Lane 3O Levene and West J Biol. Chem. 1914 16 475 ; Mendel and Coops Rec. Trav. a 2 Fitz Ber. 1871 4 442 ; Morgan and Bowen J. SOC. Chem. Id. 1924 43 3461.. 33 Farmer Trans. Faraday SOC. 1942 38 356 ; cf. Egorov J. Russ. Phy.9. Chena. 3 4 Hunter and Popjak Biochem. J. 1951 50 163. 35 Armstrong and Hilditch J. Soc. Chem. Incl. 1925 44 4 3 ~ . s6 Regemann Keppler and Boekenoogen Hec. Traw. chiin. 1950 68 439. Org. Reactions 3 267. chim. 1939 58 1133.31 Varrentrapp Annalen 1840 35 196. Soc. 1914 46 975. 182 QUARTERLY REVIEWS 2. Synthesis of Unsaturated Fatty Acids Unsaturated fatty acids have been prepared by various procedures which fall into twq main groups. Included in the first are those methods in which some naturally occurring acid or other readily accessible and closely related compound is modified to give an unsaturated acid. The second group contains those methods of condensation by which long-chain unsaturated acids may be synthesised. Modification of Other Fatty Acids.-This group is conveniently sub- divided into three sections depending on whether there is an increase a decrease or no change in the degree of unsaturation. (a) Dehy- dration of hydroxy-compounds. This method has found commercial applica- tion in the production of a drying oil from castor oil which contains a high proportion of ricinoleic acid.For the formation of individual acids this procedure suffers from the fact that dehydration may afford two isomers and from the limited availability of hydroxy-acids. 12-Hydroxyoleic and -stearic acids are the most readily available hydroxy-acids. Dehydration of 12-hydroxystearic acid with a variety of dehydrating agents yields a mixture of 11 12- and 12 13-unsaturated acids.361 37 Dehydration of ricinoleic acid (VII) or its glyceride affords octadecadienoic acids (VIII and IX) or glycerides. Dehydration is effected by heating it with various catalysts and the more unsaturated product Methods resulting in an increase in the degree of unsaturation. CH,*[CH,] ,*CH:CH*CH ,*CH:CHfCH ,] ,*CO ,H (vlll) I i CH,*[CH 2]5.CH( 0H)CH ,*CH:CH*[CH,] ,TO ,H CH,*[CH,],.CH:CH*CH:CH.[CH,I ,420 ,H (IX) has enhanced drying proper tie^.^^ The claim 39 that the conjugated acid (IX) is the main product has not been upheld.*O The octadeca-trms- 9 trans-ll-,41-45 -cis9 t r ~ n s - l l - ~ ~ and -cis-9 truns-12-dienoic acids have been isolated from dehydrated ricinoleic acid.Another acid isolated by 37 Fokin J. Russ. Phys. Chem. Xoc. 1914 46 1027 ; Griin and Czerny Ber. 1926 38 Forbes and Neville Ind. Eng. Chem. 1940 32 555. 39 Boeseken and Hoevers Rec. Traw. chim. 1930 49 1165. 40 Priest and von Mikusch Ind. Eng. Chem. 1940 32 1314. 41 Mangold Monatsh. 1894 15 307. 4 2 Boeseken and Hoevers Rec. Traw. chim. 1930 49 1161. 43 Smit ibid. p. 539. 44 Nichols Herb and Riemenschneider J.Amer. Chem. SOC. 1951 '73 247. 4 5 Jackson Paschke Tolberg Boyd and Wheeler J. Amer. OiZ Chem. SOC. 1952 59 54. 29 229. GUNSTONE PREPARATION O F STRAIGHT-CHAIN FATTY ACIDS 183 (X) Smit,43 has been shown to be the trans-8 trans-lO-is~mer.~~ The dehydra- tion reaction is obviously more complex than was a t first realised. The commonest method of introducing an unsaturated linkage involves dehydrohalogenation of a halogeno-compound. This reaction is generally effected by treatment with alkali or a nitrogenous base (diethylaniline quinoline or collidine). Alkali although used extensively has the disadvantage that the product may be accompanied by some hydroxy-acid and by isomeric unsaturated acids resulting from double-bond migration. The halogenated acids may be pro- duced in four ways (i) bromination by phosphorus and bromine giving the cc- bromo-acid (ii) conversion of some functional group already present (e.g.hydroxyl) into a halogen substituent (iii) interaction of a double bond with HX or X (X = halogen) and (iv) allylic bromination of unsaturated acids by N - bromosuccinimide. Method (i) has been widely used for the preparation of a@-unsaturated acids. Optimum yields are claimed for dehydrobromination of the neo- pentyl cc-bromo-ester with dieth~laniline.3~ Method (ii) is limited to the use of ricinoleic and 12-hydroxy-stearic acid and is of little importance. Unsaturated acids yield isomeric acids by hydrohalogenation and subse- quent dehydrohalogenation. On a purely random basis such a reaction (b) Dehydrohalogenation of halogeno-compounds.-CH,*CH,*CO 2R -+ -CH2*CHX*CO,R + -CH:CH*CO,R t -CH:CH*CHz*CHz- (XIII) t -CH ,*CH z*CH:CH- (XIV) would lead to three products (XIII X and XIV) though in practice one isomer may predominate and be isolatable. Factors affecting the product of this reaction include the position of the carboxyl group and other ethylenic linkages the degree of substitution of the carbon atoms involved and the experimental conditions. It has been claimed that (XI) and (XIII) are the main products and several octadecenoic acids have been prepared in this way.47 The reaction of N - bromosuccinimide with several unsaturated acids or esters has been examined. Schmid and Lehmann 48 brominated methyl 46 von Mikusch J. Amer. Oil Chem. SOC. 1952 29 114. 47 Eckert and Halla Monatsh. 1913 34 1815 ; Pigulevskii and Simonova J .Gen. Chem. U.S.S.R. 1939 9 1928 ; Vanin and Chernoyarova ibid. 1935 5 1537 ; cf. Arnaud and Posternak Cornpt. !reid. 1910 150 1525. 48 Schmid and Lehmann Helv. Chim. Acta 1950 33 1494. N 184 QUARTERLY REVIEWS elaidate and methyl brassidate in the allylic position and after dehydro- bromination isolated octadeca-9 ll-dienoic and docosa-13 15-dienoic acids. As the properties of the former differ from those of the known octadeca-trans-9 trans-1 l-dienoic acid confirmation of these results is desirable. Methyl undeca-8 10-dienoate has been similarly prepared from methyl ~ndec-lO-enoate.~~ Allglic bromination of methyl linoleate has also been studied.50 Dehydrohalogenation of a saturated dihalogeno-acid has been widely used for the preparation of ncetylenic acids from the corresponding ethylene -CH:CH- -j.-CHX*CHX- -+ -C:C- compounds via the dihalogen acid. 5l The dehydrohalogenating agent is generally potassium hydroxide in aqueous or alcoholic solution though sodamide in liquid ammonia has been used. Johnson 52 states that this method cannot be used to prepare 2-ynoic acids. Unsaturated acids may be prepared by partial reduction of more unsaturated compounds which are readily accessible. Partial reduction of polyethenoid acids how- ever generally yields a complex mixture of isomers for in addition to the fact that different ethylenic bonds may become saturated cis-truns-isomerism and double- bond migration occur simultaiieously ; it is not surprising therefore that only a few individual compounds have been isolated. Partial hydrogenation of sorbic acid gives hex-3-enoic acid as the main product acconipanied by appreciable quantities of hex-4-enoic acid.53 Linoleic acid is reported to give both octadec-9- and -12-enoic acids whilst linolenic acid yields first diethenoid and then inonoethenoid acids one diethenoid acid (isolinoleic) has been isolated. 5 4 Elaeostearic acid is readily hydrogenated yielding trans-octadec- 1 l-enoic acid as the main product. 36 5 5 Arachidonic acid is reported to give eicosa-5 14- and -8 14-dienoic acids (80-90% 5-10% respectively) when partially Iiydr~genated.~~ The hydrogenation of methyl prinarate (methyl octadcca-9 11 13 15- tetraenoate) has also been studied. 57 In contrast to these reactions which are of little value for preparative purposes though of considerable interest from ot'her viewpoints t'he partial hydrogehation of acetylenic acids is of great synthetic importance.58 The value of this reaction is enhanced by the fact that the resulting ethylenic acids are essentially cis or trans depending on whether the reduction is Methods resulting in a decrease in the degree of unsaturation. 4B Haskelburg J . Amer. Ghem. SOC. 1951 '73 4035. 5O Teeter J . Amer. Oil Chm. SOC. 1948 25 243 ; Sutton and Dutts J . 1949 939 ; Bergstrom and Hansson Actn C'imn. Scam€. 1050 4 435. 51 Ref. 4 pp. 4-12. 52 Ref. 4 p. 4. 53 Letch and Linsteacl J. 1934 1994. 5 4 Lemon C'n?zad. J . Res. 1944 22 E' 191 ; 1949 27 B 605 ; Lemon and Cross. 5 5 Hilditch and Pathak Proc. Roy. SOC. 1949 A 198 323 ; Woltemate and Daithert. 5 6 Mowry Brode and Brown J . Riol. Chem.1941 142 679. ibid. p. 610 ; Rebello and Daubert J . Amer. Oil Chem. Icoc. 1951 28 177 183. J . Amer. Chem. Soc. 1950 72 1233. Riley J . 1951 2579. 58 Ref. 4 pp. 41-46. GTJNSTONE PREPARATION OF STRAIGHT-CHAIN FATTY ACIDS 185 effected catalytically or by chemical The favoured catalyst is palladium though platinum and nickel have been used whilst chemical methods include the use of zinc and acetic acid metals and alkalis or reduc- tion of the halogen halide mono-addition product. Many acids have been prepared by these methods from acetylenic precursors and some examples will be given later. Dideutero-oleic acid results from catalytic deuteration of stearolic acid.60 (a) Elaidinisn- tion. Unsaturated fatty acids can exist in cis- and trans-forms and since many naturally occurring acids have the cis-structure it is possible to convert these into their more stable trans-isomers.This change has been most fully studied in the case of oleic acid which is converted into elaidic acid ; 61 the latter name has given rise to the term elaidinisation for the cis -+ trans change. The process is an equilibrium reaction and both oleic and elaidic acid yield the same isomeric mixture (containing m. 6776 of the truns-form). Mixtures of similar composition result from other mono- ethenoid acids. The reagents most frequently used include the nitrogen oxides sulphur selenium and iodine and/or ultra-violet light. Elaidinisa- tion is also known to occur under conditions of hydrogenation and during autoxidation 62 and thermal polymerisation.63 By using the reagents listed above various unsaturated acids have been converted into their truns-isomers.For non-conjugated polyethenoid acids it is considered that all the ethylenic linkages have been Converted into the trans-configuration. 64 Acids containing conjugated double bonds isomerise more readily generally under the influence of light and/or traces of iodine. trans-Octadec-2-enoic acid has been changed into its cis-isomer by a series of chemical rea~tions,~5 and the interconversion of cis- and trans- undec-9-enoic acid has been described.66 The double bond(s) present in an unsatur- ated fatty acid may migrate under certain conditions. Thus it is possible to convert the system (XV) present in many naturally occurring acids Methods involving no change in the degree of unsatumtion. (b) Double-bond migration.(XV) -CH:CH*CHZ*CH:CH- -j -CH:CH*CH:CH*CHZ- (XVI) into the conjugated system (XVI) which is readily identified by its char- acteristic ultra-violet absorption. This is the basis of a quantitative method of determining the presence of acids containing the system (XV).67 This migration which may be accompanied by elaidinisation is usually 5g Campbell and Campbell Chem. Reviews 1912 31 145 ; Crombie Quart. Revieuw 6o Khan Deatherage and Brown J Amer. Oil Chein. SOC. 1951 28 27. 61 Griffiths and Hilditch J. 1932 2315. G 2 Knight Eddy and Swern J . Amer. Oil C'hent. Soc. 1951 28 188. 63 Paschke Jackson and Wheeler I n d . Eng. Chem. 1952 44 1113. 64 Cf. Kass and Burr J . Amer. Chem. Xoc. 1939 61 1062. 6 5 Myers ibid. 1951 73 2100. 6 6 Ames and Bowman J. 1952 677. 67 Mitchell Kraybill and Zscheile Ind.Eng. Chem. Anal. 1943 15 I ; Hilditch 1952 6 128. Morton and Riley Analyst 1946 70 67. 186 QUARTERLY REVIEWS effected by alkali a t high temperatures (up to 200") though it also occurs under conditions of hydrogenation and autoxidation. Hex-2- and -3-enoic acid form an equilibrium mixture produced from either isomer by sodium ethoxide and containing ca. 90% of the 2-enoic acid. 68 Undec- 10-ynoic acid isomerises to undec-9-poic acid under strongly alkaline conditions so that the latter is often isolated in attempts to prepare tlie 10-isomer from 10 11 -clibroinomic~ecsnoic acid. Fusion of oltiic acid with potassium hydroxide yields palmitic acid inigration of the cloiil )le bond to the ccp-position preceding fission. Moore 69 has reported that prolonged hydrolysis of unsaturated fats leads to isomerisation of linoleic and linolenic acids to conjugated forms.Prom linseed oil (containing over 60% of linolenic acid) he isolated a solid acid which has been shown to be octadeca-trans-10 cis-12 trans-14-trienoic acid.44 70 Isomerisation of dehydrated castor oil acids yields a solid mixture from which an individual acid considered to be octadeca-trans-10 trans-12- ilienoic acid,71 can be isolated. I n an interesting paper Riemenschneider and his co-workers 4 4 9 see 45 isolated two acids from alkali-isomerised linoleic acid which they believe to be the trans-10 cis-12- and the cis-9 trans-1 l-isomer. When treated with iodine these acids elaidinise to the known wholly trans-isomers. The authors assume that the double bond which does not shift retains its configuration and suggest that when the migrating bond was trans the new bond is either cis or trans whilst if i t was cis the new bond is predominantly trans.Arachidonic acid isomerises to a mixture from which a solid acid with four conjugated double bonds has been isolated.72 Unsaturated acids have also been prepared from more readily accessible compounds by methods of chain extension and degradation. By the nitrile method undec- 10-enoic acid has been converted into dodec-ll-enoic acid,73 and linoleic acid by successive applications of the Anidt-Eistert procedure has yielded nonadeca- 10 13-dienoic and eicosa-11 14-dienoic acids.'* Barbier-Wieland degrad- ation of oleic acid affords heptadec-8-enoic and hexadec-7-enoic acids,75 but erucic acid is reported to give a glycol of the expected C, acid.76 The preparation of undec-10-enoic acid by pyrolysis of castor oil is now carried out on an industrial ~cale.~7 Electrolysis of compounds such as KO,C*[CH,],*CO,R gives in addition to the main product RO,C*[CH,],,*CO,R an unsaturated ester of the type Other methods of preparing unsaturated acids.68 Kon Linstead. and Maclennan J . 1932 2454. Moore Biochem. J. 1937 31 141. 'O Kass and Burr J. Amer. Chem. ~Soc. 1939 61 3292. 71 von Mikusch ibid. 1942 64 1580. 'i2 Mowry Brode and Brown J. Biol. Chela. 1941 142 671. 73 Tomecko and Adams J . Amer. Chem. SOC. 1927 49 522 ; Chuit Boelsing 7 4 Karrer and Koenig ibid. 1943 26 619. 7 5 Mitter and Bagchi J . Indian Chem. Soc. 1941 18 461. 7 6 Buu-Hoi and Janicaud BUZZ. Soc. chim. 1946 13 147. 77 Krafft Ber.1877 10 2034; Vernon and ROSS J . Arner. Chern. SOC. 1936 Hausser and Malet Helv. C'him. Acta 1927 10 113. 58 2430; Barbot Ann. China. 1939 11 619. GUNSTONE 1 PREPARATION OF STRAIQHT-CHAIN FATTY ACIDS 187 CH :CHfCH2],p2*C0,R. Several such acids have been prepared in this way.78 Unsaturated acids with the double bond in this position have also been prepared from the w-hydroxy-ester by pyrolysis of the palmitoyl ester.79 Condensation Reaction$.-Several condensation reactions have been utilised in the preparation of unsaturated fatty acids. In some the double bond is formed at the point of condensation; in others the double bond or some suitable precursor is present in one of the reacting components. It is in this section that most advance has been made in recent years.The use of malonic ester to extend chain length by two carbon atoms has already been discussed as a means of preparing saturated acids. It has also been applied with success to the preparation of several unsaturated acids. Another met'hod frequently used involves condensation of an aldehyde with malonic acid generally in the presence of pyridine to give an ap-un- saturated acid 8o which is believed to have the truns-structure.81 Sorbic Malonic acid and malonic ester condensations. acid 82 and other polyunsaturated acids intermediates in the synthesis of herculin and pellit~rine,*~-~~ have also been prepared by this means. When dimethylaniline or triethanolamine replaces pyridine the By -acid results .86 Condensations involving organo-metallic compounds. The higher un- saturated acids were first synthesised from simpler components by means of the Grignard reaction.In 1934 Noller a,nd Bannerot 87 described the first synthesis of oleic and elaidic acids the main reaction being condensation of 1 2-dibromo-9-chloro-l-methoxynonane (XVII) with octylmagnesium (1) Br ; ( 2 ) WeOH-HBr Cl*[CH,]7*CH,CH0 - Br-Mg.[CH,] ,CH ClfCH,] ,-CHBrCHBr*OMe - + (XVII) ( 1 ) Z n ; (2) NaCN ; ---+ (3) Hydrol. Cl*[CH 2] ,*CHBrCH( OMe)*[CH,] ,GH3 (XVIII) HO,C.[CH,],*CH:CHfCH,],*CH 78 Crum Brown and Walker Annalen 1893 274 41 ; Walker and Lumsden J. 1901 79 1197 ; Carmichael J. 1922 121 2545 ; Fairweather PTOC. Roy. Soc. Edin- burgh 1926 46 71. 79 Baudart' Bull. SOC. chim. 1946 13 85. 80 Bachman J . Amer. Clwnt. SOC. 1933 55 4279 ; Tulus Rev. Fac. Sci. Univ. 8l Refs. quoted by Crombie J.1952 2999. 8 2 Allen and van Allan Org. Synth. 1944 24 92. 8 3 Cromhie Chem. and I n d . 1952 1034. 8 4 Jacobsen J . Amer. Chem. SOC. 1950 72 1489. 85 Crombie J. 1952 2997. E G Boxer and Linstead J. 1931 740 ; Howton and Davies J. Org. Chem. 1951 87 Noller and Bannerot J . Amer. Chem. Soc. 1934 56 1563. Istanbul 1944 9 A 105. 16 1405. 188 QUARTERLY REVIEWS bromide yielding ti- br 01110- 1 - chlor o- 9 -methoxyheptadecane (XVIIT ) . Rte - moval of the 8 9-substituents by treatment with zinc gave a double bond in this position? and the chloride was converted into the acid via the nitrile. The final product was a mixture of elaidic and oleic acids. Even this is not a complete synthesis since the chlorononanal was obtained from butyl oleate. Noller and Girvin 88 later attempted a similar synthesis of linoleic acid by the annexed scheme.The product obtained in poor yield gave no tetrabromostearic acid on bromination though a little tetrahydroxystearic acid was isolated after oxidation indicating the presence of some linoleic acid. C'H,*[C'H,],.MgBr + CH,:CH*CHO -+ PBr CH ,-[ CH ,] ,CH( OH)*CH:CH + CH 3*[ CH ,],*CHBr *CH:CH + CH,fCH,],CH:CH.CH,Br * Mg- CI fCH J ,*CHBr*CHBr.OMe ( 1 ) Zn ; ( 2 ) NaCN ; (3) Hydrol. CH,*[CH,]4~CH:C€~~CH2~CH(OMe).CHRr.[CH~]7*Cl * CH sf CH 2] ,.CH:CH*CH ,CH:CH.[CH ,] ,CO 2H Baudart has also prepared (i) oleic and elaidic acids 89 and (ii) linelaidic acid 90 by a slight modification of this process. The starting material (XIX) for the linelaidic acid preparation was obtained from glutaraldehyde and the final product yielded a little tetrabromostearic acid identical with that obtained from linelaidic acid.(1) CH,-[CH,],-MgBr ; (2) BrPuIgfCH21,.OMe + Br*CH( OEt)*CHBr*CH,*CHBr*CHBr*OEt (XIX) ( 1 ) Zn; ( 2 ) Br ; (3) HBr ; (4) Zn CH,*[CH,],*CH( OEt).CHBr.C!H,.CHBr*CH( OICt)fCH,],.OMe -f (1) Nal ; (2) CH,(CO,Et), etc. CH,fCH,~,.C1H:CH~C'H2CE2CHfCH2]6*13r - * CH,*[CH,],.CH:CH*CH2*CH:CH*[CH2],*C0,H Elaidic and vaccenic (trans-octadec-11 -enoic acid) acids have recently been prepared by another modification 91 (shown below) in which the double bond is already present in one of the starting materials. The products were contaminated with their cis-isomers and with a vinylpalmitic acid resulting from reaction of the Grignard complex with (XX). An improvement of this method has recently been published.g2 Delaby et aLg3 have used the Grignard reagent to prepare several un- saturated acids.Interaction of an alkylmagnesium halide with acraldehyde gave a vinyl secondary alcohol (XXI) which on bromination affords the 88 Noller and Girvin J . Amer. Chern. SOC. 1937 59 606. s9 Baudart Cornpt. rend. 1943 217 399. 9O Idem Bull. Soc. chim. 1944 11 336. 91 Gensler Behrmann and Thomas J . Amer. Ghem. SOC. 1951 73 1071. 92 Gensler and Thomas ibid. 1952 74 3942. B3 Delaby and Guillot-Allegre Bull. SOC. chim. 1933 53 301 ; Delaby and Lecomte ibid. 1937 4 738 749 1007 1016. GUNSTONE PREPARATEON OF STRAIGHT-CHAIN FATTY ACIDS 189 C,H,(CO),NBr CH2:CHCH2.[CH2],,*C02Me + CH,:CH-CHBr*[CH,],,CO ,Me + ( r ~ = 7 or 9) (XX) CH,.[CH Jm.MgBr (m = 6 or 4) Br*CH2*CH:CH*[CH2]noC02Me - CH,fCH2],~CH2*CH:CH~[CH2],-C02Me This yields an unsaturated acid via the alcohol (A2) Acids of the C6-cJ9 series have been so prepared.compound (XXII). or the nitrile (A3). CHZ0[CH2]n*MgX -1- CH2:CH.CHO + CH3.[CH2],.CH(OH)*CH:CH2 pBr3/ (xxl) CH,fCH,],.CH:CH*CH,Er + CH3.[CH2],,CHBrCH:CH2 (XXII) NaOAc Hydrol. ; oxidn. L_ Hydrol. -1 CH,*[CIH2],*CH:CH*CH2*OL4c _____f C‘H,.[CH2],*CH:CH*C02H i) CH,*[CH2lfi*CH:CH.CH2.CN - CH,.[CH,]fi*CH:CH*CH,.C02H The organo-cadmium compounds have been little used for preparation of unsaturated acids though the preparation of octadec-17-enoic acid by this means has been reported.94 The important reaction is between diundeu- 1 O-enylcadmium and 6- carbethoxyhexanoyl chlori dc Cd([CH2],.CH:CH2)2 -1- 2Cl*CO.[CW215*CO,Et + 2CH2:CH~[C~H2],-COfCH2],*C02Et The preparation of unsaturated acids via acetylenic precursors provides a versatile method which has been widely and successfully exploited in recent years.There is however one Condensation of ucetylenic compounds. well-known reaction of acetylenic compounds which has been used for a longer period. It provides a convenient route to the a@-acetylenic acids and hence to the ccp-ethylenic acids. Acids of this type are readily obtained by reaction of the sodio-derivativc or Grignard complex of an ethynyl compound with carbon dioxide ethyl carbonate or ethyl chloroformate. Most of the acids of this type in the range C,-C1 have h e n so prepared 95 and also some polyunsaturated Eccids.85 96 CH,*[CH,],,*C$H -+ CH3fCH2]lh*C~CM + CH,fCH,],,.C:C.CO,R I n 1928 behenolic acid was obtained by condensing a sodium acetylide CH,*[CH,] ,*CiCNa + Br*[CH,],,*CO,Me -+ CH,*[CH2] ,*C:C-[CH,] ,CO ,H with an cu-br~mo-ester.~~ Ten years later tetradec-5-ynoic acid was prepared by the condensation of dec-l-yne with 3-chloropropyl toluene-p- CH3fCH2],*C?’H -t C,H,Me*S02~[CH2],CI -+ CH,fCH2],C~C.[CH,],.C1 + CH3.[CH2],*C~C.rCH2]3*~~2H (81 == Na or hlgX) (R = H or Et) 9 4 Huber J .Amer. Chem. ~Soc. 1951 73 2730. g5 Moureu and Delange Bull. SOC. chim. 1903 29 648 ; Zoss and Hennion J . ,4mer. Chem. SOC. 1941 63 1151. 96 Raphael and Sondheimer J . 1950 115 120. 97 Bhattacharya Saletore and Simonsen J. 1928 2678. 190 QUARTERLY REVIEWS sulphinite in the presence of sodamide the condensation product being subse- quently converted into the acid via the nitrileeg8 Another ten years elapsed before the general usefulness of this reaction was demonstrated by Strong and his co-workers,gg who showed that ethynyl compounds (XXIII) interact as their sodium derivatives or Grignard complexes with ccw-dihalogeno-compounds (XXIV).The resulting acetyl- enic compound (XXV) is readily converted into an acid partial catalytic hydrogenation of which affords the cis-ethylenic acid (X-XVI). This is of CH3*[CH2Jm*C:CH + I*[CH,],*Cl + (XXIII) (XXIV) CH,fCH2]mC:C.[CH2Jn*Cl -+ CH,*[CH,],.CH:CH*[CH,],*CO,H particular importance since it permits the synthesis of the naturally occur- ring cis-acids. These methods have been used by others 9 4 2 loo for a wide range of unsaturated fatty acids. Similar reactions have been applied to the synthesis of the diethenoid linoleic acid,lol which was achieved independently by three sets of workers.The methods used are similar though not identical and only the first description due to Raphael and Sondheimer is shown in the accompanying CH,*SO,CI CH,*[CH ,],-C~C.CH,*OH ---+ CH a[ C H ,] ,*CiC*CH a 0 *SO ,*CH EtMgBr (XXV) (XXVI) I- ( 1 ) NaI ; ( 2 ) CHiCNa C1.[CH2J6*Cl - > HC:C*[CH,],*CI (1) NaI ; ( 2 ) CH,(CO,Et), etc. (3) H,-Pd CH,*[CH J4*C:C*CH2*C:C.[CH,],Cl + CH,*[CH ,],*CH:CH*CH,*CH:CHfCH 2] ,CO ,H reaction sequence. The product gave tetrabromostearic acid (63 yo) indicating the presence of natural linoleic acid. Attempts to synthesise the insecticides herculin and pellitorine have led to the preparation of dodeca-2 8-dienoic and deca-2 6-dienoic acids as intermediates. Various stereoisomers have been obtained by methods based mainly on the use of acetylenic compounds 8 5 96 lo2 and this work which provides a good example of the flexibility of these methods has led to a revised formula for pellitorine 83 and to doubt concerning the structure of herculin.Siirensen and his collaborators lo3 have prepared some highly unsaturated 9s Johnson Schwartz and Jacobs J . A m e r . Chem. SOC. 1938 60 1882. g9 Ahmad and Strong ibid. 1948 70 1699 ; Ahmad Bumpus and Strong ibid. p. 3391 ; Taylor and Strong ibid. 1950 72 4263. loo Lumb and Davies J. 1952 5032 ; Fusari Greenlee and Brown J . Amer. Oil Chern. SOC. 1951,28,416 ; Newmanand Wotiz J . A m e r . Chem. Soc. 1949 71 1292. lol Raphael and Sondheimer J. 1950 2100 ; Gensler and Thomas J . Amer. Chem. SOC. 1951 '73 4601 ; Walborsky Davies and Howton ibid. p. 2590. lo2 I d e m J. 1951 2693 ; Crombie J.1952 4338. loS Bruun Haug and Sorensen A c t u Chem. Scund. 1950 4 850 ; Bruun Christen- sen Haug Stene and Sorensen ibid. 1951 5 1244 ; Christensen and Sorensen ibid. 1952 6 602; Baalsrud Holme Nestvold Pliva Xorensen and Sorensen ibid. p. 883 ; Christensen and Stirensan ibid. p. 893. GUNSTONE PREPARATION OF STRAIGHT-CHAIN FATTY ACIDS 191 derivatives of methyl decanoate by oxidative coupling in attempts to con- firm the structures of compounds isolated from the essential oils of several species of Comnpositae (see p. 194). The method is illustrated by the pre- paration of methyl deca-trans-2-ene-4 6 8-triynoate (XXVII). Other related compounds have been similarly prepared and the method has been used by Black and Weedon 104 for octadec-17-ene-9 11-diynoic acid CH,*C?XjCH + HCjC*CH:CH*CO,Me -+ CH,*C:C*C:C*C:C*CH:CH*CO,Me CH,:CH*[CH,],*C~C*C~C*[CH,I ,CO ,H (XXVIII).(XXVII) ( xxvm ) Condensations yielding acyhi?zs or alkozy-ketones. Another method of preparing unsaturated acids involves the use of acyloiiis or alkoxy-ketones as intermediates. The former may be prepared by Ruzicka's acyloin synthesis lo5 or alternatively bot,h may be prepared by Bowman's ketone synthesis.lo6 In either case the intermediate is readily converted into an unsaturated compound via the dibromide thus -CH( OH)*CO- t -CH( 0Me)CO- An advantage of the acyloin method is that the orp-glycol may be separated into threo- and erythro-forms which subsequently afford the trans- and the &-unsaturated acid respectively. In general excellent results are obtained but in some cases the alkoxy-ketone procedure is preferable.Ames and Bowman107 have compared the two methods. Baudart,I0* using Ruzicka's acyloin synthesis prepared the cis- and the trans-forms of octadec-9-enoic and hexadec-9-enoic acid thus Na CH,*[CH2],*COzEt + EtO,C*[CH,],.OEt 4 (n = 5 or 7) Ni-H CH,.[CH,],*CO*CH(OH)fCH,]7.0Et --+ (1) HBr-AcOH ; CH,f"H,]nCH(OH).CH(OH)-[CH2]7*OEt * (Two isomers (2) Zn separated) (1) KCN ; (2) hydrol. CH,*[CH21n*CH:CH*[CH,I,.Br ~ -+ 104 Black and Weedon Chem. and Ind. 1953 40. 105 Ruzicka Plattner and Widmer Helv. Chim. Acta 1942 25 604. lo6 Bowman J. 1950 325. 1O7 Ames and Bowman J. 1951 1079. 108 Baudart Bull. Xoc. chim. 1946 13 87, 193 QUARTERLY REVIBWS In the preparation of heiidec-6-enoic acid (XXIX) tlre ethoxy-ester was replaced by an cu-unsaturated ester subsequent oxidation of which gave the desired acid.CH,fCH2],*C02Et + EtO,C*[CH,],*CH:CH -+ Al( OPri) CH,*[CH,]4*CO*CH(OH)fCH,I,.CK:CH:CH2 + ( 1 ) Ac,O ; ( 2 ) 0 ; CH,*[CH ,] 4*CH( OH).CH( OH)*[CH ,] ,*CH:CH + (3) oxidn. ( 1 ) Hy-drol. ; CH,fCN2],*CH:CH*[C~H2],*CO ,H (XXIX) have prepared several unsaturated acids in addihion to certain branched-chain compounds. In each case pure cis- and truwisomcrs werc obtained. The details of this procedure have already been discussed and two examples only are given in the annexed schemes. CH,fCH,],~CH(OAc)~CH(OAc)fCH2],C0,H -+ (2) HBr ; (3) NaI -%ii Bowman and his collaborators lo7 9 A cglo in. CO ,R I I C0,R CH,*[CH,],*CH(OH)*COCl + NaC.[CH,J,*CO,R -+ (R = PhCH,) CO ,R I (2) decarboxyln. ; I (3) cat. redn. CO .R (1 ) Hydrogeiiolysis ; CH,~[CHZ],~CH(OH)*C'O.C.[CH,I,.CO2R + (1) HBr-BcOH-H,80i ; CH,*[CH,]3CH(OH)CH(OH).[CH2]7*C02H + (Two isomers separated) ( 2 ) %I1 CH,*[CH,]3*CH:CH*[CH2]7*C0,H dlkoxy -ketone.C0,E I I CO ,R CH,*[CH,],CH(OMe)COCI + Na*C.[CH,],,*CO,R -j (R = Ph.CH,) CO,R (1) Hydrogenolysis ; I ( 2 ) decarboxyln. ; 1 (3) Al(OPri) CH,fCH,] ,CH( OMe).C'O*CfCH,] ,,*CO ,R + CO,R (1) HBr-AcOH-H,SO ; CH ,*[CH ,] ,CH( OMe)-CH( OH ) -[ CH ,] ,GO ,H + (2) Zn CH,-[CH,],~CH:CHfCH,]ll*C02H The Robinson procedure (p. 177) or one of its modifica- Other methods. tions has been used for preparation of a few unsaturated acids.17 111 l o 9 Bowman J. 1950 177 ; Boughton Bowman and Ames J. 1952 671. llOAmes and Bowman J. 1951 1087. 111 Kapp and Knoll J . Amer. Chern. Soc. 1943 65 2062 ; Stenhagen Arkiv Kenti 1949 1 99.GUNSTONE PREPARATION OF STRAIGHT-CHAIN FATTY ACIDS 193 3. Recent Contributions to our Knowledge of Naturally Occurring Fatty Acids The remainder of this Review will be concerned with (i) methods of isolation of pure acids from natural sources and (ii) a brief account of acids which have only recently been reported or the structure of which has been adequately described only in recent years. The Isolation of Fatty Acids from Natural Sources.-Partly because of the plentiful occurrence of several fatty acids and partly because of the difficulties only now being overcome of synthesising many of these com- pounds much effort has been expended in attempts to isolate pure acids from natural sources. The difficulty of isolating pure acids from mixtures of closely related acids is well known to workers in this field.The improve- ment of older methods and the development of new techniques however make it increasingly possible to achieve this separation. The procedures most used in the past were distillation (generally of the methyl esters) and crystallisation of the acids or their metallic salts whilst the polyunsaturated acids have generally been isolated as polybromides the acids being subse- quently recovered by debroniination. It is well to remember that whilst distillation may separate acids of different chain length it does not give much enrichment of acids having the same number of carbon atoms but of varying unsaturation ; that normal methods of crystallisation can only be applied to solid acids ; that crystallisation of salts (e.g. lead salts from alcohol or lithium salts from acetone) is of more value for preparation of concentrates than for isola'tion of pure compounds ; and that whilst it is possible to prepare a pure polybromide doubt has been expressed concerning the homogeneity of the debrominated acid.112 The main recent advance in this field has been the isolation of unsaturated acids by physical means only. Thc more recent technique of forming urea complexes ha's already been used to prepare concentrates of single acids,113-l15 but it is too early to say how extensively this method will be used in the future. Brown and his colleagues have been mainly rcsponsiblc for demonstrating the value of low-temperature crystallisation for the isolation of fatty acids. By this technique it is possible to crystallise compounds that are liquid a t room teniperature.The isolation from suitable natural sources of oleic (purity > 99.6y0) linoleic (93.5%) linolenic (88%) arachidonic (95%) and ricinoleic acid (95.6%) has been described.l16 Improvements in the separation of linoleic (97-100:/,) 117 and riciiioleic acid (99%) 118 have since been reportcd. The method is clearly of value for preparation of 112 Matthews Brode and Brown J . Amer. Chew%. Soc. 1941 63 1064 ; Frankel 113 Ligthelm Schwartz and von Holdt J. 1952 1088. 114 Nunn J. 1952 313. 115 Swern and Parker J. Amer. Oil Chem. Soc. 1952 29 431. 116 Cf. Brown Chem. Reviews 1941 29 333. 117 Frankel Stoneburner and Brown J . Amer. Chem. SOC. 1943 65 259. 118 Hawke J.S. African Chem. Inst. 1949 2 1. and Brown ibid. 1943 65 415. 194 QUARTERLY REVIEWS mono- and di-ethenoid acids in high purity but of less value for more un- saturated acids.It is not surprising that the methods of chromatography so widely used in other branches of chemistry have also been applied with success to the problem now under consideration. Riemenschneider et al. separated the methyl esters on a column of silicic acid in an atmosphere of nitrogen or carbon dioxide. The preparation of methyl linoleate (100 yo pure) and methyl linolenate (1OOyo) has been described.llg By a combination of this method with distillation and low-temperature crystallisation methyl arachi- donate of high purity lZo and concentrates of methyl eicosapentaenoate and docosapentaenoate have been isolated from lipids of fresh beef suprarenal glands.121 This technique coupled with those previously used makes it possible to prepare unsaturated acids in a high state of purity even when they were originally present in very small amounts.The methods are such that degradative or other undesirable changes are reduced to the minimum. Fatty Acids of Recent Description.-The acids now to be described are either major component acids of fats not previously investigated acids present in small quantities but not previously reported in fats already examined or aliphatic acids of non-fatty origin. Sorensen and his co-workers lo3? 122 have isolated a number of highly unsaturated derivatives of methyl decanoate from the essential oils of several species of Cornpositz. Structures are based largely on spectroscopic evidence and on the isolation of methyl decanoate after quantitat'ive hydrogenation.Matricaria and related acids. The following have been described Matricaria ester . . . . . . . Composit-cumuleen I . . . . . . Dehydromatricaria est,er . . . . . or Dihydromatricaria est.er . . . . . Lachnophyllum est,er . . . . . . CH,CH CH*C. C*C i C.CH:CHCO,&le (cis-2 cis-8 and cis-2 trans-8) CH,-[CH,],.CH C C CHC0,Me CH,*CiC.CiC-CIC-CH:CH.CO,Me CH,.CH:CH*CfC*CiC*CiC.CO,Me CH,.CH CH-C. C*Ci C-[ CH21,.C0,JIe CH,*[ CH,],*C:'C-C i C-CH CH*CO,Me (not the trans-2 isomer) (cis-8) (probably cis-2) Deca-2 4-dienoic acid. The composition of Stillingia oil indicated by early analyses * did not conform with the superior drying properties of this oil which are now believed to be due to the presence (ca. 50/,) of deca- 2 4-dienoic acid.lZ3 This is the first polyethenoic acid containing less than 119 Riemenschneider Herb and Nichols J .Amer. Oil Chenz. Soc. 1948 26 371 ; see also Hilditch Patel and. Riley Analyst 1951 76 81. 120 Herb Riemenschneider and Donaldson J . Amer. Oil C'hem. SOC. 1051 28 55. 1 2 1 Herb Witnauer and Riemenschneider ibid. p. 505 ; cf. White and Brown 1 2 2 Sorensen and Stene Annalen 1941 549 80 ; Holman and Sorensen Actcc 1 2 3 Crossley and Hilditch J. 1949 3353 ; Devine J. h'ci. Food Agric. 1950 1 *Where references are not given to early work details are to be found in Hil- J . Amer. Chem. Xoc. 1948 70 4269. Chem. Scand. 1950 4 416; Sorensen and Stavholt ibid. pp. 1080 1567 1575. 58 ; ditch (ref. l) or in the references quoted for the more recent work. Crossley and Hildit'eh ibid. p. 292. GUNSTONE PREPARATION O F ST'RAIGHT-CHAIN FATTY ACIDS 195 sixteen carbon atoms wliich has been isolated from a fat.A tentative report 124 of the occurrence of dodeca-2 4-dienoic acid needs to be confirmed. The relation between deca-2 4-dienoic acid and pellitorine has been noted.83 The antibiotic niycomycin is a highly unsaturated deriva- tive (XXX) of tridecanoic acid. The compound is optically active by reason of the allene group and is readily isonierised to isomycomycin (XXX) CH~C*C~C.CH:C:CH*CH:CH42H:CH*CEC2*C02H (XXXI) CH,.C~C.C~C.C~C*CH:CH.CH:CB.CH,.CO,I-I Mycomycin. (XXXI) .I35 Hem-7 10 13-trienoic acid. This acid occurs among rape-leaf glycer- ides. 26 A concentrate was prepared by distillation and low-temperature crystallisation. Its constitution was derived from a study of the hydrogena- tion and oxidation products.Alkali isomerisation produced triene conjuga- tion analogous to that observed with linolenic acid. Octadec-1 l-enoic acid. Recent work suggests that the individuality of vaccenic acid (trans-octadec- 11 -enoic acid) from land-animal fats is again in question. trans-Octadec-1 l-enoic acid has been synthesised and com- pared with natural vaccenic acid. Although the infra-red spectra were essentially identical their X-ray diffraction patterns differed significantly 12' Hilditch and his collaborators have concluded from a study of oxidation products that the truns-octadecenoic acid present in animal fats is a mixture of the Ale- and All-isomer.128 More recently beef fat has been shown to contain both elaidic and vaccenic acid which are considered to result from oxidative changes.129 cis-Octadec-ll-enoic acid not previously reported from natural sources has now been isolated from the lipids of horse brain 13* and of LactobaciEZus ara binosus.13 1 The question of whether all samples of octadeca- dienoic acid of natural origin are identical with the widely occurring linoleic acid is still a matter for discussion but no other isomer has been isolated directly from a natural fat.Spectroscopic corroboration of the reported occurrence of free octadeca-9 ll-dienoic acid 132 is desirable. Xymenynic acid which has been obtained from three species of the Ximenia genus,l13 contains one ethylenic and one acetylenic linkage and has the structure (XXXII) or (XXXIII). The former is preferred on the basis of ozonolysis experiments. -and it is suggested that the natural acid may contain isomers.Octadecadienoic acid. Acetylenic acids with eighteen carbon atoms. 12* Hanks and 'Potts J . Amer. Oil Chem. SOC. 1951 28 292. 125 Celmer and Solomons J . Amer. Chern. Soc. 1952 74 1870 2245 3838 ; 1953 126 Heyes and Shorland Biochem. J. 1951 49 503 ; Nature 1945 156 269. 1-27 Bwnpus Taylor and Strong J . Amer. Chern. Soc. 1950 72 2116. l2* Gupta Hilditch Paul and Shrivastava J. 1950 3484. Swern Knight and Eddy J . Amer. Oil Chem. SOC. 1952 29 44. I3O Morton and Todd Biochem. J . 1950 47 327. 131 Hofmann Lucas and Sax J . Biol. Chem. 1952 195 473. 132 Kartha and Menon Proc. India?& Acad. Sci. 1943 17 A 11. 75 1372. 196 QUARTERLY REVIEWS A recent report lo4 indica’tes that erythrogenic (isanic) acid obtained CH3fCH2],*CH:CH*C~CfCH2]7*C0,H CH3*[CH2],*C~C*CH:CHfCH,I,.CO2H (XXXII) (XXXIII) from the seed oil of Onguekoa Gore (Engler) is probably identical with synthetic octadec-17-ene-9 11-diynoic acid (XXI’IlI).An isomer of ricinoleic acid 9-hydroxyoctadec-12-eiioic acid has been shown t o occur in the seed oils of three Xfrophunthus species. 33 Hyclrosy-acids are also reported in Origuekoa Gore (Engler) seed oil 134 in Mallotus philippinensis seed 0il,13~ in Rhus trichocarpa wax,13G and in the niother-liquors from the crystallisation of ~ a n t 0 n i n . l ~ ~ The unsaturated acids in human- hair fat appear to have their ethylenic linkages in unusual positions. Hexadec-6-enoic acid has been isolated and the presence of tetradec-5-enoic penta- hepta- and octa-dec-6-enoic hepta- and octa-dec-8-enoic oleic and possibly octadeca-6 9-dienoic acid were indicated by oxidative tech- niques.138 Two acids have recently been described which contain these cyclic systems.Sterculic acid obtained from the seed oil of Sterculia foetida and some other AS. specaies is a C, acid with the remarkable structure (XXXIV). 114 On hydrogenation Hydroxfy-acids confuini?iy eiiylitwii em-boii ctfoms. The free fatty acids of hurnan-hair fat. Acids containing a cyclopropane or cyclopropene ring. /CH2\ /HZ (XXXIV) CH,*[CH,],*C- CfCH,] ,*CO 2H (XXXV) CH3.[CH 2]ta.CH--- CH*[CH2]14 - .CO ,H one mol. of hydrogen is absorbed to give a saturated compound which reacts with a second mol..of hydrogen to give a mixture of acids probably consisting of nonadecanoic acid and 9- and 10-methyloctadecanoic acids. Oxidation gives azelaic and nonanoic acids as main products.The fatty acids of Lactobacillus arabinosus contain inter alia lacto- bacillic acid 131 which has the structure (XXXV). Nonadecanoic acid has been isolated after hydrogenation ; methyloctadecanoic acids are probably also present. The suggestion 139 that n = 5 is not proved. Eicos-ll-enoic and docosa-13 16-dienoic acids. Eicos-ll-enoic acid previously reported only in a seed wax and possibly in some fish oils is 133 Gunstone J. 1962 1274; J . Sci. Food -4gric, 1962 3 185; 1953 4 129. 134 Riley J. 1951 1346 ; Kaufmann Baltes and Herminghaus Fette u. Seifen 1951 53 537. 135 Gupta Sharma arid Aggarwal J . Sci. I n d . Res. (India) 1952 11 463 ; Calder- woode and Gunstone Chem. and Id. 1953 436 ; cf. Puntambekar Proc. I n d i a n Acad.Sci. 1952 35 A 57. 136 Tsukamoto J . Pharrn. SOC. Japan 1942 62 375. 137 Kariyone Fukui Kiguchi Ishimasi and Miki ibid. 1948 68 269 271 272. 138 Weitkamp Smiljanic and Rothman J . Amer. Chem. *Sot. 1947 69 1936. 139 Kosower Science 1951 113 604. GUNSTONE PREPARATION OF STRAIGFIT-CHAIN FATTY ACIDS 197 now known to be present in certain Cruciferue seed fats 141 and in cod liver oil? A docosadienoie acid (almost certainly A l3 Is) was also isolated from rape Small quantities of eicos-1 l-enoic and eicosa- dienoic acids are reported in certain land-animal fats. 143 Eico~-12-enoic,l~~ eicosa-11 14-dienoic and eicosa-8 11 14-trienoic acids 145 have been reported. Matsnda 146 has studied the highly unsaturated acids of bonito oil. The structures of several acids are discussed but the results must be accepted with reserve in view of the known difficulties of working with these compounds.Bergman and Swift 14' in an examination of sponge lipids have described the hitherto unknown hexacosa-17 24-dienoic acid along with an octacosenoic acid and octacosatrienoic acid the detailed structures of which are not reported. Acids of marine origin. The Reviewer acknowledges with thanks the advice given to him by Professors J. W. Cook F.R.S. and T. P. Hilditch PXS. and by several members of this Department during the prepnration of this manuscript. 140 Hopkins Canad. J . Res. 1946 24 B 211 ; Yoimgs Mallard Craig and Sallow ibid. 1951 29 B 871. 141 Baliga and Hilditch J. 1949 S 91. 142 Hopkins Chisholm and Harris Canad. J . Res. 1949 27 By 35. 143 de la Mare and Shorland Analyst 1944 69 337 ; ATuturey 1945 155 48 ; 144 Hata and Kunisaki J .Chem. SOC. Japan 1942 63 1585. 145 Baudart Bull. SOC. chim. 1944 11 174. 146 Matsuda J . SOC. Chern. I n d . Japan 1942 45 3 4 6 8 40 134 158. 14' Bergmann and Swift J . Org. C'henz. 1951 16 1206. Biochem. J. 1945 39 246.

ISSN:0009-2681    

DOI:10.1039/QR9530700175

出版商:RSC    

年代:1953

数据来源: RSC

摘要:

TKE REACTIONS OF METHYL RADICALS By A. F. TROTMAN-DICKENSON M.A. R.Sc. PH.D. (I.C.I. RESEARCH FELLOW UNIVERSITY OF MANCIIESTER) A LARGE proportion of contemporary research on reaction kinetics is devoted to the study of atomic and free-radical reactions both in the gas phase and in solution. First atomic and free- radical reactions are formally very simple ; they are less influenced by their environment than are ionic reactions ; they exemplify clearly the factors governing reactivity ; they are often very symmetrical and are suitable for theoretical study; they may provide the avenue by which we shall arrive at a fuller understanding of the factors influencing the rates of reactions. Secondly they are of extreme practical importance in the petroleum chemicals industry and in the production of high polymers.Thirdly they are involved in many combustion and oxidation processes. Fourthly they are relatively difficult to investigate and their study involves the use of many of the most advanced chemical techniques so they provide a challenge to the worker in reaction kinetics. Here we shall be concerned with the reactions of methyl radicals in the gas phase which have been more fully investigated and are better under- stood than those of any other free radicals. As a result of intensive research in five or six laboratories during the last seven years we now have some quantitative knowledge of most types of methyl-radical reaction. Conse- quently it is possible to write a fairly comprehensive review of these reactions in the expectation that new work will amplify what is written here and fill in the many gaps but that drastic revision will not be required.Here will be described the methods of research used in the study of methyl- radical reactions and the results so obtained in the hope that this particular account may be a general guide to free-radical research in the gas phase. To this end the parallel behaviour of other radicals which are much more difficult to investigate will be referred to when this seems to be illuminating. Early Work on Free Radicals.-The existence of short-lived alkyl free radicals was first demonstrated twenty years ago by Paneth and his co- workers. In the subsequent decade investigators were primarily con- cerned in detecting the presence of free radicals in reacting systems. Paneth showed that when organic vapours were passed through a furnace at a convenient temperature and over a metallic mirror the mirror was removed and metallic alkyls were formed ; by this means it was shown that aliphatic free radicals were intermediates in a large number of pyrolyses and photo- lyses.Hinshel- wood showed in 1936 that the addition of very small quantities of nitric oxide to the reacting system greatly inhibited the pyrolysis of many organic vapours. Nitric oxide is a molecule containing an odd number of electrons and it was expected that it would combine very rapidly with free radicals 19s There are many reasons for this. Two other methods were developed to accomplish this end. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 199 to give a compound with the usual even number of electrons. Since the free-radical chain-carriers in a pyrolysis are present in very small concen- trations (often of the order of 10-10 mole per I.) a very small quantity of nitric oxide should greatly inhibit the overall reactions.Hinshelwood also showed that propene in larger quantities had a similar effect. Hence reactions which are inhibited by nitric oxide and propene probably involve free radicals. Patat and Sachsse showed that the reacting mixtures in pyrolyses would accelerate the ortho-para-hydrogen conversion as would be expected if free radicals were involved. All of these techniques and their applications to particular systems are described fully in Steacie’s definitive m0nograph.l The theory needed to explain many of these observations was provided by Rice and Herzfeld who showed that the experimental data on pyrolysis reactions could be interpreted on the basis of free-radical .mechanisms in- volving several simple elementary processes about which reasonable assump- tions could be made.At that time no particular mechanism could be rigorously tested because not enough was known about the elementary reactions. Even today our knowledge of some of the postulated steps is inadequate for unequivocal judgments of the mechanisms favoured by Rice. However it has been shown that Rice’s anticipation was often remarkably accurate. gteacie gives very complete accounts of these mechanisms. Modern Developments.-During the last decade the interest of most investigators has shifted from the qualitative study of complex systems to tlhe quantitative study of the elementary processes occurring in pyrolyses photolyses and polymerisations.In order to avoid complicating side reactions these reactions are normally carried to very low percentage con- versions and in consequence the analytical problems are great. The re- searches have been made possible by advances in analytical technique and by the increasing availability of isotopic tracers. The important analytical techniques which were mostly developed for oil companies in the United States are low-temperature distillation Blacet and Leighton’s analysis and the analytical mass-spectrometer ; as yet the recording infra- red spectrometer has been comparatively little used in the study of free- radical reactions. As exaniples of the power of these methods it may be mentioned that by low-temperature distillation it is now possible to estimate 0.1 ml.(S.T.P.) of ethane in the presence of 15 ml. of propane to an accuracy of & 3% in 1 9 hours. The proportion of ethylene in an ethylene-ethane sample of 20 pl. may be determined in 40 minutes to an accuracy of & 0.05 pl. with Blacet and Leighton’s apparatus. Under favourable conditions the proportion of CD,H in CD may be determined in 15 minutes to better than 0.1% on a mass-spectrometer. These are powerful new tools for the investigation of gas-reactions. The Types of Methyl-radical Reaction.-There are three principal classes of methyl-radical reaction 1. Combination reactions CH + XY -+ CH,XY e . g . CH + CH -+ C,H,. Methyl radicals will combine with methyl radicals other free “ Atomic and Free Radical Reactions ” Reinhold New York 1917.Irzd. Eng. Chem. Anal. 1931 3 266. 0 200 QUARTERLY REVIEWS radicals atoms or '' odd electron " molecules to give normal saturated molecules. 2. Metathetical reactions CH + XY + CH,X + Y e.g. CK + C2H + CH + C2H5. Methyl radicals will extract atoms from molecules to produce saturated methyl derivatives and a new free radical or atom. This class of methyl- radical reaction has been intensively studied especially those reactions in which a hydrogen atom is extracted. At least two cases of the extraction of a radical from a molecule are known namely that of acetyl from diacetyl and that of methyl from dimethylmercury. 3. Addition reactions CH + XY -+ CH,XY e.g. CH + C2H -+ C,H,. Methyl radicals will add to molecules containing multiple bonds to give more complex free radicals.Only these three types of methyl-radical reaction have been established beyond reasonable doubt. All the more wmplex alkyl radicals can undergo the following two other sorts of reaction which make the study of their behaviour very difficult. 4. Decomposition reactions e.g. C2H5 + C2H + H. That decom- position reactions of this type occur has been established but very few have been studied quantitatively because there are few suitable radical sources. Mercury photosensitisation has so far proved to be the best source and the decomposition of the radicals derived from the abstraction of a hydrogen atom from ethane,3 propane,4 n-butane 2-methyl~ropane,~ methyl alcohol,6 and diinethyl ether 7 has been studied in this way. The reaction CH + CH + H is theoretically possible but probably has an activation energy of at least 80 kcal.and will not become appreciable until temperatures of 1000" K are reached. By contrast the decomposition of the n-butyl radical can be detected a t 500" K. + C,H + C,H,. Very little is known about reactions of this type but they certainly occur under some conditions for Ivin and Steacie 8 have accurately studied the disproportionation of ethyl radicals in the photolysis of diethylmercury . The only evidence for the reaction CH -+ CH CH + CH comeb from the work of Bawn and Tipping 9 which appears to be quite unrelated to normal work on homogeneous gas-phase reactions probably because the reaction was studied in an atmosphere of sodium vapour. From this list we can see that all known reactions of methyl radicals are bimolecular a t high pressures.Consequently the reactions may be 5. Disproportionation reactions e.g. C2H5 + C2H5 + CH + A -+ B (a) CH + X -+ Y + Z ( b ) Bywater and Steacie J . Chem. Physics 1951 19 172. I d e m ibid. p. 319. Phibbs and Darwent, ibid. 1950 18 495. Marcus Darwent and Steacie ibzd. 1948 16 987. Proc. Roy. Xoc. 1951 A 208 25. Discuss. Paraday SOC. 1947 2 104. 5 I d e m ibid. p. 326. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 201 represented by equation (a) or (6). constants E and k6 are defined by the equations In these two cases the respective rate & G d[B]/dt = - d[A]/dt = k,[CHJ [A] and R z d[Y]/dt = R G d[Z]/dt = - d[X]dt = Eb[CH3] [XI where the letters in brackets are the concentrations of the substances and R is the rate of formation of Y and so on this notation will be used throughout.Hence if the methyl-radical concentration is known the rate constant in the first case can be found by measuring the formation of B or the disappearance of A and in the second case by the disappearance of X or the formation of Y or Z. The rate constants all obey the Arrhenius equation E = A exp( - E/RT) within the limits of experimental error where E is the activation energy of the reaction and A which is usually called the pre-exponential or A factor is a number having the dimensions of a rate constant. The Arrhenius equation may be written in terms of the collision theory of chemical kinetics for a bimolecular reaction as E = PZ exp( - E/RT) where P is known as the steric factor and 2 the collision frequency of the reacting species is given by where G ~ ~ is t'he mean molecular (collision) diameter of X afid Y ; Tnx and UL!! are the masses of the respective molecules and k is Boltzmann's constant.The great value of the collision theory is that it provides a very simple picture of chemical kinetics as a large number of reactions is known in which P = 1. A weakness is that 2 is not a well-defined quantity because of the uncertainty as to the appropriate values for the collision diameters. To preserve the simplicity of the theory collision diameters which might he determined by viscosity and other methods depending on the transport properties of the gases should be selected. Almost all workers on methyl radicals have done this when calculating steric factors but despite the uniformity of practice it is probably less likely to cause confusion if the directly determinable A factors are given.Throughout this Review d factors will be quoted but for purposes of comparison and as an uide-rnhinoire the two following values of Z are given Z for the collision of two methyl radicals a t 455" K with collision dia- meters of 3-5 A = 2 x 10-10 molecules-1 C.C. sec.-l = 1 x 1014 mole-1 C.C. sec.-l. 2 for the collision of a methyl radical at 455" K with a molecule of mole- cular weight 50 and a collision diameter of 5.5 A = 6 x molecules-1 C.C. sec.-l = 4 x mole-1 C.C. sec.-l. There are two principal difficulties which must now be considered in the study of methyl radicals first a suitable source of them must be selected and secondly some way of determining the steady state concen- tration of methyl radicals usually about 10-l2 mole/c.c.must be found. Sources of Methyl Radicals.-Hitherto the methyl radicals required for 202 QUARTERLY REVIEWS kinetic studies have almost always been produced by either the pyrolysis or the photolysis of compounds containing methyl groups. For most pur- poses photolyses are more convenient because they are easily controlled and can be used over a wide range of temperature. Unfortunat'ely all convenient pyrolyses have activation energies at least three times that of the majority of methyl-radical reactions so the accessible temperalure range of study and hence the accuracy of the determination of activation energy is much reduced. The most widely used photolytic sources are acetone dimethylmercury acetaldehyde azomethane and methyl iodide of which acetone is far the best.Acetone is convenient because it is readily obtainable is relatively unreactive and thermally stable and has a convenient vapour pressure and a broad absorption band in the near ultra-violet and a measure of the carbon monoxide produced can be used as an internal actinometer. More- over through the work of W. A. Noyes junr. and his school l o its photolysis is very well understood. The best pyrolytic source of methyl is di-tert.-butyl peroxide which decomposes in two stages (Me,C*O) -+ ZMe,C*O -+ ZCH + 2Me,CO its big disadvantage is that the decomposition has an activation energy of about 37 kcal.,l19 l2 and so it can only be used in the temperature range 130-170" c. Acetyl peroxide l3 in solution and azomethane l4 in the vapour have also been used as pyrolytic radical sources.Met hods of Investigation .-T h e difficulty of de t errn ining met h y 1 - r adi ca 1 concentrations cannot be dealt with apart from the general problems of this type of study which we will consider now. Noyes and his school lo have shown that when acetone is photolysed above 100" c all the methane and ethane can be quantitatively accounted for by the reactions (2) and (3) :* CH3 -+- CH + C2H6 (2) CH t CH,*COCH + CH + CH2.C0.CH (3) RCpH = k2[CH312 and RCH4 = L3[CH3] [CH,*CO*CH,] Now Hence and R ~ ~ 4 / R ~ ~ H = k3[CH3*CO*CH3]/k,f Therefore by determining this ratio over a range of temperatures E - +Ez and A3/A2' can be found. Furthermore in principle when a photolytic system involves reactions lo W. A. Noyes junr. and Dorfman J . Chem. Physics 1948 16 788. l1 Raley Rust and Vaughan J.Amer. Chem. Soc. 1950 70 88. l2 Murawski Roberts and Szwarc J. Chem. Physics 1951 19 698. l3 Edwards and Mayo J. Amer. Chem. Soc. 1950 72 1265. l4 A. 0. Allen and Sickman ibid. 1934 56 2031. * For reaction ( l ) see p. 203. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 203 of the type M + hv = nA A + B = X and 2A = Y so that the rate of formation of one product is dependent upon the first power of the concen- tration of A and the rate of formation of the second is dependent upon the second power of this concentration it is possible to use the method of intermittent illumination to find the two rate constants involved. In two recent articles l5 reference has been made to the application of the method of intermittent illumination to the determination of absolute rate con- stants in polymerisation and liquid-phase oxidation reactions.A full description of the mathematical theory of the method has been given by Burnett and Melville.16 A " pilot " reaction of the type A + B = X is used to measure the average concentration of the transient radical A during the run for if B is in excess the average concentration of A is directly pro- portional to the rate of production of X. However while sufficient quan- tities of X must be obtained for accurate analysis it is essential that the con- centration of A in the system should not be appreciably disturbed owing t'o formation of X. In the polymerisations and oxidations this difficulty does not arise because the over-all chain process may be used as the " pilot " reaction in which a new radical is formed each time the radical A reacts with B ; but for the study of methyl-radical reactions high light intensities and low temperatures must be used so the amount of methyl reacting with B is a negligible (ca.0.5%) part of the total amount of methyl released in the system. All the accura,te absolute rate constants of methyl-radical reactions are based upon rotating sector determinations of the rate of met h yl-radical combination. When a mixture of acetone and another hydrogen-containing compound CH +RH -+ CH + R ( 1 ) is photolysed the reaction (1) will take place as well as reactions (2) and (3). Now RCH = k,[CH,I [CH,*CO*CH,I ki[CH,I [RHI and RCG,/@-,H = k3[CH3*CO*CHJ/kt + kl[RH]/@ But the term k,[CH,*CO*CH,]/k~ has already been determined so kl/k$ and consequently E - +E2 and Al/A$ can be found.All the results listed in Tables 3 and 4 for which the radical source was acetone or dimethyl- mercury were obtained in this way. An alternative procedure is to use fully-deuterated acetone for which k,*/k$~ may be obtained as before for reactions (3") and (2*) CD + CD -+ C,D (2*) CD + CD,*CO*CD -+ CD + CD,*CO*CD (3*) In the presence of a hydrogen-containing compound reaction (1") occurs CD + R H -+ CDaH + R (I") Hence El */k3* = Rcn3H [ CD,*CO*CH,]/R,D ,[ RH] The ratio RLD,H/RCD can be rapidly and accurately determined so kl*,E,* Bolland Quart. Reviews 1949 3 1 ; Burnett %bid. 1950 4 292. l6 Proc. Roy. Soc. 1947 A 189 456. 204 QUARTERLY REVIEWS can be found. Since the relation between k,* and k has been determined this is a method of finding k,.All the results listed in Tables 3 and 4 for which the radical source was hexadeuteroacetone were obtain6d in this way. An extension of this principle is involved in t,he method which has beeii used for the study of very fast methyl reactions. If the number of methyl radicals produced in a system is known and there are only two methods by which the radicals can disappear such as reactions (4) and (5) CH + I -+ CHJ + I (4) CH + H I -+ CH + I ( 5 ) RCH3 = Rate of methyl production - R,3,d = E,[CH3] [I,] then RCH~ = kJCH3I [HI] &H&] - Therefore k / k = Unfortunately k has not yet been determined absolutely so only relative constants are obtained by this method. The Combination Reactions of Methyl Radicals.-Because the methyl radical contains only four atoms one of them heavy and three light there is a possibility that the rate of methyl-radical combination with other small radicals and atoms will be markedly dependent on the pressure in the system in which the reaction is studied owing to third-body effects.This phenomenon is the exact converse of that observed in those unimolecular decomposition reactions the rate of which falls off a t low pressures and is similar to the third-body effect observed in the combination of hydrogen bromine and iodine atoms. Lindemann 0. K. Rice Ramsperger and Kassel l8 have developed the basic quantitative treatment of these “ quasi- unimolecular ” reactions. It is usually convenient when dealing with combination reactions to make use of the relation kf/kr = K where the rate and equilibrium constants refer to the reactions [Rate of methyl production - RCH4J [HI] kf A + B + M C + M The problem of the combination of A + B in the presence of a third body can then be “ inverted ” so as to be the problem of the decomposition of C in the presence of a neutral gas.Thus stated the problem is more tractable for a number of reasons including the fact that the definition of a two-body collision is clear-cut whereas t’hat of a three-body collision is not. Marcus and Rice l9 recently considered the effect of pressure in the combination of methyl radicals with other methyl radicals and with iodine atoms. They concluded that energy-transfer effects should become important in the region of a few millimetres’ pressure for the combination of methyl radicals l7 J . Cherra. Physics 1951 19 85. 18 See L. 8 . Kassel “ Kinetics of Homogeneous Gas Reactions ” Chemical Catalog lo J .Phys. Colloid Chem. 1961 55 894 ; see also Marcus J . Chern. Physics 1952 kb Co. New York 1932. 20 359. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 205 and at pressures of hundreds of millimetres for the combination of methyl with an iodine atom. The most important combination reaction of methyl radicals is that in which two of them combine to give ethane. This reaction has been very accurately studied by Gomer and Kistiakowsky,17 who used the photolysis of both acetone and dimethylmercury as radical sources the total pressure in the reaction system being 10-50 mm. Using the rotating sector tech- nique they found the rate constants given in Table 1 where Ic2 is in mole-l C.C. sec.-l. From these figures it may be seen that the activation TABLE 1 .Rate constants for the combination of methyl radicals Hadical source Temp. k x Radical source Temp. k x 10- l 3 ~~ ~~ Acetone . . . . 125" 4.5 Dimethylmercury 175" 4-6 Acetone . . . . 175 4.2 Dimet,hylmercury . 220 6.7 energy of the reaction is very low and that the collision yield for the reaction is about 0.5. This work seems to be very reliable and the results obtained will be used throughout this Review for the calculation of rate constants based on the rate of formation of ethane in systems a t relatively high pressures. I n fact most methyl-radical reactions have been investigated in systems a t pressures of 50-100 mm. where the rate constant for the com- bination reaction is almost independent of pressure. The first attempts to detect the falling-off of the rate constant for methyl combination were not conclusive 2o largely because experimental errors and complicat,ions increased markedly as the pressure was lowered so that it was difficult to be sure that the observed trend was not fortuitous.However Kistiakowsky and Kirk Roberts 21 have now found that the rate constant for the combination of methyl radicals definitely falls to about one-third of its high-pressure value when the total pressure in the system is reduced to 1 mm. This is in good agreement with Marcus's prediction. l 9 Lossing Tickner and Ingold have also measured the rate of combination of methyl radicals by a mass-spectrometric method 22 by which it is possible to observe directly the concentration of methyl radicals and ethane in a flow-reaction vessel attached to the ionisation chamber of the mass-spec- trometer.Di-tert.-butyl peroxide dimethylmercury and ethylene oxide at a few microns' pressure in the presence of 5-19 mm. of helium as a carrier gas have been used as radical sources. The rate constant found at 160" c agrees within 50% with those of Gomer and Kistiakowsky a t high pressures. The rate constant decreases with increasing temperature according to the equation Ic cc exp[(2200 & 500)/RT] over the range from 160" to 800" C. 2o Trotman-Dickenson and Steacie J . Chem. Physics 1950 19 1097 ; Nicholson J . Amer. Chem. Soc. 1951 73 3981 ; Linnell and W. A. Koyes junr. ibid. p. 3986. 21 Personal communication. p 2 Lossing and Tickner J. Chem. Physics 1952 20 907 ; Lossing K. U. Ingold and Tickner Discuss. Faraday SOC.1953 14 ; also personal communication from Dr. Lossing. 206 QUARTERLY REVIEWS Surprisingly; no evidence was found for the variation of rate with helium pressure. The only other combination reaction which has been quantitatively studied is that of methyl with nitric oxide. The productls of tlhe reactlion (6) are not known with certainty and are complex. Formaldoxime ammonia hydrogen cyanide and carbon monoxide have all been detected so it is likely that a single molecule perhaps CH,*NO is first formed which is un- stable under the conditions of the experiment and rearranges or decomposes to give the observed products. The reaction has been studied by two methods the first for the pressure range 5-100 mm. and the second for the range around 0.2 mm. Since the complex formed as a result of the reaction contains only six atoms it would not be surprising if this rate constant were also dependent upon pressure and this appears to be the case.I n the first method 23 the reaction is studied by photolysing acetone or dimethylmercury in the presence of nitric oxide at room temperature. A very low concentration of nitric oxide is kept constant by steadily leaking a known quantity of the gas into the reaction vessel during the run. After a convenient time ( t ) the reaction mixture was analysed for ethane and nitric oxide. Now I]c2H,1 = tk2 [cH31 and The amount of nitric oxide found on analysis may be regarded as the steady- state concentration for some 200 times this amount is added during the course of the run. From these equations and the accepted value of k2 k is found to be 2 x loll mole-1 C.C.sec.-l at 28" c over the whole range of pressure. The second method first used by F ~ r s y t h ~ ~ has been greatly improved by Durham and S t e a ~ i e ~ ~ who produced the methyl radicals by passing a stream of di-tert.-butyl peroxide through a furnace and down a tube into which nitric oxide could be injected. The concentration of methyl radicals at any point in the tube could be measured by following the rate of removal of a radioactive tellurium mirror. In this way the effect of the pressure of nitric oxide on the radical concentration along the reaction tube could be found and hence the rate constant for the reaction of the radicals with nitric oxide. The value of k6 = 3.3 X 10lo mo1e-l C.C. sec.-l a t 25" c is much lower than the high-pressure value but as there is no reason to suspect the experimental accuracy of either determination this difference must be ascribed t o the pressure dependenw of the rate constant.Unfortunately insufficient is known about the products of reaction (6) for the phenomenon to be treated theoretically. A mass-spectrometer can also be used for methyl-radical detection,2z CH 4- NO -+ X (6) total NO consumed = tk6[CH3][NO] 2 3 Marcus and Steacie 2. Nccturforsch. 1949 4 n 332 Miller and Steacie. J . 2 4 Forsyth T ~ I L S . Faraday SOC. 1941. 37 313. 2 5 J . Chem. Physics 1952 20 582. C'hem. Physics 1061 19 73. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 207 and in this way the rate constant was found to be loll mole-1 C.C. sec.-l at 950" c with rather a large experimental error; however this figure may be taken as good evidence that the activation energy of the reaction is very small indeed.It is generally believed that a large number of combinations of methyl radicals with other radicals occur but only in a few cases have the products been identified because of the analytical difficulties involved in the separa- tion of small quantities of R*CH from large quantities of RH where R is a large radical. However the products of the combination of methyl with acetyl acetonyl n-propyl and isopropyl have all been found though none of the rate constants has been measured. Ivin and Steacie have found that ethyl radicals combine on about one collision in two to give butane so it is very probable that the reactions of methyl with ethyl and of methyl with prop91 have similar collision yields.These combinations of methyl with large radicals may be regarded as independent of pressure under all accessible conditions. Thc combination of methyl with a benzy! radical reaction (7) has not been detected but there is no reason to suppose that it CH + C,H,*CH -+ C,H,*C,H ( 7 ) does not occur. The activation energy for the decomposition of ethyl- benzene as measured by Szwarc 26 may be combined with the C-H bond strengths in toluene and methane and the heats of formation of toluene methane and ethylbenzene to give the activation energy of reaction (7) as 1 & 4 kcal. Furthermore if reasonable assumptions are made about the properties of the methyl and benzyl radicals the entropy change in the reaction may be calculated and hence the equilibrium between methyl a'nd henzyl radicals and ethylbenzene.On this basis the rate constant of reaction (7) a t 182" c has been found to be 10l2 molep1 C.C. sec.-l E being assumed equal to 0 kcal. It may be supposed that under suitable conditions methyl radicals would combine with atoms but there is little direct evidence for such reactions. The rate constants will certainly be very dependent upon the total pressure of gas in the system and it is likely that the " high-pressure " rate will only be approached at several atmospheres which is not a usual pressure at which to st6dy free radicals. Under the normal conditions of flow pyrolysis the rates of the reverse reactions the decompositions of methyl bromide 27 and methyl iodide,28 are markedly dependent upon the overall pressure.The quantitative data on the combination of methyl radicals are sum- niarised in Table 2 where k and A are in mole-1 C.C. sec.-l. There is very little quantitative information on tjhe rates of combination of other sma811 radicals though in a fair number of cases the products have been detected. The satisfactory interpretation of a very large amount of information on pyrolysis reactions such as have been described by Szwarc 29 has been based This result is probably not very accurate. 2 0 J . Chew. l'hysirs 1949 17 431. 2 i Sehon and Szwarc Pjoc. Roy. S o c 1951 A 209 110. 28 Horrex and Lapage Disczcss. Zf'aratlay Soc. 1951 10 233. 29 Chem. Reviews 1050 47 75. 208 QUARTERLY REVIEWS Reaction CH + CH3 + C2H6 CH + C6H,.CH + c6H5.C2H5 CH + NO + X upon the supposition that small radicals always combine with zero activation energy On these grounds rather than as a result of direct experiments we must conclude that simple radicals combine with very low activation energies.At the ot'her end of the scale of molecular size it is known l5 that growing polymer radicals combine with low activation energies but that the rate constants are usually lower t'han for small radicals being of the order of 1O1O molep1 C.C. sec.-l. k a t 182' c A E kcal. 4.5 x 1013 4.5 x 1013 0 f 0.7 (1012) (1012) I f 4 2 x 1011 (at 28" C ) 2 x lox1 (min.) 4-5 (max.) TABLE 2. Combination reactions of methyl radicals Metathetical Reactions of Methyl Radicals.-As yet only the class of metathetical methyl radical reactions represented by the general equation CH + RH + CH + R has been comprehensively studied in a quanti- tative manner.There are two good reasons for this the first being that the important products of these reactions from the point of view of a kinetic study 'uix. methane and ethane are fairly easily separated from Ohe rest of the reaction mixture by distillaDion. Other difficulties apart an investi- gation of for example the reaction CH + C,F12 -+ CH,F + C5F, would be complicated because CH,F and C2H have boiling points which are very close together so a mass-spectrometer is needed for analysis. The second reason is that our knowledge of the dissociation energies of C-H bonds is more extensive 29 than of those between any other two atoms. It has long been thought that there should be a relation between the strength of a bond and the ease with which the atom attached by the bond can be removed by free-radical attack.Much research has been carried out with this possibility in mind. The first extensive work on reactions of the type mentioned was that of H. S. Taylor with Cunningham 30 and with Smith.31 They investigated the photolysis of dimethylmercury in the presence of hydrogen deuterium ethane n-butane 2-methylpropane and neopentane and several unsaturated and aromatic compounds. It has been shown 32 that in the majority of cases not very much reliance can be placed upon the quantitative aspects of the work but the general pattern of the results which they obtained was undoubtedly correct. They found that the activation energy for the reaction of methyl with an alkane containing only primary hydrogen atoms was greater than that for reaction with one containing secondary hydrogen atoms which in turn was greater than that for one containing a tertiary 30 J .Chem. Physics 1938 6 359. 3 2 Steacio Darwent and Trost Discuss. Faraday Soc. 1947 2 79 Trotman- Ibid. 1939 7 390; 1940 8 543. Dickenson and Steacie J. Phys. Colloid Chenb. 1951 55 908. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 209 hydrogen. In addition it was found that the reaction with toluene and propene was rapid while that with benzene was slow. All these points have been verified by later investigations. Shortly afterwsrds Allen 33 used the photolysis of acetone to investigate the reactions of methyl wit,h propane. The investiga,tion was cursory and the results obtained are not of quantitative significance. In the last few years a large number of methyl-radical reactions of this t,ype have been investigated chiefly a t the University of Rochester N.Y.and in the laboratories of the National Research Council of Canada in Ottawa. All of t'he results which are suitamble for tabular presentation are included in Tables 3 and 4. Before considering their significance we will try to assess their accuracy. The results were obtained by the methods outlined above. TABLE 3. Reactions of methyl rccdkls with hydrogen R adic a 1 Hydrogen source lsotopc HgMe . . . Acetone Acetone . . Acetaldehyde . Acetone . . . Acetone . . . Acetone-d . . Acetone-d . . CdMe . . E . kcal. 9-3 & 0.5 9.2 f 0.3 13 f 2 13.2 & 0.4 15.3 & 1.0 11.7 & 0.2 14.3 & 0.6 10.2 & 0.2 10.9 4- 0.3 ~ 1 Ref k (at 182" c) a lo-l, x 10-6 14 5 14 1.5 25 1.5 0.5 6 2 30 15 2500 300 60,000 70 300 50 40 34 35 36 37 37 35 37 35 35 The most remarkable feature of the figures is the excellence of the agree- ment obtained by different workers using different sources of methyl radicals and usually different types of radiation when the same substance is photo- lysed.This gives us great confidence that the results are accurate and that no complications due to "hot" radicals arise. The rate constant k at 182" c is the most directly determinable quantity ; this temperature is chosen as being near the middle of the temperature range of most investiga- tions. Different workers usually agree on the magnitude of this rate within a fact'or of 1.5. In a series of experiments values can usually be reproduced to within & The probable errors in the activation energies are given in the table ; these errors are derived solely from the deviations of the points from the Arrhenius relationship ; no weight is given to un- certainties in tjhe assumed mechanism.The values for the activation energy are based on E = 0 kcal. and the values of A on A = 4.5 x l O I 3 moles It should be noted that errors in the diflerence.9 of C.C. sec.-l. 33 J . Awzer. Chem SOC. 1941 63 708. 3 4 Phibbs and Darwent' Trans. Farachy SOC. 1949 45 541. 35 Xajury and Steacw Discuss. Fcaraday SOC. 1953 14. 36 Anderson and H. A. Taylor J . Phys. Chem. 1952 56 498. 37 Davison and Burton J. arner. Chem. Xoc. 1952 74 2307. 210 QUARTERLY REVIEWS TABLE 4. Metathetical reactions of methyl radicals * Reactant Alkanes Methane . . . . . Ethane . . .. . . ueoPent,a.ne . . . . . 2 2: 3 3-Tetramethyl- )%-Butane . . . . . butane n-Pentanc . . . . . n-Hexane . . . . . 2-Methylpropane . . . 2 3-Dimethylbutane . 2 3 4-Trimethylpentane Alkenes Ethene . . . . . . Propene . . . . . But-2-ene . . . . . 2-Methylprop-2-ene . . 2 3-Uimethylbut-2-ene . Rut-l-ene . . . . . Pent- 1 -ene . 3-Methylbut-l-ene . . Alkynes But-2-yne . . . . . But-l-yne . . . . . Cy clanes cycZoPropane . . . cycZoButane cycZoPentane . cycZoHexane . Aromatic hydrocarbons Benzene . . . . Toluene. . . AAlcohols Methanol . . . . . Ethanol . . . . Propan-2-01 . . Radical source t Acetone -d Acetone -d Acetone and acetone -d Acetone-d Ace tono He;Me HgMe2 %Me Acetone Acetone Acetone HgMe Azometharie Acetone Acetone -d Acetone-cl Acetone - d Acetone -d Acetone-d Acetone-d Acetone-d Acetone -d Acetone -d Acet one-d Ace tone -d Ace tone -d Acetone- d Acetone-d Acetone and acetone-d Acetone HgMe Acet one-d Acetone - d DTBP HgMe2 Acetone Acetone-d Acetone-d %Me E kcal.12.8 10.4 f 0.4 10.0 f 0.3 9.5 f 0.4 8.3 & 0.2 8.2 -J= 0.5 9.5 f 0.5 8.1 f 0.2 8.1 f 0.2 7.6 _t 0.2 7.3 f 0.3 6.6 _tr 0.3 6.0 -+ 0.2 7-8 & 0.4 7.0 f 0.4 - 10.0 0.4 7.7 & 0-4 7.7 & 0.4 7.3 0-4 7.8 f 0.4 7.6 & 0.4 7.6 f 0.4 7.4 f 0.4 8.6 f 0.4 9.1 f 0.4 10.3 + 0.4 10.2 f 1.0 9.3 + 0.4 8.3 f 0.2 8.3 0-2 9.2 & 0.4 8.3 * 0.3 7 + d 11 & 2 8.2 & 0.2 8.2 + 0.5 8.7 & 0.4 7.3 & 0.4 k x 10-8 0-17 2.0 3-3 5.2 11 22 10 13 14 17 22 16 35 40 34 i n 2.9 12 30 26 76 34 35 53 33 34 1.1 1.5 11 24 22 1.0 14 5 6 5 20 31 A x 1O-Io (Assumed 19 20 17 11 18 33 10 12 1 0 6 7 21 20 - 3 I I 7 6 14 8 40 15 15 18 42 76 9 12 28 24 22 2.5 14 1 4.8 4.4 29 10 Ref.$ 38 39 30 39 39 40 40 31 3 9 39 3 9 41 42 39 3 9 3 9 43 43 43 43 43 43 43 43 44 44 44 45 44 44 44 44 44 31 46 44 45 44 44 * Values of k refer t o 182" c and both k and 4 are expressed in terms of moles-1 t DTBP = Di-te?t.-butyl peroxide.$ Where this mark is appended to the reference it indicates that tile quantities C.C. sec.-l. were not calculated in this manner by the original authors. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 211 TABLE 4. Metathetical reactions of methyl radicals * (continued) Reactant Amines and imines etc. Methylamine . . . Dimethylamine . . Ethyleneimine . . Trimethylamine . . Ammonia . . . . Azomethane . . . Ethers and epoxides Dimethyl ether . . Diisopropyl ether .. Ethylene oxide . . Aldehydes Acehaldehyde . Ketones Acetone . . . . Acetone-d . . . . Diacetyl . . . . Peroxides Di-tert.-butyl peroxide . Metal alkyls Dimethylmercury . . . Dimethylcadmiurn . . Halogenated methanes Methyl fluoride . . Methylene fluoride . . Methyl chloride . . . Methylene chloride . . Chloroform . . . . . Methyl bromide . . . Methylene bromide . . Hydrogen halide Hydrogen chloride . . Radical source t Acetone-d Acetone -d DTBP Acetone-d Acetone-d Azomethanc Acetone HgMe CH2*OCH Acetone 4 HgMe2 HgMe DTBP Acetone Acetone Acetone DTBP Acetone-d Diacetyl DTBP HgMe HgMe YdMe lcetone leetone leetone lcetone 4cetone lcetone lcetone Icetone icetone E kcal. 8.4 & 0.4 7.2 0.4 4.8 f 0.3 8.8 f 0.4 10.0 f 0.4 7.6 9.5 f 0.2 8.4 & 1.5 10 f 2 7.3 & 0.4 9.0 & 1.0 9.6 f 2 8.0 & 0.3 9.7 & 0.1 9.6 f 0.4 9-5 f 0.2 9.5 * 1.0 10.3 + 0.8 10.6 f 0.3 7.1 f 0.2 (15) 9.0 & 0.5 11.0 (14) 8.7 & 0.3 6.2 & 0-3 9.4 & 0.3 7.2 f 0.3 5.8 f 0.3 6.8 10.1 f 0.3 8.7 & 0.3 2.1 k x lo-' 19 70 200 44 - 20 1.2 9 9 12 38 1-5 2.8 220 10 8 11 9 4 6 17 2 10 3 > d 25 3 0 25 6 0 100 40 100 ! x 105 A x 10-lo 20 19 5 70 7 - 10 30 10 70 12 3 11 90 40 30 40 27 40 7 0 5 (3000) 20 4u (700) 40 3 70 2u 6 300 150 200 Ref.$ 44 44 47 44 44 42 44 45 44 48 45 7 49 5 0 511 17 52 50 35 53 17 5.4 36 51 I 56 55 55 55 55 56 55 55 56 I I * Values of k refer to 182' c and both k and A are expressed in terms of moles-' f- DTBP = Di-tert.-butyl peroxide. C . C . sec.-l. Where this mark is appended t<o the reference it indicates that the quantities were not caleulat,ed 1x1 this manner by the original authors.21 2 QUARTERLY REVIEWS activation energies derived from a series of experiments on different com- pounds may often be much less than the errors in the absolute values. When this consideration is of importance for the interpretation of the experimental data attention will be drawn to the matter. The results given in Table 3 for the reaction of methyl with hydrogen are taken straight from the original papers and show the confused state of the literature. The random experimental errors are quite likely to be on the low side but the discrepancies are too large to be assigned to this cause alone. Wijnen and Steacie 57 have shown that if of those runs done by Davison and one takes notice only of those in which the percentage conversion of the reactants was low and the photolysis was not likely to be complicated by side reactions then the work gives a value of 10.5 & 1 kcal./mole for the activation energy of the reaction.In their opinion all the most reliable published work leads t o a value of 10.0 5 0.5 kcal./mole for the activation energy. Unfortunately this solution does not resolve all the difficulties for the activation energy of the reaction H + CH + H + CH 4- 1 kcal. appears t o be a t least 12 kcal./rnole and therefore the back reaction must have an activation energy of a t least 13 kcal./mole. No satisfactory explanation of this discrepancy has yet been given. Several series of compounds have been studied sufficiently fully for it to be possible to draw certain conclusions about the trends in reactivity within the groups.The best investigated of all these series is that of the alkanes. Here it is apparent thatc the compounds fall into three groups of activation energies for the reaction with methyl of (i) about 10 ; (ii) about 38 Trotman-Dickenson and Steacie J . Phys. Colloid Cherrz. 1951 55 908. 39 Trotman-Dickenson Birchard and Steacie J . Cher12. Physics 1 951 19 163. 40 Gomer J. Amer. Chem. Xoc. 1950 72 201. 41 Rebbert and Steacie personal communication. 4 2 Jones and Steacie personal communication. 43 Trotman-Dickensoii and Steacie J . Chem. Phys;cs 1951 19 169. . 4 4 Idem ibid. p. 329. 4 b Phibbs and Darwent C’awdia~z J . Res. 1950 B 28 395. 48 Roberts and Szwarc Trows. Paraday SOC. 1950 48 625. 47 Brinton and Volman J. Chena. Physics 1952 20 25. 48 Gomer and W.A. Noyes jun. J . Amer. Chem. Xoc. 1949 71 3390. 4B Brinton and Volman J . Chem. Physics 1952 20 1053 ; there is strong evidence that this is the most reliable value but for a different view see Dodd Trans. Paraday SOC. 1951 4’7 56. Trotman-Dickenson and Steacie J . Chem. Physics 1950 18 1097. 51 Saunders and H. A. Taylor ibid, 1941 9 616. 5 2 Jacquiss Roberts and Szwarc J. Amer. Chem. SOC. 1952 74 6005. 53 Blacet and Bell Discuss. Faraday Xoc. 1953 14. 5 4 Gomer and W. A. Noyes junr. J . Amer. Chem. SOC. 1949 71 3390. 5 5 Raal and Steacie J . Chem. Physics 1952 20 578. The error in these results is in some cases probably greater than is indicated because complicating side reaction3 may have occurred. Cvetanovii and Steacie Canud. J. Chern. 1953 31 158. 67 Discuss. Paraday Soc.1953 14. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 213 8.2 and (iii) less than 8 kcal./mole and that these contain respectively (i) only primary (ii) primary and secondary (iii) primary and tertiary hydrogen atoms. Furthermore since the A factors do not vary widely this trend in activation energies is reflected by the trend in the rate con- stants. Now 2 2 3 3-tetramethylbutane contains three times as many primary hydrogen atoms as ethane and 2 Z-dimethylpropane twice as many. Since the three compounds all react with methyl with nearly the same activation energy the hydrogen atoms in these compounds may be considered equivalent. Similarly 2 3 4-trimethylpentane has three reactive tertiary hydrogen atoms while 2 3-dimethylbutane has two and Z-methylpropane has one.We can by inspection decide how many ‘‘ active ” hydrogen atoms there are in an alkane and after making a very small correction for the presence of less active types of hydrogen atoms in the conipound find by division the reaction rate characteristic of the “ active ” hydrogen atom. Thus for n-butane there are four “active” hydrogen atoms and six less active primary atoms. By consideration of the results obtained with compounds containing only primary hydrogen atoms it can be found that the rate constant characteristic of a primary hydrogen atom at 182” c is ca. 3 x 106 mole-1 C.C. sec.-l. Hence for n-butane the rate constant characteristic of a secondary hydrogen atom is &[ll - (6 x 0.3)] = 2.3 x lo6 mole-‘ C.C. see. -l. In this manner Table 5 has been obtained.TABLE 5. Rate constunts characteristic of uarioiis types of hydrogen utoms in alkanes lo-% characteristic a t 182” c (mole-’ C.C. sec-ljatorn) Type of hydrogen atom 0.3 0.2 0.3 1 Secondary 2.3 2-0 2.0 1 Tertiary . . . . . 18 17 10 I This procedure is justified solely by the interesting nature of the results which show that it is reasonable to regard the different types of hydrogen atom in a molecule as if they were present in separate molecules in a multi- component mixture. In two recent reviews 5* reference has been made to a relation suggested by Polanyi between the heat of one reaction in a series and its energy of activation. Polanyi stated that where there is no resonance stabilisation in the transition complex or a constant amount of stabilisation throughout a series then for reactions of the type X + YZ -+ XY + Z it may be ex- pected that E = aH + const.where E is the activation energy and H the heat of the reaction and a has a value between 0 and 1. The results quoted above indicate that all primary C-H bonds and all secondary C-H bonds are very similar ; if this uniformity is accepted where the evidence is less 58 Warhurst Quart. Reviews 1951 5 44 ; Bolland ibid. 1950 4 292. 214 QUARTERLY REVIEWS good for all tertiary C-H bonds we may generalise Stevenson’s electron- impact data 59 as follows D(CH,-H) . . . . . 102 kcal. D(C-H) secondary . . . 94 kcal. D(C-H) primary . . . 97 kcal. D(C-H) tertiary . . 90 kcal. From these figures heats of reaction can be obtained for the reaction of methyl with each type of hydrogen atom ; these values for the heats are plotted against the activation energies in Fig.1. The value of E for CH + CH -+ CH + CH was not determined directly as the rate has effectively only been measured at one temperature. The straight line drawn in Fig. 1 is for a = 0.5 which would be expected from considerations of symmetry based upon the similarity of the bonds broken and formed; 5 FIG. 1 The relution between activation energy and heat of rencfioli fbr the reactions of methyl m d i c n l ~ with alkanes I{ = 12-5 + 0.6F1. 0 -5 -1u -15 H (kcal.) the positive deviation of the value of E for the tertiary hydrogen atom from the line rr ght also be expected. This is the only case in which Polanyi’s relation has been subjected to direct experimental test. The striking fact about the results obtained from the study of thc alkenes is that apart from ethene they all react with methyl with the sanic activation energy within the rather small limits of experimental error (the relative values of the activation energies are here good to 0.2 kdal./mole).It may be seen that where possible it is always the a-methylenic hydrogen atom which reacts. Thus there are three “ active” hydrogen atoms in propene twelve in 2 3-dimethylbut-2-ene two in but-1-ene and one in 3-methylbut-1-ene. In Table 6 are given the rate constants per active hydrogen atom for primary secondary and tertiary a-methylenic hydrogen atoms and assuming a constant value of E of 7.6 kcal. the values of A divided by the number of active hydrogen atoms This table shows first that each type of hydrogen atom has a particular rate constant for reaction with methyl in the alkene as well as in fhe alkane series.Secondly that the changes in reactivity are due to changes in the A factor and not in 59 Discuss. E’uraday Soc. 1951 10 35 ; for a different view cf. Leigh and Szqvarc J . Chem. Physics 1952 20 407. activation energy as was tlie case with the alkanes. No explariation for this most interesting fact has yet been advanced. No other series of conipounds has been investigated thoroughly apart from the cyclanes where the variations are of a different kind from those previously considered. It is noteworthy that the variations in rate found among the cyclanes had been previously predicted by Brown 6o by considera- tion of the strains involved in the molecule and in the transition state. It is possible however that other attractive explanations could be found.TABLE 6 Rate constants at 182" c and frequency factors per in alkenes (both i n hydrogen atom characteristic of diflerent types of hydrogen atoms C.C. sec.-l) Type of hydrogen atom 10- %/H 10-loA/H Primary . . . 4 5 4 fJ Secondary . . . 17 18 Tertiary . . . 1 Class of compound Alkane I Alkene Alkynr Ether 2 7 23 Alcohol Proin tlie results in Table 4 as a whole three facts stand out. First that the spread of activation energies is small only 8 kcal./mole whereas tlie spread of C-H bond strengths is between the weakest bond in toluene arid that in methane. Secondly the general rule that primary hydrogen atoms react less readily than secondary and these in turn less readily than tertiary holds throughout as shown by the values of the rate constant/num- ber of * ' active " hydrogen atoms for each class of compound in Table 7 .Type of hydrogen atom lO-%/H a t 182' c (mole-l C.C. sec -'/atom) Primary . . . . 0.3 1.6 Tertiary . . . . Secondary . . . I Thirdly although there is a considerable variation in the A factors yet they all except for two doubtful cases lie in the range 10104 - as is shown by Fig. 2. and lop4. The figures show that the concept of reactivity as applied to free-radical reactions is very vague when studies have only been made at one temperature. Whenever possible activation energies and A factors should be determined and if this cannot be accomplished great caution 4iouId be exercised in interpreting the results. The rates of three reactions of methyl radicals relative t o the rate of This means that the steric factors lie between e0 J .Amer. C'he,tL. Soc. 1951 73 212. P 216 QUARTERLY REVIEWS reaction (4) (p. 204) have been studied. The method (described in the section on methods) was first used by Anderson and Kistiakowsky 61 and later by Williams and Ogg.62 The later work was considerably more CH +HX -+ CH + X (8) extensive and involved the determination of the relative rates of reactions r FIG. 2 The jrequemy of occurreim of d juclvt s jot* methyl-radical mxctioizs. (4) and (8) where X is C1 Br or I over a range of temperaturezs. E8 - E and A8/A4 were found ; the values are given below Tlius Reaction E' - >J4 kcal /molt &'A CH + HBr. . . 0.95 0.13 CH + HCI . . 8.4 0.04 CH,+HI . . 0.75 0.23 Williams and Ogg considered that i ' hot " methyl radicals were involved in the reaction with hydrogen chloride so the meaning of the figures is doubtful.For this reason the results cannot be direct'ly compared with those obtained from the photolysis of acetone in the presence of hydrogeri chloride.56 The experiments are very difficult to conduct and to interpret SO little reliance should be placed upon the precise nuiiierical values obtaiiied. The supposition that reactioii (4) takes plac*e 011 every collision is reasonable but not proven. Large numbers of other gas-phase reactions of methyl radicals involving hydrogen abstraction have been postulated but not quantitatively investi- gated. Steacie lists many of these. No metathetical reactions of methyl in the gas phase have been quanti- tatively investigated in which atoms other than hydrogen are abstracted though these certainly occur.Of particular importance are the reactions with the halogens which ocCIA1' ho rapidly that they crtiinot be stuc1ic.d h ~ present techniques. trl J. Chem. Physics 1943 11 6. 6 2 Ibid 1917 15 &t;. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 21 7 Benzene . . . Acetono . . . . Toluene . . . . Oct-1-ene . . . cycloHexane . . . Two reactions have been found in which a methyl radical extracts a radical from a molecule. They are CH + CH,*HgCH + C,H + Hg + CH and CH + CH,*CO*CO*CH --+ CH,*CO*CH + COGH The rate constant of the f i s t is approximately represented by the equation k = 107e-1000/RT and of the second by I% = 4.8 x 1010e-5600/RT mole-l C.C. 8ec-l. Reactions of this type seem to be very rare and until more are found it is not possible to state with what sort of molecules they are likely to occur.No methyl-radical reactions have been investigated in solution sufficiently fully to determine rate constants. Indeed apart from the greater analytical difficulties it is to be expected that in many cases complications may be caused by the fact that two methyl radicals released as a pair from a molecule by photolysis (as in the case of acetone and dimethylmercury) may be caged in and have a greater probability of combining than would be expected from the overall concentration of methyls and the rate constants in the gas phase so that the rate of formation of ethane is not a reliable guide to radical concentration. Edwards and Mayo l3 have investigated the rates CH + CCI -+ CH,Cl + CCl (9) of a number of reactions of type (1) relative to the rate of reaction (9) a t 100" c.The radicals were produced by pyrolysis of acetyl peroxide and the reactions were followed by the relative rates of production of methane and methyl chloride. The rate constants Jc,/lc in solution are compared in Table 8 with the rate constant's k, determined by Trotman-Dickenson and Steacie 44 for the five compounds common to the two investigations (the E value for oct-1-ene was assumed equal to kpent-l-ene + kn-l'erltnIle - kethane). The table shows a remarkable parallelism between the two sets of data cydohexane apart the constancy of the last column is much 0.04 0.40 0.75 3.2 4.5 TABLE 8. Relative rate constants for the reactions of methyl radicals in the gas phase and in solution Compound 1 0 - V ~ ~ (gas) a t 100" C mole-' C.C.sec.-l 10-V~~ (gas) kl/ks (solution) - I-__ 0.091 1.0 1.9 7.7 3.4 2.3 2.5 2.5 2.4 0.8 better than the reliability of the figures would lead one to expect. The result is of importance because it is the first case in which a free-radical reaction has been accurately studied in the gas phase and in solution. However there is some evidence that the reacting species in Mayo's work i s not a methyl radical a t all but the CH,*CO*O radical. This difficulty is chasacteristjc of reactions in solution. 21 8 QUARTERLY REVIEWS The metathetical reactions of other radicals or atoms have been very litole investigated in the gas phase or in solution. In Table 9 are collected the data on some of the other metathetical reactions in the gas phase which may be compared with the methyl reactions.The informat'ion is fragment - ary but as far as it goes i t leads us to suppose that the gradations in the reactivity of methyl radicals with various compounds will be reflected in the reactivity of other radicals with the compounds. On the other hand there are some notable exceptions to this rule and even for the reactions presented in the table there exist data which conflict with this conclusion. I n solution the transfer-reaction velocity constants which have been measured for the thermal polymerisation of styrene in various solvents 6 3 correspond to metathetical reactions of the polystyrene radicals. I n this case where an extreme difference in molecular size is involved there appears to be littlle correlation with the methyl reactions. TABLE 9. Activatim enwgies (in kcal.,/molc) of unrious ?wta- th c tical reactions R H .. . . . . . CH . . . . . . C,H . . . . . . BUS . . . . . But . . . . . . CH,*CH:CH*CH . . CH,:CHCH . . . 10 12.8 10-4 8.3 7.6 7.7 7.7 (I) CH + RH -+ CH,+ (11) H S RH -+ H,+ R Ref 64 64 64 64 61 64 6.2 R He;rLtion I1 I Ref I I11 1 Rrf. 65 66 66 86 66 66 66 B r f R H -+ (IV) Na + RC1 + 9.4 70 8.6 7 0 7.8 TO 5.3 TO -~ HBr + R NaCl 4- R Addition Reactions of Methyl Radicals.-Large numbers of addition reactions of methyl radicals of the type CH + X-Y -+ CH,-X-Y- have been identified with a wide variation of the groups X and Y. A list of these types is given below. For only one addition reaction however T> pe of multiple bond Exanil)le L j 1 " crf In1lltll)le b o r l d b:xaIllpl~ C L C . . Many alkenc5 C-0 . .C'arbon monoxide c-c . . Ethyne N-N . . Azomethaiic c-c-c- c . . Rutadieric 0 0 . . Oxygen has the velocity constant been detwniiiied ~ i z . for CH 0 + products. Marcotte and Noyes '1. found the ratie constant for this reaction hy corn- 63 Burnett Quart. Reviews 1950 4 292. 6 5 Farkas and Farkas Proc. Roy. SOC. 1935 A 152 124. 6 6 Darwent and Roberts Discuss. Faraday SOC. 1953 14. 6 7 Bodenstein and Lutkemeyer 2. physikal. Chem. 1935 114 208. Kistiakowsky and Van Artsdalen J. Chem. Physics 1941. 12 469. G9 Anderson and Van Artsdalen ibid. p. 479 70 Warhurst Quart. Reviews 1951 5 44. 71 J . Arne?. Chem. LS'OC. 1952 '74 783. 6 1 See Tables 3 and 4. TROTMAN-DICKENSON THE REACTIONS OF METHYL RADICALS 219 Alkeiie radical Etheno . . . . . Propene 2-Methylpropene . paring the rate of disappearance of oxygen from an illuminated acetone- oxygen mixture with the rate of product,ion of methane.They found the activation energy of the reacttion to be 0 & 0.5 kcal./mole and that B =7 8 x 10lO molew1 c c. sec.-I. The reason why it has been impossible to determine t,he velocity con- stant of reaction (10) is that the propyl radical rapidly reacts with another ethene molecule combines or disproportionates with a methyl propyl or higher radical or a t temperatures above 520" K decomposes at an appreci- able rate. The situation is thus extremely complicated and cannot be sorted out by our present techniques. An attempt has been made 7 2 to give a general kinetic treatment of the reactions which occur when acetalde- hyde is photolysed in the presence of a number of different alkenes.No reliable rate constants for the individual steps have been derived by this method and the study illustrates clearly the great difficulties which have to be overcome before quantitative results can be obtained by this straight- forward approach. Some information about the addition of methyl radicals to alkenes may bc obtained indirectly by studying the kinetics of the reverse reaction. Thus although it has not been possible to determine the activation energy of (lo) yet the activation energy of the reverse reaction (11) can be measured. This has been done by Bywater and S t e a ~ i e ~ 4 y who produced the propyl radicals by mercury photosensitisation. They found E = 20 kcal.jmole. If the C,H7-H and CH,-H bond strengths are known it is possible to calculate AH for reaction (I 1) from well-established thermochemical data.The data due to Stevenson 45 on the CH3-H and primary secondary and tertiary C-H bonds which have been referred to above can be used for this purpose. In Table 10 all the information is set out which can be calculated in this way from the published data for the addition of hydrogen atoms or methyl or ethyl radicals to alkenes. All the data on the decomposition of the ( 3 3 3 +C,H4 + C3H7 (10) C3H7 + C&34 +CH3 (11) Hence AH = 23 kcals. AH = El - Elo Now therefore El = - 3 kcal. Hydrogen atom Methyl radical Ethyl radical - 1 (- 8) TABLE 10. Activation energies (kml./moZe) for the addition of radicals to rclkenes radicals come from the papers by Bywater and Steacie ; Stevenson's bond strengths 59 have been used. When the decomposition mechanism assumed i 2 Raal Drtnby and Hinshelwood J .1949 2226. 220 QUARTERLY REVIEWS involves the internal rearrangement of one of the fragments the result is placed in parentheses as being of doubtful value. The results in the table are uncertain to about &- 4 kcal. so the only conclusion which can be drawn is that t'hese addition reactions have very small activation energies. The entropy change in Dhe equilibrium formed by reactions (10) and (ll) for example can be calculated with a reasonable degree of confidence because most of the uncertainties due to our lack of knowledge of the pro- perties of the radicals occur on both sides of the equilibrium. So if ,4, and El are known we can calculate A, and E, from bond-strength and thermodynamic data. Thus we find 53 that the additions of methyl radicals to ethylene and propene have frequency factors of the order of 106 mole-1 C.C. sec.-l. This remarkable conclusion is supported by the fact that similar calculations for the reactions of hydrogen atoms give results which are in good agreement with the measured rates. 73 Trotman-Dickenson Disc%95. Faradmy h'oc. 1953 14.

ISSN:0009-2681    

DOI:10.1039/QR9530700198

出版商:RSC    

年代:1953

数据来源: RSC