ANNUAL REPORTSON TEEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. GENERAL.IN spite of the aloofness of the atomic nucleus from ordinarychemical affairs, the problem of its structure is in some ways themost fundamental one so far presented to chemistry. The greatdifficulty has been the absence of even the &st beginnings of a theoryabout the forces holding the various components of the nucleustogether. The radiations from radioactive substances, the displace-ment law, the identity of nuclear charge and atomic number, theexistence of isotopes, and the production of protons by artificialdisintegration, all go to show that protons, a-particles, and electronsare in some way involved in the make-up of the nucleus. Thatthere is profound interaction of some kind between these componentsis revealed perhaps most strikingly by the mass defect.Thatthere are sub-structures within the main structure is implied in allthe theories in which the a-particles in the nucleus retain theiridentity. The existence of energy levels is strongly indicated byanalysis of the y-ray emissions. The size relationships of thisextraordinary system are inconceivable in terms of macroscopicanalogies, and most physical pictures which have been suggestedinevitably contain inconsistencies and contradictions. Never-theless, that some satisfactory form of nuclear statics and dynamicswill presently be evolved seems almost certain. This anticipationis based upon the fact that in some respects nuclear processes, inspite of the difficulty of visualising them, are so very simple in theirexternal results.One example may be quoted. The most strikingexperimental advance during the past year has been the artificialdisintegration of elements by protons accelerated by extremelyhigh voltages.2 The lithium nucleus, when hit by a proton of1 Cf. Discussion on Structure of Atomic Nuclei, Proc. Roy. SOC., 1932, [A],136, 735; A., 791.J. D. Cockcroft and E. T. S. Walton, ibid., 137, 229; A., 89314 GENERAL AND PHYSICAL CHEMISTRY.several hundred thousand volts energy, appears t o capture theproton and break up into two a-particles: Li7 + H1 = 2He4.This opens up the prospect of a whole system of nuclear chemistry,by which theoretical predictions of stability relationships can betested.The Gamow theoryY3 treating the nucleus as a system containinga-particles confined within a high positive potential barrier throughwhich they escape at a slow steady rate, enables a fairly accurateaccount to be given of the relation between the energy of a-particlesand the half-life of the atoms emitting them.But if there areelectrons as such in the nucleus, they would not be confined by thissame kind of barrier : thus the picture is seen to be an incompleteone. F. A. Lindemannl has expressed the view that attempts torepresent the nucleus in spatio-temporal terms cannot possiblysucceed, or be more than metaphors.W. Heisenberg has recently started to construct a theory of thenucleus, which, while not spatio-temporal in the classical sense, ismuch more fundamental and direct than theories expressed in termsof potential barriers or other semi-empirical conceptions.The great simplifying factor which has made Heisenberg’s newtheory possible is the discovery of the neutron.5 This entity,which turns up when beryllium is bombarded with a-particlesfrom polonium, appears to have unit mass and no charge.It couldbe conceived for some purposes as an electron and a proton fusedtogether. The evidence that the beryllium radiation really doesconsist of neutrons is too detailed to be snmmarised briefly here, andthe result will be accepted for the purpose of discussing the theoryof nuclear forces.If there are neutrons, it is no longer necessary to postulate theexistence of free electrons in nuclei.The atomic weight has tobe about twice the atomic number. Instead of interpreting thisby saying that there are about twice as many protons as electronswe can now say that there are about equal numbers of protons andneutrons. According to Heisenberg, the best way is to regard theneutron, not as something containing a proton and an electron,but as an independent fundamental component of the nucleus. Itis to be thought of, however, as capable of generating an electronand a proton in some way. The theory considers the forces betweenthe various components of the nucleus. In the first place, there isthe ordinary Coulomb repulsion between the protons, and, secondly,Cf. Ann. Reports, 1930, 27, 26.2. Physik, 1932, 77, 1; 78, 156; A., 594, 1074.J. Chadwick, Proc.Roy. SOC., 1932, [ A ] , 136, 692; A . , 790; (Rlme.) I.Curie and F. Joliot, Nature, 1932, 130, 57 ; A., 895RINSHELWOOD : QENERAL. 15there are attractive forces betwesn neutrons and between neutronsand protons. The attractive forces are treated quantum-mechanically. Those between neutrons and protons are of the“ exchange ” type.6 (It may be well briefly to recall what this means.If a neutron and a proton are in proximity, and the negative chargechanged places, passing into what was originally the proton, thefinal state would be indistinguishable from the initial. In wavemechanics the probability of a given state is determined by theamplitude of a certain function which varies harmonically with time.If two states are indistinguishable, the corresponding amplitudeswax and wane alternately at the expense of one another.Thiswaxing and waning is analogous to the interchange of amplitudebetween two similar pendulums in resonance, and does indeed comeabout for the same mathematical reason, since it depends upon theidentical frequencies associated with states of equal energies. Re-sonance is always associated with the production of a new frequencylower than the undisturbed frequency. Throughout quantummechanics the connection between frequency and energy is offundamental importance. Thus the same equations which predictthe “ interchange ” of, say, the negative charge between the neutronand the proton, provide also for the existence of a state of lowerenergy than that corresponding to the energies of the completelyseparated particles.In other words, an attractive force exists.)The magnitude of the force is, in principle, derivable from “ exchangeintegrals.” Heisenberg constructs the Hamilton function for thenucleus, and from considerations of a rather general character arrivesat a number of interesting results. Considering the influence ofthe exchange forces only, he concludes that the minimum energy,i.e., maximum stability, would be reached when the numbers ofneutrons and protons present are about equal. The influence ofthe other forces is to displace the stable number somewhat in favourof neutrons.From the known stability of helium nuclei, it must be supposedthat a system of two protons and two neutrons forms somethinganalogous to a “ closed ” or “ completed shell.” The picture ofP-ray disintegration is as follows : a nucleus consisting only ofneutrons would change neutrons into protons by sending out P-raysuntil the energy which is gained by adding a proton is exactly equalt o that which is used up in removing a neutron.For smaller numbersof neutrons the nucleus is stable towards (3-disintegration. If thenumber of neutrons gets to‘o small, the Coulomb repulsion of thepositive charges leads to u-ray decay : a-particles, and not protons,are emitted, since (3-disintegration ceases at a point where the removal* Cf. Ann. Reports, 1930, 27, 1416 GENERaL AND PHYSICAL CHEMISTRY.of a proton still requires energy, though an a-particle, being lesstightly bound than a proton, can escape.The ratio, n,/n2, of thenumber of neutrons t o protons has, for a given value of n2, an upperand a lower limit, corresponding to (3- and a-disintegration respec-tively. Owing to the great stability of the helium nucleus, thereare often two successive P-ray changes if initially the atomic numberis even, but if one starts from an odd atomic number, there mayonly be one. p-Ray changes may be followed by a-disintegrationuntil nl/n2 once again rises above a limiting value.Heisenberg investigates the stability of nuclei with even andodd numbers of neutrons, and also dea,ls with the question of thescattering of y-rays by atomic nuclei.In the last Report, reference was made to the view that theemission of y-rays is associated with the transition of a-particlesbetween energy levels in the nucleus.Further work lends additionalsupport to this idea,. It has been shown, for example, that certainy-rays, known to be associated in some way with thorium4 orthorium-C’, are given out as an immediate consequence of thedisintegration of thorium-C.7 Again, actinium emanation emitstwo groups of a-particles : in the transformation of the emanationinto actinium-A, y-rays are emitted, the quantum energy of whichis found to be of the right order of magnitude to correspond to thedifference in energy of the two a-particle groups.*Perhaps one of the most striking results of quantum mechanicsis the prediction of enhanced probability of transition betweentwo states of a complex system when the total energy of one stateis very nearly equal t o that of the other.(The phenomenon iscalled resonance, since it depends mathematically upon equalityof frequency in the wave functions describing the different states.)From the general point of view, therefore, great interest attachest o the interpretation given by 5. Chadwick and J. E. R. Constableto their experiments on the artificial disintegration of fluorine andaluminium nuclei by a-particles. When these elements are born-barded with a-particles from polonium, the protons liberated canapparently be resolved into definite groups. (These groups,moreover, occur in pairs, suggesting that there are two ways inwhich an a-particle can be captured, the first giving an excitednucleus and a short-range proton, the second giving a stable nucleusand a long-range proton.) The four groups of two found withaluminium are supposed t o indicate the existence in the nucleusof four “resonance levels.” Penetration of the nucleus by the’ C.D. Ellis, Proc. Roy. SOC., 1932, [ A ] , 136, 396.* (Lord) Rutherford and B. V. Bowden, ibid., p. 407.Ibid., 135, 48 ; A., 318HMSHELWOOD : GENERAL. 17a-particle with insufficient energy to surmount the “ potentialbarrier ” can occur if the particle has exactly the energy correspond-ing to a resonance level. A detailed consideration of the techniqueof the kind of experiment upon which these conclusions are basedis obviously far outside the scope of this Report.It ought, however,to be mentioned that in certain cases difficulties of interpretationseem to arise.1° This means that, while the theoretical interest of theproblems raised is very great, even more investigation is necessarybefore the fullest confidence can be felt in any general conclusion.Another line of attack on the nucleus which looks like beingsuccessful is the investigation of nuclear magnetic moments andwhat are called “ g(1) factors,” Le., ratio of magnetic to mechanicalmoment, based upon the measurement of the hyperfine structureof spectral lines.11 This is just mentioned here, but it is not pro-posed to discuss the results in detail.It will be evident, even from the few examples quoted above,that nuclear chemistry is in a state of rapid development.We will now turn to the consideration of certain matters connectedwith the more accessible parts of the atom, starting with somerecent work on the nature of the chemical bond.The customary distinction between an ionic bond and a covalentor electron-pair bond appears to be quite sharp and definite as longas attention is fixed upon extreme cases. But the question whetherthere is a continuous transition from one to t’he other has alwaysbeen a subject for discussion.From a “ semi-quantitative ”quantum-mechanical treatment of the problem, L. Pauling 12arrives a t the conclusion that there will be a continuous transitionfrom one type of bond t o the other only when the lowest ionic stateof the molecule and the lowest covalent state have the same numberof unpaired electrons.Making approximate estimates of differentkinds of binding energies, he concludes that alkali halides are ionic,that the molecules HC1, HRr, and HI have electron-pair bonds,while HF is “ largely ionic.”When two electronic structures of about the same energy arepossible for a molecule, the quantum-mechanical resonancephenomenon comes into play with rather strange results. Thewave function for the normal state of the system is best representednot by either of the functions describing the two separate statesbut by a linear combination of the two functions. The meaningof this is supposed to be that the molecule oscillates rapidly betweenlo Cf. discussion a t the end of the paper by E.Steudel, 2. Physik, 1932, 77,l1 Cf. J. C. McLennan, Proc. Roy. SOC., 1932, [ A ] , 136, 735; A., 791.la J . Amer. Chem. SOL, 1932, 54, 988; A., 561.139 ; A., 98018 GENERAL AND PHYSIUAL UHEMISTRY.the two possible structures. Carbon monoxide, according to Pauling,provides an example of this kind of behaviour and fluctuates betweenthe structures given by :C::b’: and :C:::O:, the latter being thepredominant f orm.13It is a striking fact that the energies of individual bonds asderived from heats of formation and heats of combustion areapproximately ~0nstant.l~ The quantum-mechanical translationof this fact may be expressed by saying that the properties of abond are often “ determined by one single-electron orbital wavefunction for each atom and are not strongly affected by other atomsin the molecule.” To what extent this principle can be establishedrigidly by a priori reasoning the reviewer is not competent to state.But even if largely empirical, the rule is a useful one.Pauling l5concludes from an examination of therrnochemical evidence thatthe energies of normal covalent bonds are additive. This meansthat relations of the following kind hold : A:B =&(A:A + B:B),where A:B represents the energy of a bond between A and B.This applies only to normal covalent bonds, by which are meantbonds in which the electrons are equally shared by the two atoms.If A and B are not equally electronegative the bond assumes acertain ionic character. According to Pauling, the energy of anactual bond must be a t least as great as that for a normal covalentbond.Moreover, the difference between the actual energy and thatcalculated by assuming additive relationships will be greater themore pronounced the ionic character of the bond. For example,H:H is 4.44 v.e., F:P is 2-80; both of these are normal bonds, sincethe two atoms are in each case identical. From the additive principle,the normal covalent bond between H and P should have an energy+(4.44 + 2-80) = 3.62. The actual value for H:F is 6-39, which isin fact much greater than the “ normal ” value. The difference,A, decreases steadily as we pass to the heavier halogens : with H:Ithe value calculated from additivity is 2.99, while the real value is3.07, giving A = 0.08.Pauling finds A to be positive in 20 out of21 examples. It then appears that there are regularities amongthe A values themselves : the values of All2 are observed to beapproximately additive. This relation is illustrated by the follow-ing numbers, the unit being the electron-volt.C-H actual ..................... 4.34 C-F actual ..................... 5.40C-H from additive relation ... 4.02 C-F from additive relation ... 3.20~ 1 ’ 2 ................................. 0.57 A’/2 ................................. 1.48A .................................... 0.32 A .................................... 2-20~~~13 See (12); also Proc. Nat. Acad. Sci., 1932,18, 293; A . , 562.1 4 Cf. Ann. Reports, 1931, 28, 385.15 J . A m r . Chem. SOC., 1932, 54, 3570 ; L.Paiiling and D. M. Yost, Proc.Nut. Acud. Sci., 1932, 18, 414; A., 901HZNSHELWOOD : CJENER&. 19Thus Similarly from N-H and N-F it isfound that A& + A& = 2-06.This suggests that the actual value of any AAB can be expressedin the form (xA - xB)2, where x, and zB are co-ordinates of theelements in some scale. Thus if the following numbers are assignedto various elements :+ A& = 2.05.H P I S C B r C l N O F0.0 0.10 0.40 0.43 0.55 0.75 0.94 0.95 1.40 2.00the value of any Am can be calculated. For example,will be (0.55 - 0)2 = 0.552,AeF will be (2.00 - 0 ~ 5 5 ) ~ = 1-45,’ and so on.Since the magnitude of AAB depends upon the ionic characterwhich the bond acquires by the unequal sharing of electrons betweenthe two atoms, the greater its value the further apart in a scale ofelectronegativity must the two atoms be.Thus the above seriesgives a quantitative measure of the electronegative character ofthe different atoms. The arrangement of the atoms in this definiteorder is extremely useful for purposes of discussing the propertiesand reactions of chemical substances. Quite often the relativedegrees of electronegativeness of various atoms have had to beassumed ad hoc for the purposes of this or that theory, but the presentseries provides a standard I based upon independent measurements.Incidentally, the series is useful for computing bond energies whichare not easily accessible to measurement.The forces which atoms exert upon one another are not of asimple nature.The Heitler-London type of valency force, whichgives rise to a bond consisting of two electrons with antiparallelspin moments, is reinforced or opposed by various other inter-actions including “ polarisation forces.” If two atoms with parallelspin moments approach, the effect predicted by the Heitler-Londontreatment is repulsion. This is opposed by the attractive force dueto mutual polarisation. For two hydrogen atoms the influence ofthis factor is considered to be unimportant, but with the alkalimetals it seems that the energy relations are quite different and that“ polarisation molecules ” may be formed. According to H.Kuhn,lG there occur in alkali-metal vapours, near the principalseries lines, absorption bands due to such molecules.The bandsare said to be quite Werent from the well-known bands of the Na,type, and occupy a, very narrow spectral region near the atomiclines, on account of the smallness of the energy of dissociation.Kuhn suggests that the following sequence should be traversed byalkali absorption spectra as the pressure is increased : atomic,2. Physik, 1932, 76, 78220 GENERAL AND PHYSICAL CHEMISTRY.true molecules (singlet state) , polarisation molecules, and finally,continuous absorption from atoms a t the moment of collision-What is interesting from our present pointof view is not the validity of any given interpretation of particularspectroscopic observations, but the elaborate possibilities of atomicinteraction which appear in general to be possible.We now advance one stage further in complexity, namely, tocarbon compounds.The success with which organic chemistry has solved its problemsby the aid of its own conceptions about the nature of chemicalbonds has, during the last few years, stimulated theoretical physiciststo attempt the translation of these conceptions into the language of.quantum mechanics.It is as well to realise a t the outset that eventhe simplest problems of organic chemistry are much too complicatedfor anything like a complete and fundamental treatment not basedupon drastic simplification and not introducing a considerablemeasure of assumption. The theoretical investigation, therefore,can hardly be expected to predict new phenomena in organicchemistry.Nevertheless, it is satisfactory that the known phenomenacan be described in terms acceptable to physicists, and that the rulescan be formulated in ways which at least are not inconsistent withquantum-mechanical principles. In previous Reports referencehas been made to theoretical interpretations of the rigidity of doublebonds, the stability of ring systems, and substitution into thebenzene n~c1eus.l~ Such matters have been further dealt withby F. Hund,18 and by E. Huckel,l9 and H. Eyring 2O has discussed theproblem of steric hindrance.Huckel refers the characteristic behaviour of benzene to theexistence of a kind of closed group of six [p]h electrons (the properfunction of which has a node in the plane of the ring). Me treatstheir interaction by a method similar to that used by Bloch for work-ing out the interaction of electrons in metals, and extends the dis-cussion to include naphthalene, anthracene, phenanthrene, di-phenyl, and conjugated chain systems.All the rings are assumedto be plane, the plane arrangements being “ stabilised by the chargedistribution of the [p]h electrons with the node of the proper functionsin the plane of the atoms.” He makes calculations about thesymmetry of the various proper functions, and arrives at variousconclusions. Condensed ring systems all possess completed electrongroups like benzene, and the binding energy per electron is not veryquasi-molecules.” < Cl 7 Huckel’s views on this matter have been criticised by A. Lapworth andl8 2.Physik, 1932, 73, 565; A . , 215.2o J . Amer. Chem. Xoc., 1932, 54, 3191; A., 996.R. Robinson, Nature, 1932, 129, 278.Ibid., 76, 628(6 TRUE ” DEGREE OF DISSOCIATION OF STRONG ELECTROLYTES. 21different from that of the electrons in benzene. Huckel remarksthat the addition of alkali metals occurs with different ease withthe different compounds, and that the “ same order exists for theenergy of the lowest unoccupied states.” The position of the lowestunoccupied state (i.e., its energy level) is a measure of the“ Abgeschlossenheit ” (i.e., completeness, closed nature, orstability) of the electron group in respect to the taking up of electrons.Eyring’s discussion of steric hindrance is based upon differentprinciples. He uses potential-energy curves first in consideringthe approach and “ collision ” of two molecules, and then in treatingthe rotation of two methyl groups about an axis joining the twocarbon atoms.The transition between covalent and electrovalent bonds, andthe complexity of atomic interactions in general, are subjects whichcome very much into prominence in the theory of electrolytes.The Debye-Huckel theory having shown that the most importantproperties of dilute solutions of strong electrolytes can be accountedfor by assuming complete ionisation, the question arises whetherexisting deviations from the theory are partly due to the existencein solution of real molecules even of such substances as sodiumchloride.This matter, and also the question of heat of dilution,which depends upon interionic forces and the forces between ionsand dipole solvent molecules, is discussed in the following sections.C.N. H.2. THE “ TRUE ” DEGREE OF DISSOCIATION OF STRONUELECTROLYTES.This problem presents itself in several rather complicated aspects.In the first place it involves the prior question as to whether any-thing equivalent to a molecule really exists in the solution of a strongelectrolyte; if this question be decided in the negative, it is stilllegitimate to enquire whether it is not desirable on the grounds ofexpediency alone to treat as molecules complexes of oppositelycharged ions associated with a certain degree of permanence, and thussomewhat arbitrarily to divide the solution into ions and molecules.The second major problem, which arises if either of the first twoquestions is answered in the affirmative, is that of determining the“ true ” degree of dissociation.The answer to the first question-whether molecules exist insolutions of strong electrolytes or not-may be sought in two distinctways.On the one hand, we may examine the electrolyte for pro-perties which we have reason to believe are characteristic of undis-sociated moleoules ; this is the more distinctively experimentalapproach. On the other hand, we may endeavour to refine th22 GENERAL AND PHYSIUAL CHEMISTRY. WOLBENDEN :original calculations of Debye and Hiickel so as to extend theirapplicability to less dilute solutions ; if the mathematical difficultiesinvolved in this can be overcome, we can then compare thetheoretical predictions with the experimental data and thus testthe adequacy of the purely electrostatic picture of a moderatelyconcentrated solution.The only properties characteristic of undissociated molecules,which are available in this connexion, are their volatility or solubilityin a non-polar solvent and their optical properties.The vapourpressure of hydrogen halides above their aqueous solutions isunmistakable qualitative evidence of the existence of a small con-centration of molecules in solution, but no quantitative estimateof their amount can be made without introducing a hypotheticalpartition coefficient for the molecules. By using arguments byanalogy with alkyl halides or with hydrogen cyanide, respectively,the concentration of molecules in 0-O1M-hydrogen chloride solutionwas found to be 5.9 x 10-l2 by L.Ebert 21 and 3 ‘x 10-lO by K.Fajans.22 Treating the vapour pressure data in a different may,W. F. K. Wynne-JonesZ3 has estimated the concentration of un-dissociated hydrogen chloride in M-solution to be 4 x 10-8. Thesevalues are probably of’ the right order and indicate the extremelylow concentration of molecules present a t a concentration where theconductivity ratio is about 0.97. Partition methods are inapplic-able to salts, and here we have to rely on the optical propertiespeculiar to undissociated molecules ; these are respectively the re-fractive index, the absorption spectra, and the Raman spectra ofelectrolytic solutions.Independently of‘ his rather speculativetheory of deformable ions, I<. Pajans 24 has shown that the changeof the refraction of salt solutions with increasing concentration runsparallel with the changes in refraction with concentration of the corre-sponding acids where the refraction is tending towards the refractionof the pure covalent acid; this may be regarded as qualitative evi-dence of incomplete dissociation. Faj am’s other more quantitativearguments to the same end are based on his hypothesis of deform-able ions and are more equivocal. E. Schreiner 26 has endeavouredto make a quantitative estimate of the degree of dissociation ofhydrogen chloride and bromide in 4N-solution from refractiondata ; his values, 94.6% and 96-676 respectively, correspond tomuch less complete dissociation than the partition data suggest.z1 Naturwiss., 1926, 13, 393.23 Trans.Il’araday SOC., 1927, 23, 357; A., 1927, 1023.23 J . , 1930, 1064; A., 1930, 859.24 See E. Lange, Physikal. Z., 1928, 29, 767.35 Naturwiss., 1925, 13, 245(( TRUE ” DEGREE OF DISSOCIATION OB STRONG ELECTROLYTES. 23The absorption curves of nitric acid and of various salts over arange of concentrations show a common intersection point, accord-ing to H. von Halban.26 Such a phenomenon would occur if thesolute were changing progressively from one form with its character-istic absorption curve into another. Halban regards the two formsas molecules and ions respectively; he finds further evidence forincomplete dissociation in the deviations from Beer’s law shownby numerous salts in concentrated solution.Of the experimental methods available for the detection of un-dissociated molecules in solution, there can be little doubt that thestudy of the Raman spectra of electrolytes is by far the most elegantand the most satisfactory from a theoretical point of view.Theinteratomic linkage formed when two ions unite to form a moleculemust lead to the development of one or more distinctive Ramanlines. If, therefore, the Raman spectrum of a solution of anelectrolyte shows lines other than those known t o be characteristicof the solvent and of the constituent ions of the electrolyte, it maybe safely inferred that midissociated molecules are present ; 27since ions whose electron shells are of the inert-gas type produceno Raman lines themselves, the criterion is peculiarly clear-cut forsalts like the alkali halides.The principal defect of the method isthat, a t the present state of development of technique, the line-producing molecule must be present in substantial concentrationif it is to be detected; Raman spectra cannot therefore be expectedto show the presence of undissociated molecules whose concentrationis much less than, say, 0-1N. The experimental results of L. A.Woodward 2s and others reveal PO molecules as present in aqueoussolutions of potassium chloride, hydrogen chloride, potassiumcyanide, hydrogen fluoride, iodic acid, and sodium hydroxideamongst others, whereas solutions of nitric acid, mercuric chloride,and mercuric cyanide show molecules; the Raman spectra ofsolutions of sulphuric acid show very clearly the progressive dis-appearance of the molecules and intermediate ions as the concen-tration diminishes.Perhaps the only surprising feature of the resultsis the absence of any evidence for molecules in solutions of hydrogenfluoride.a 6 2. Ebktrochem., 1928, 34, 489.Except for the theoretical possibility that the mutual approach of theions in concentrated solution may remove the “ Verbot ” on an existingfrequency inside om of the ions by disturbing the symmetry property whichpreviously forbade its appearance; see G. Placzek, 2. Physik, 1931, 70, 84;A., 1931, 893, and Leipzigsr Vortrage (“ Molekiilstruktur ”), 1931, p.71.(Private communication from Nr. L. A. Woodward.)This paper contains a usefulbibliography.28 Physikal. Z., 1931,32,777 ; A., 1931,136724 GENERAL AND PHYSICAL CHEMISTRY. WOLFENDEN :Summarising the evidence derived from the study of propertiesbelieved to be characteristic of undissociated molecules, one maysay that, apart from the acids, there is virtually no unequivocalevidence of the existence of molecules in solution of " strong "uni-univalent electrolytes at any concentration.The more noteworthy of the attempts to extend the range ofvalidity of the ionic-atmosphere calculations to less dilute solutions,while preserving the principle of complete dissociation, are the so-called " second approximation " of P. Debye and E. Huckel z9 andthe treatment of T.H. Gronwall, V. K. LaMer, and K. Sand~ed.~OThe former of these replaces the point charges of the simple theoryby spheres of finite size with a least distance of approach a. Theintroduction of this parameter into the expression for the logarithmof the activity coefficient has the effect of increasing the activitycoefficient to an extent which increases with the size of a ; that isto say, with ions of finite size the activity coefficient diminishes lessrapidly with increasing concentration than is predicted for point-charge ions. Quantitatively this " second approximation " iscapable of expressing the experimental activity coefficients forelectrolytes with Earge ions up to concentrations of the order ofO-lN, using quite plausible values for a ; on the other hand, forsome electrolytes, such as potassium nitrate and potassium iodate,the expression leads to impossibly small values for a.Thus thesingle auxiliary assumption of a finite size for the ions is seen to beinadequate to account for the facts in more concentrated solution.A more thorough and more complicated extension of the simpletheory is that of Gronwall, LaMer, and Sandved. Their treatmentnot only introduces the least distance of approach, but also takesinto account the further terms of the series for the potential energyof the ion due to the atmosphere, a series of which the simplifiedtreatment neglects all but the first term. The notable featuresof the resulting equation for the logarithm of the activity coefficientare that, for small ionic radii, activity coefficients less than those ofthe simplified theory are predicted, and also that the behaviourof electrolytes like potassium nitrate and potassium iodate isadequately represented up to O.1N-concentrations by postulatingsmall but not impossible values for a.Thus, so far as activity coefficients are concerned, the treatmentof these authors gives an adequate representation of the facts up to0-1N-solutions with the aid of an admittedly complicated equation,which, however, contains only one adjustable parameter a, whosevalues are always physically plausible.When the same treatment29 Physikat. Z., 1923, 24, 185; A., 1923, ii, 469.30 Ibid., 1928, 29, 368; A., 1928, 841“ TRUE ” DEGREE OF DISSOCIATION OF STRONG ELECTROLYTES.25is extended to heats of dilution, as has been done by E. Lange andJ. Meixner,31 it is, however, found to be inadequate to explainthe facts, and, in particular, the a values necessary to account forthe heats of dilution of a series of salts are sometimes graded inmagnitude in the opposite sense to the values necessary to makethe activity coefficients “ fit.”Although neither the “ second approximation ” of Debye andHuckel nor the treatment of Gronwall, LaMer and Sandved (norseveral other attempts in the same direction) has succeeded inaccounting for the behaviour of electrolytes outside the limitingrange of concentration in purely electrical terms, the conclusionmust certainly not be drawn that the postulation of undissociatedmolecules is therefore necessary at these concentrations.The factof the matter is that the difficulties of any complete treatment of theelectrical forces in concentrated solutions are beyond our mathe-matical equipment at the present time. The attempts just describedwere only made possible by concentrating on one or two of the com-plicating factors and neglecting the remainder. Apart from suchfactors as the influence of the electrolyte on the dielectric constantof the solvent and the temperature variation of a, the proximityof the ions in concentrated solution must certainly add to the long-range Coulomb forces between the ions the far from negligible short-range forces generally characterised as “ van der Waals forces.”Pending an adequate mathematical treatment of the problem,there is some justification for regarding the postulation of undis-sociated molecules in such solutions as an unnecessary hypothesis.Mid-way between the purely electrostatic picture of a solution andthe view which assumes the existence of undissociated moleculesis the “ion-association” theory of N.Bjerr~m.3~ He points outthat the Debye-Huckel postulate, that the potential energy of anion is much less than its kinetic energy, is less likely to be true thehigher the valency of the ions, the lower the dielectric constantof the solvent, and the closer the ions can approach one another(i.e., the smaller their radii). He shows that the probability of ax-valent ion being at a distance r from a similar ion of opposites i p passes though a minimum value given by the equationwhere E is the electronic charge, D the dielectric constant of thesolvent, k the Boltzmann gas constant, and 17 the absolute temper-ature.Inside this radius the probability increases very rapidlyowing to the strong attractive forces exerted between the ions.31 Physikd. Z., 1929, 30, 670; A., 1928, 1389.33 Ergebnisse d. exakt. Xaturwiss., 1926, 5, 12526 GENERAL AND PHYSICAL CHEMISTRY. WOLFENDEN :Por aqueous solutions of uni-univalent electrolytes a t 18”, rmin. hasthe value 3.52 A. An electrolyte with ions the sum of whose radiiis greater than this critical value, is treated by Bjerrum as completelydissociated and susceptible to the unmodified Debye-Huckeltreatment.If the sum of the ionic radii is less than rmin.3 Bjerrumarbitrarily divides the ions into two groups, namely, those whosedistance apart is more than rmin., which are assumed to be free, andthose within the minimum distance, which he treats as “ ion-pairs.”The proportion of ion-pairs is calculated by integrating the probabilityfunction over the interval from rmin. down to the sum of the ionicradii.Although the line of demarcation between free and associatedions. is thus drawn at a quite arbitrary point (the probability mini-mum being associated with no physical discontinuity) Bj errumapplies the mass-action law to the equilibrium between ion-pairs andfree ions. The activity coefficient of the ion-pairs is put equal tounity and that of the free ions is calculated from the Debye-Hiickelsecond approximation,” rmin.being put in as the a parameter.In this way a series of degrees of “ ion-association ” are calculatedwhich increase with concentration and also with diminution in theradii of the ions concerned. The over-all activity coefficients maythen be calculated and are found to be in good agreement withexperiment up to concentrations of the order of 0.L” Like theexpression of Gronwall, LaMer, and Sandved (and in contrast tothe “ second approximation ” of Debye and Huckel), Bjerrum’streatment leads to values of the ionic radii which are always positiveand of plausible magnitude.I n spite of its somewhat arbitrary mathematical derivation, thehypothesis of “ ion-association ” has various attractive features.It represents the experimental facts as adequately as the morecomplete mathematical analyses ; it gives a clearer physical pictureof the solution; and it is perhaps worth noting that the possibilityof “ion-complexes” (composed of more than two ions) at highconcentrations in solvents of low dielectric constant offers a possibleexplanation of the increase of equivalent conductivity a t highconcentrations after passing through a minimum as observed byW alden .The “ ion-association ” hypothesis can hardly be said to be oneof complete dissociation, since the ion-pairs of Bjerrum are regardedas temporary juxtapositions of undeformed and completely solvatedions whose equilibrium with “ free ’’ ions is for reasons of expediencytreated as subject to the mass-action law.There remain to be con-sidered two points of view in both of which is postulated an equili-brium of the true Arrhenius type (corrected for activity coefficients)< '' TRUE " DEGRZB OF DISSOCIATION OF STRONG ELECTROLYTES. 27between undissociated molecules and ions subject to the electro-static forces of the Debye-Ruckel limiting equations. The Grstof these is primarily associated with the name of W. Nernst and isbased on a consideration of heats of dilution; the second, due toC. W. Davies and to L. Onsager in the Grst instance, is based onconductivity data.Nernst 33 divides the experimentally observed integral heat ofdilution into two parts; the first of these is the heat absorbed in thedissociation of the un-ionised portion of the electrolyte, and thesecond is the electrostatic heat of dilution of the ionised portion.This leads to the equationv, = - &(1 - a) + E a d Zwhere Q is the heat of ionisation of the molecules, c the concentrationof the solution, oc the true degree of dissociation, and B the numericalcoefficient of the electrostatic heat of dilution (see equation 3 ;p.30). The validity of the mass-action law for the dissociationof the ions being assumed, it is possible by applying the van 'tHoff isochore to the measurements of the heat of dilution of anelectrolyte at two temperatures to evaluate the two unknownsQ and a by a series of successive approximations, and thus to pre-dict the variation of the integral heat of dilution over the wholerange of concentrations.Several approximations and assumptionsare employed ; instead of the theoretical proportionality factorbetween electrostatic heat of dilution and the square root of theconcentration, Nernst equates B to the observed slope for lithiumchloride which is thus regarded as an ideal completely dissociatedelectrolyte ; furthermore, the activity coefficient of the ions is equatedto unity over the complete concentration range ; finally, it is assumedthat the electrostatic contribution to the heat of dilution maintainsits linear relation with the square root of the concentration up tothe highest concentrations involved. In spite of these simplifyingassumptions, it is found that the Nernst equation represents theexperimentally determined heats of dilution satisfactorily up toconcentrations of the order of N / 3 and N .The degrees of dis-sociation of sodium chloride and potassium nitrate in 0-1N-solutionare given as 98.9% and 95.2% respectively at 18". In spite of itsconcordance with experimental facts for the uni-univalent saltsstudied, the Nernst treatment cannot be regarded as entirelysatisfactory since it embodies several assumptions that are certainlyuntrue; it is also a t variance with the individualities in the heatsof dilution of electrolytes (referred to on p. 32) a t very low con-centrations where the undissociated portion, which is roughly pro-a3 2. Elektrochem., 1927, 33, 428; A., 1928, 12728 GENERAL AND PHYSICAL CHEMISTRY.portional to the first power of the concentration, can no longer beof significance.A recent paper by E. Plake,34 in which the heatsof dilution of uni-bivalent and bi-bivalent electrolytes are treatedfrom the Nernst point of view, arrives a t the conclusion that,whereas uni-univalent electrolytes are incompletely dissociated,the electrolytes of higher valency are completely dissociated ; thisinference is so much at variance with accepted views that it canhardly fail to shake one’s confidence in the underlying hypothesis.The derivation of true degrees of dissociation from conductivitymeasurements has been treated by L. On~ager,~5 C. W. D a v i e ~ , ~ ~M. and other workers ; their respective treatments areidentical in principle although the most accurate method is probablythat of Davies, which may be taken as representative of the others.The fall of equivalent conductivity with increasing concentrationis attributed jointly to (1) the decrease in mobility due to electro-static forces as calculated by the Debye-Hiickel-Onsager equationand (2) the diminution in number of the ions free to conduct owingt o the formation of undissociated molecules.Since the first effectis readily calculable, the magnitude of the second can be found.The method of calculation employed by Davies is as follows:Let cc be the true degree of dissociation of an electrolyte, whoselimiting equivalent conductivity is A,, a t a concentration where theequivalent conductivity is A,.Then a is not given by &/Ao butby &/Azy where A, is the sum of the ionic mobilities in the solutionconsidered. Since the concentration of the ions is cA,/A,, the valueof A, is given by the Onsager equation, which for an aqueous solutionof a uni-univalent electrolyte at 25” isA, = A, - (0.22711, + 59-78)dcAC/AzThis is a cubic equation in A, and is solved as such by Wien ; Daviesprefers to evaluate A, by a short series of successive approximations.When A, has been determined in this way, the true degree ofdissociation is immediately evaluated as &/Ax. Davies then appliesthe mass-action law, corrected for the activity coefficients of theions, to the true concentrations of ions ci and undissociated mole-cules c, obtained in this way, and writescFf?/cu = Kthe activity of the undissociated molecules being put equal to unity.The constancy of this relation can be tested directly or graphically34 2.physikal. Chern., 1932, [ A ] , 182, 257.35 Physikal. Z., 1927, 28, 277; A., 1927, 617.3% Trans. Farahy Soc., 1927, 23, 351.37 See H. Falkenhagen, “ Elektrolyten,” p. 299WOLFENDEN : THE THERMOCHEmSTRY OF ELECTROLYTES. 29in the following manner :taking logarithms, we may therefore write the above equation asAt high dilutions - lOgfi = A 6 ;log c?/c, = log K + 2 A f iPlotting log@/c, against fi, we should therefore expect to geta straight line whose slope is 2A and whose intercept on the axisof zero concentration is log R.Davies has evaluated the true degrees of dissociation of a numberof salts in this way, and has obtained corrected mass-action constantswhich are a very marked improvement on the Ostwald ‘‘ constants ”for the same electrolytes.Its extension to non-aqueous solutions,where incomplete dissociation is much more common, is likely to beof great value ; unfortunately, its application is there handicappedby the scarcity of reliable values for A, and by the very small con-centration range over which Onsager’s equation is valid in solventsof low dielectric constant. Although the validity of this methodof determining true degrees of dissociation can only be tested overthe range of concentrations in which Onsager’s equation is applicable,it is important to notice that, provided that a satisfactory constantcan be evaluated for a given electrolyte over this range, the degreeof dissociation can then be found a t higher concentrations frommeasurements of activity alone.The only limit to such an extensionis imposed by the condition that the activity of the undissociatedmolecules must approximate to the concentration. It is unfortunatethat the method does not lend itself to cases where dissociationmust be very nearly complete ; the mode of calculation is susceptibleto considerable error unless the un-ionised fraction is present inappreciable amounts. Thus, in the case of nearly all uni-univalentsalts in water, the un-ionised fraction only becomes measurablea t concentrations where the Onsager equation is inapplicable, andrecourse must be had to an empirical conductivity equationembodyinga viscosity correction.Notwithstanding these limitations and thefact that no physical picture i s afforded of the nature of the “ un-dissociated ” portion of the electrolyte, the Davies method oftreating conductivity data is probably the least equivocal way ofgaining infomtion as to the degree of dissociation of electrolytes.J. H. W.3. THE THERMOCHEMISTRY OF ELECTROLYTES.At the time when the thermochemistry of electrolytes wm lasttouched on in these Reports,38 it was necessary to record a seriousdiscrepancy betwccn the predictions of the interionic attractiontheory concerning the heat of dilution of electrolytes and the38 Ann. Reports, 1027, 24, 2330 GENERAL AND PHYSICAL CHEMISTRY.experimental data available at the time.Theory predicted that theheat of dilution of the ideal electrolyte in aqueous solutions mustbe positive, whereas the measurements then published showednegative heats of dilution for the majority of electrolytes. Precisemeasurements of heats of dilution of electrolytes a t very low con-centrations carried out over the last five years by E. Lange 39 andhis collaborators have served to remove this discrepancy and toconfirm in a general way the interionic attraction theory in thisfield.The heat evolved when a volume of solution sufficient to containone mol. of electrolyte is diluted to infinite dilution is called theintegral heat of dilution and is usually denoted by the symbol Vc.In the ideal electrolyte of the Debye-Hiickel theory this heat effectis due to purely electrostatic forces, and its magnitude may becalculated by the application of the Gibbs-Helmholtz equation tothe electrical free energy of the solution.where QC is the heat of dilution per c.c., and F,, the electrical freeenergy per C.C.of the solution, is negative for all finite concentrationsof the ideal electrolyte and converges to zero as the concentrationbecomes infinitely small. The solution of this equation for a binaryelectrolyte consisting of two x-valent ions leads to the expressionWe thus haveQC = P, - T(aB',/aT), . . . . . (1)Nc2z2 v--- 8xz2E2N (1 + 21 dD) 2/c . . . D 1OOODET D'dT c -where N = Avogadro number,E = electronic charge,II: = Boltzmann gas constant,D = dielectric constant of the solvent,and c = concentration of the solution in mols./litre.Giving the universal constants their numerical values, inserting thedielectric constant of water and its temperature coefficient, and con-verting from ergs to calories, we obtain the expression for aqueoussolutions a t 25" :Vc = + 4 9 0 ~ ~ 6 calories .. . . (3)39 Thirty-six papers have already appeared, of which the last is by H.Hammerschmid and E. Lange, 2. physikal. Chem., 1932, [ A ] , 160, 445 ; A.,913. For summarising paper, see E. Lange and A. L. Robinson, Chem.Reviews, 1931, 9, 89.40 0. Gatty (Phil. Mag., 1931, 11, 1082; A., 1931, 685) and, later butindependently, G. Scatchard ( J . Amer. Chem. SOC., 1931, 53, 2037 ; A., 1931,913) have pointed out that this equation involves the erroneous assumptionthat (dD/dT)v and .,(dD/dT), are mutually interchangeable. The correctedequation includes an extra term involving the thermal expansion of thesolvent ; this term is small for water but of significance in non-aqueous solventsWOLFENDEN : THE THEBJklOOHEHCSTRY OF ELECTROLYTES.31The important features of this expression are (1) that the heat ofdilution (or more precisely the electrostatic contribution to the heatof dilution) is always positive in aqueous solutions-this is equallytrue for virtually all solvents of high dielectric constant (see below) ;(2) that the heat of dilution is proportional to the square root oftha concentration ;(3) that the heat of dilution is identical for electrolytes of the samevalency type.The positive sign of the electrostatic contribution to the heat ofdilution is remarkable. It seems at first sight unreasonable to ex-pect that the dilution of a completely dissociated electrolyte, inwhich the formation of ionic atmospheres is well known to lead to a,predpminance of attractive over repulsive force, should lead to theevolution of heat.The solution of the paradox depends on theforces exerted by the ions on the dipole molecules of the solvent.N. Bjerrum 41 expresses this by saying that the energy absorbed inincreasing separation of the ions with progressive dilution is morethan compensated by that evolved as more and more solvent dipolemolecules give up their kinetic energy by orientation round the ions,Le., that the compensating factor is, in effect, the energy released byincreased " electrostatic solvation." Such a physical picturecannot, of course, be rigidly deduced from the thermodynamiccalculation itself.Examination of the latter shows that the heatof dilution will only have a positive sign when the temperaturecoefficient of the dielectric constant of the solvent has a sufficientlylarge negative magnitude to make the term (1 + T / D . dD/dT)in equation (2) negative. This proviso is equivalent to the conditionthat the negative value of dD/dT must be large enough to cause theelectrical free energy of the solution to increase its numerical(negative) value with rise of temperature (owing to increased electro-static forces between the ions) sufficiently rapidly to cause the term2"(Ue/ljT)v to have a larger numerical value than the term Fe inequation (1). Since dD/dT depends, roughly speaking, on the dipolemoment of the solvent molecules, it is possible to see in 8 qualitativeway how the thermodynamic condition for positive heats of dilutionagrees with Bjerrum's physical picture. An examination of theavailable dielectric constant data shows that TID . dD/dT isalgebraically less than - 1 in the case of all common ionisingsolvents, although the values for some solvents of lower dielectricconstant, such as acetaldehyde42 (D = 21-1, T/D .dD/dT =-0.88)and phosphorus trichlorida" (D = 3.5, T/D . dD/dT = -0.79),41 Z.physika1. Chem., 1926,119,145; A., 1926, 476.ps T.M. Lowry, J., 1932,207; A., 322.P. Drude, ibicl., 1897, 25, 26732 GENERAL AND PHYSICAL CHEMISTRY.lead to negative values of the hypothetical heat of dilution of idealelectrolytes dissolved in such media.The quantitative test of the theoretical expression in any solventis of peculiar difliculty for two reasons. First, it involves themeasurement of temperature changes of the order of a few millionthsof a degree. Secondly, the predicted value of the heat of dilution isextremely sensitive to small errors in the temperature coefficientof the dielectric constant of the solvent, a quantity whose magnitudeis very uncertain; even in water the numerical coefficient of equa-tion (3) is subject to an uncertainty, on this account,of about 10%.Lange and his collaborators have overcome the experimentald8iculties with great skill by developing a differential methodbased on the well-known principle of the twin calorimeter.ADewar vessel is divided into two halves separated by an insulatingdiaphragm containing a thermocouple of 1000 junctions, sensitiveto temperature differences of lo-''. The dilution is carried out inone half of the vessel while the other half, containing solvent only,serves t o balance the effect of the heat of stirring, heat loss due toevaporation, etc. The technique has been refined to the pointwhere heats of dilution can be measured down t o M-con-centration. Precision of this order has enabled them to test thetheoretical equation within the " limiting range " of Debye-Hiickelcalculations.Their measurements cover electrolytes of uni-uni-, bi-uni-, andbi-bi-valency types but have been confined to aqueous solutions.The principal results may be summarised as follows :(1) The integral heat of dilution is invariably positive at lowconcentrations.(2) The integral heat of dilution is proportional to the square rootof the concentration up to M/100 for uni-univalent electrolytesand over a correspondingly smaller concentration range for thehigher valency types.For a minority of salts, such as potassiumnitrate, the range of obedience to the square-root relation is a gooddeal more limited.(3) Within the limits imposed by our uncertainty as to thevalue of dD/dT, the limiting slope of V, plotted against &agreeswith the predicted value.(4) Even at the lowest concentrations experimentally attainable,small but quite definib differences in limiting slope persist amongvarious salts of the same valency type ; this is true of uni-univalentsalts and is more marked with ions of higher valency.The individuality of electrolytes, Le., their deviation from theideal behaviour postulated by the Debye-Huckel theory, seems topersist in their thermochemical properties down to concentrationWOLFENDEN : THE THERMOCHEMISTRY OF ELECTROLYTES.33substantially lower than those a t which activity and conductivitydata suggest virtually ideal behaviour. It is similarly found that a tintermediate concentrations thermochemical differences betweenelectrolytes of the same valency type are much more striking thanthose observed in the activities and conductivities of the sameelectrolytes.W.Nernst44 has sought to account for these deviations by in-complete dissociation of the electrolytes concerned ; his view isbriefly discussed in the section on " the true degree of dissociationof electrolytes " (p. 27). Lange and his associates prefer to lookfor their cause in the simplifying assumptions and second-orderterms of the purely electrical treatment. In particular, they haveexplored the possibilities of three refinements in the simplifiedtreatment. Of these, the &st is the introduction of a series of avalues characteristic of the least distance of approach of the ions,which are no longer assumed to be point charges.The individualvalues that can be given to this added parameter make it possibleto account for differences between electrolytes of the same valencytype. Unfortunately, it is found, not only that the sequence inorder of magnitude of the necessary a values bears no consistentrelationship to the radii of either the ions in the crystal or thesolvated ions, but also that the sequence is in some cases the reverseof that which must be adopted to account for the activity data.The second refinement is the introduction of a term for the temper-ature coefficient of these a values, individual for each electrolyte.This involves a considerable complication in the theoretical treat-ment ; investigation shows that it involves an added negative termwhich is proportional to the first power of the concentration and there-fore unlikely to be of significance at the lowest concentrationsat which the individualities persist.The third and final avenueexplored by Lange is the possible effect of the electrolyte on thedielectric constant of the solvent. Here again the effect is probablyproportional to some higher power than the square root of theconcentration so that its significance will be small a t high dilutions.Furthermore, E. Lange and A. L. Robinson *5 have shown that,although the addition of urea reduces the temperature coefficientof the dielectric constant of water so much as to lead to the predic-tion of negative heats of dilution, when aqueous urea solutions areused as %L solvent the experimentally determined heat of dilutionof potassium chloride in such a solvent is only very slightly differentfrom that of the same salt when dissolved in pure water.The general conclusion to be drawn from the work of Lange and44 W.Nernst, 2. Elektrochern., 1927, 33, 428; A., 1928, 127.4 5 J. Amer. Chem, SOC., 1930, 52, 4218; A., 1931, 42.REP.-VOL. XXIX. 34 GENERAL AND PHYSICAL CHEMISTRY.his collaborators seems to be that, although the positive sign, thevariation with concentration, and the valency effect in the heat ofdilution of aqueous solutions are in harmony with the interionicattraction theory, certain residual individualities persist in thethermochemical properties of electrolytes at high dilutions for whichthe electrostatic theory in its present form is unable to account.Thermochemical measurements are seen to constitute a peculiarlysensitive means of exploring deviations from ideal behaviour inelectrolytes although it is not, at the moment, a t all clear whythis should be so.The reason is perhaps to be sought in thepeculiarly dominant r6le which ion-solvent forces (as distinct fromion-ion forces) play in heats of dilution.J. H. W.4. QUANTUM MECIIANICS AND ELECTROCHEMISTRY.The application of the new ideas of quantum mechanics to electro-chemistry has not been long delayed and some preliminary papersrecently published suggest that they are likely to give us a muchclearer insight into some electrochemical phenomena. The elucida-tion of electrode processes, of which the thermodynamic account isalready eminently satisfactory but whose mechanism has hereto-fore been obscure, is likely to prove particularly valuable.A recent paper by R.W. Gurney46 provides an interestingmechanism for overvoltage as well as sketching a physical pictureof the discharge of an ion a t an electrode; an important featureof Gurney’s mechanism for overvoltage is that the phenomenon isregarded as a primary effect and not in any way due to secondaryeffects such as bubble formation, gas films, or the combination ofdischarged atoms to form molecules.Fig. 1 represents the potential-energy curve of an electron alonga line joining the surface of an electrode of an inert metal t o aneighbouring hydrated cation such as the hydrogen ion.Thehorizontal lines MM represent the occupied electron levels in themetal, 4 being the work function of the metal. On the right is theCoulomb field and vacant electron level of the hydrated ion; owingto the positive heat of hydration of the ion W , the distance (E) ofthis vacant level below the standard level of zero energy is not I ,the ionisation potential of the ion-producing atom, but 1 - W ;E is the energy evolved when the ion is neutralised.In a second paper (ibid.,1932, [A], 136,378; A,, 699) Gurney deals with the relation between the con-tact potential difference at a metal-metal interface and the E.M.P. of thevoltaic cell. His treatment of this subject is interesting but not, however,essentially novel (see, e.g., J. A.V. Butler, Phil. Mag., 1924, 48, 927; A.,1925, ii, 42).4 6 Proc. Roy. SOC., 1931, [A], 134, 137; A., 26WOLFENDEN : QUANTUM' MECHANICS AND ELECTROCHEiVfISTRY. 35Although classical mechanics forbids the transition of an electronover the energy barrier, quantum mechanics represents an electronin the metal by a wave-function which does not end abruptly a tthe surface of the metal but dies away exponentially into thepotential barrier. Corresponding to this there is a finite prob-ability of an electron " leaking through " the barrier from the metalinto a vacant level of eqml energy in the neighbouring ion. In thecircumstances represented in the diagram (corresponding, e.g., to aplatinum electrode dipping in a solution of an acid). neutralisationof the hydrogen ion cannot take place because the vacant level inFIG. 1.I StandardLevel gfISurfBce of metal Nude us of cationLine perpendicdar t o surface o f metalthe ion is higher than the highest occupied electron level in themetal.In order that neutralisation may take place andcurrentmay peas through the electrode, the electron levels in the metalmust be raised by building up a negative (i.e., a " cathodic ") poten-tial in the metal. The negative potential necessary to causecurrent to flow is determined by the condition E >The above picture of the process of discharge of the hydrogenion is over-simplified in so far as (a) the hydration energy is notdefinite but is spread over a series of energy levels correspondingto a series of vibration levels in the hydrated ion, and (b) the metallicelectron levels are not all empty above nor all occupied below.Both of these distributions may be calculated; the former obeys a- EV36 GENERAL AND PHYSICAL CHEMISTRY.Boltzmann distribution, the latter is governed by the Fermi-Diracstatistics.The condition for the passage of a finite current through thecathode with the liberation of hydrogen (or the discharge of anyother cation) is that an appreciable number of high-energy electronsin the metal shall overlap the vacant levels in the positive ion.The variation of this overlap (and the consequent variation incurrent density) with the cathodic voltage and the temperature isthe main object of Gurney’s calculations.Having worked out thetwo distributions indicated above, he has calculated the probabilityof the transition or leakage of an electron across the potentialbarrier from the metal to the ion.By integration of this prob-ability between appropriate limits, the current density a t thecathode is calculated in terms of the cathodic voltage and thetemperature. His result, embodying certain reasonable approxim-ations, islog i = E~ - ‘1 + + log T + constantYkTwhere i is the current density, V the cathodic potential, T theabsolute temperature, k the Boltzmann gas constant, E, - El + ZVcorresponds t o the range of energies over which the probability isintegrated, and y is a small factor greater than unity and, to a firstapproximation, constant. Differentiating with respect to voltageand temperature respectively, we have d log i / d V = ~ / y k T andd log i / d T = (E, - E, - &V)/ykT2 + 1/T.These two equationsare in qualitative agreement with F. P. Bowden’s experimentalobservations : 47(a) that d log i / d V = A/T, where A is independent of the natureof the inert-metal electrode and of whether it is used as anode forthe discharge of oxygen or cathode for the discharge of hydrogenand( b ) that d l o g i / d T = B, where B decreases with increasing V .Furthermore, if y is given the not improbable value of 2, the agree-ment between &/@ and the empirically determined A is excellent.If, in addition, E, - El + EV (which corresponds to the overlap ofenergy levels over which the probability is integrated) is set at thereasonable value of one electron-volt, the temperature coefficient oflog i predicted is in good agreement with the observed values of B.I n this way Gurney has shown that two important characteristicsof overvoltage, vix., the variation of current density with appliedvoltage and with temperature, can be adequately and quanti-tatively accounted for by regarding the determining factor as theA ., 1930, 169.4 7 Proc. Roy. SOC., 1929, [A], 125, 446; A,, 1929, 1391; ibid., 126, 107WOLFENDEN : QUANTUM MECHANICS AND ELECTROCHEMISTRY. 37probability of the quantum-mechanical transition of an electronfrom the electrode to the cation to be discharged (or from the anionto be discharged to the electrode).Another application of quantum mechanics to an electrochemicalproblem is to be found in a paper by L.Farkas 48 on the conductivityof concentrated solutions of sodium in liquid ammonia. It is wellknown that, as the concentration of such a solution increases, theequivalent conductivity a t first diminishes proportionally t o thesquare root of the concentration, corresponding to electrolytic con-duction by sodium ions and probably solvated electrons; at aconcentration about O-lM, the equivalent conductivity passesthrough a minimum and then increases very rapidly until in satur-ated solution the specific conductivity is comparable with that ofliquid mercury. Corresponding to this rise in conductivity, thecontribution of the sodium ions to the carriage of the currentdiminishes rapidly and becomes insignificant in the more concen-trated solutions.Heretofore the rise in equivalent conductivity in concentratedsolution has received only a qualitative explanation which attributesit to the increasing proportion of free unsolvated electrons as theconcentration of sodium in the solution rises.The shift in theequilibrium between free and solvated electrons with increasingconcentration necessary to account for the observed rise in equi-valent conductivity is so great as to render this explanation far fromprobable.Farkas attributes the conductivity in concentrated solution tothe quantum-mechanical transition of electrons between neighbour-ing sodium atoms, which under the influence of an applied potentialgradient will take place more frequently towards the anode thantowards the cathode.Fig. 2 represents the potential-energy curveof an electron relative to two sodium atoms in a uniform potentialgradient such that the anode lies to the left of the figure. I isthe ionisation potential of the sodium atom, d, is the distancebetween the two sodium atoms, and the applied potential gradientis equal to (tanB)/(electronic charge). The probability of anelectron transition in either direction by leakage through the poten-tial barrier can be calculated by the Gamow-Condon-Gurneyformula and expressed in terms of the above quantities togetherwith the mass of the electron (m), the principal quantum number(n), and the orbital radius ( r ) of the outermost electron in the sodiumatom, the concentration of the solution (c), the Avogadro number( N ) , and Planck’s constant (h).By subtracting the two prob-abilities, the excess of electron transitions towards the anode can4 8 2. physikal. Chern., 1932, [A], 161,35538 GENERAL AND PHYSIUAL CHEMISTRY.be calculated, and hence the specific conductivity.approximation the result isTo a firstIf it is now assumed that the sodium atoms are distributed regularlythrough the solution as in a simple cubic lattice,* the distance apartof the atoms dc at a concentration c is given byac = I/VC x 6 x 1020Putting n equal t o 3, T equal to 1-7 x lo-*, and giving the universalFIG. 2.Direction o f (negat;~e)potent/b/gradient-t--constants their numerical values, we obtain the following expressionfor the specific conductivity at concentration c1 4.3 x 1oqqyFK~ = 3.10 x 10l1 * - <IThis equation leads t o a curve of specific conductivity againstconcentration very similar to but slightly steeper than that observedexperimentally.The value of I necessary to give the observednumerical values lies between 9000 and 10,000 calories per mol.;this is about 12 times as small as the ionisation energy in vucuo,whereas the dielectric constant of liquid ammonia is about 22. Inview of the approximate nature of the calculations and the absenceof arbitrary constants, the concordance is as good as could beexpected.If the atoms are distributedover a range of distances apart, the small number of atoms near the minimaldistance will play a dominant part in the quantum-mechanical transitions andthe probability of occurrence of this distance will change too slowly withincreasing concentration to account for the experimental facts.* This assumption is essential to the theoryHINSHELWOOD : CHEMICAL KINETICS.39In spite of the somewhat arbitrary assumption of lattice-likedistribution of' atoms in the solution, as well as the fundamentaldifficulty (which is also met with in the theory of the conductivityof metals) that each atom in the latt'ice is regarded a t one and thesame time as ionised (in order that it may receive an.electron) andun-ionised (in order that it may give up an electron), the quanti-tative success of the calculation is sufficient to make it of greatinterest as an application of quantum mechanical principles toconductivity.J. H. W.5. CHEMICAL KINETICS.The study of chemical kinetics depends essentially upon observ-ation of the progress of chemical reactions with time. Thence,conclusions can often be drawn, on the one hand, about the natureof transiently formed intermediate products, and on the other,about the physical laws determining molecular transformations.In both these respects the application of spectroscopic methods hasyielded information in a much more direct manner than kineticmeasurements could, and, in the second matter, quantum-mechanicaltheories can be of great assistance in predicting which kinds ofatomic and molecular processes are possible or probable. As anexample of the elucidation of reaction mechanisms by spectroscopicmeans, it is enough to refer to the identification of the various atoms,radicals, or molecules concerned in the emission of flame spectra(see p.59). To illustrate the application of such means in thediscovery of the physical nature of molecular transformations, weneed only take the investigation of photochemical primary processes(cf . following section).A theoretical classification of chemical rearrangements or de-compositions, which seems likely to prove of great importance, isthat which distinguishes " adiabatic " from non-adiabatic processes.The former kind occur with an accompanying electron transition,the latter without, and there are important differences betweenthem. The following is an example.According to G. H e r ~ b e r g , ~ ~the molecule of nitrous oxide has a singlet ground state, while N,and 0 would correspond t o a triplet state. Hence, if N,O changesinto N, + 0, there must be an electron transition, in fact theunimolecular decomposition of the nitrous oxide molecule wouldhave to be a " predissociation." It is believed that " radiationlesschanges " of this kind ordinarily occur between states of the samemultiplicity. " Intercombinations " can occur, but with a muchsmaller probability. Thus the life of an activated nitrous oxide49 2. physikal. Chem., 1932, [B], 17, 68; A., 680; cf. also R. Mecke, ibid.,18,53; A., 91540 GENERAL AND PHYSICAL CHEMISTEI’.molecule should be abnorindly long, before chemical transformationtakes place.Nitrous oxide absorbs continuously from 2000 A. to1680 A. and from 1550 A. to the edge of the Schumann region. Itis transparent a t longer wave-lengths, although the energy ofremoval of an oxygen atom is not great. These facts illustrate thenon-dissociability of nitrous oxide into N, and 0 in a primaryphotochemical act. Presumably, we must reckon with the occur-rence of non-adiabatic transformations also in the reactions of morecomplex molecules : some of these changes may be “ forbidden ”or associated with very small probabilities. The modification ofthe transformation probabilities by the “ perturbing ” action ofexternal forces may be one important factor in “catalytic ’)phenomena. But in any example of even moderate complexitya priori calculations are almost hopelessly difficult, so that it isprobable that only direct kinetic experiments can decide howimportant factors of this kind really are.The general theoreticaltreatment of adiabatic and non-adiabatic chemical processes is,however, exemplified in the papers of F. London,50 and of H. Pelzerand E. Wigne~-.~l The latter authors, discussing reactions of thetype A + BC = AB + C, show that the probability of electronicexcitation during the chemical rcaction is small when the lowest“ energy surface ” is far removed from the others. (Diagrams canbe plotted giving the potential energy of the system for all relativepositions of the atoms, as in the work of Eyring and Polanyireferred to in last year’s Report. These are the energy surfaces :there will be a different one for each of the possible states ofelectronic excitation of the system.)In previous reports 52 the question of quantum-mechanicalpassage through energy barriers has been mentioned.It appearsthat usually, or a t any rate in examples of chemical interest,transition probabilities calculated by means of this kind of theorydo not differ very much from the classical probability of passageover the energy barrier. The transition probability contains afactor involving the negative exponential of the mass of the particlepenetrating the barrier, the mass coming in from the mass termin the original Schroedinger equati0n.~3 When the particle is anelectron, the non-classical transition probabilities become very high.When the particle has the mass of an ordinary atom, the classicaland the non-classical probability become much closer.R. P. Bell 545 0 z. Prbysik, 1932, 74, 143; A . , 324.51 2. physikal. Chem., 1932, [B], 15, 445; A., 343.52 Ann. Reports, 1930, 27, 26 ; 1931, 28, 23.53 Cf. Gamow, “ Atomic Nuclei,” Oxford, 1931.54 Proc. Roy. SOC. (in the press)HINSHELWOOD : CHEMICAL KINETICS. 41has pointed out, however, that the hydrogen atom, or proton,occupies an exceptional position, and that, owing t o its small mass,appreciable deviations from classical behaviour may be expected.Among the consequences of these deviations is a departure from theArrhenius equation for the variation of reaction velocity withtemperature, in the sense that a t lower temperature, higher valueswould be found for the reaction rate than those predicted by theequation.As Bell points out, no really suitable data for testingthis exist. Spurious deviations from the Arrhenius equation 55 areof course quite common, so that it may be all too easy to " confirm "the operation of quantum-mechanical factors in this particularfield.From what has been said above about the application of methodsand theoretical ideas more or less connected with spectroscopy tothe problems of kinetics, it might be inferred that the more ordinarymethods of investigation were largely superseded, but this wouldhardly be a well-balanced judgment. The difficulty or evenambiguity of quantum-mechanical calculations in examples whichare not almost ideally simple will probably restrict their functiont o stimulating or interpreting rather than replacing or anticipatingdirect experiment.Moreover, methods which depend upontheoretical calculations or upon spectroscopic identification ofintermediate products can only assist in understanding details ofmechanism, and this knowledge is not of much use unless interestin the descriptive chemistry of the complete process is presupposed.The actual unfolding of phenomena in time has always been con-sidered worth observing for its own sake, whether by the contempla-tion of complex emergent qualities which make the changingpicture of nature as a whole, or by the scientific study of reconditeconstituents of this picture, such as chemical reactions.An interesting piece of descriptive chemistry has been growingup in connexion with reactions in the solid state, the type of changemost convenient for investigation being that where one solid yieldsanother solid and a gas.56 It is not usual that the second solidforms solid solutions in the first.This means that molecules orions of the second are more stable when placed in their own spacelattice than when uniformly disseminated among the molecules orions of the initial substance. Consequently, the chemical changecan take place more easily if there is ready formed some of the55 E.g., those due to the existence of two concurrent reactions with differentenergies of activation.Among systems recently investigated are CuS0,,5H20 + CuS04,H,0 +4H,O, M. L.Smith and B. Topley, Proc. Roy. Soc., 1931, [ A ] , 134,224, A., 26 ;Ag,CO,,"Ag,O + CO,, W. D. Spencer and B. Topley, J., 1929, 2633;Trans. Faraday Soc., 1931, 27, 94.B 42 GENERAL AND PHYSICAL CHEMISTRY.lattice of the reaction product to which fresh elements can attachthemselves. Thus reactions of this kind usually spread fromnuclei. These nuclei seem first to be formed on the surface of thecrystals. The conditions governing their formation are independentof those determining the rate a t which they grow as the newlyformed crystal face advances through the unchanged material.The nuclei can be “poisoned” and prevented from growing bythe action of foreign gases in the system.57 As the chemical changeprogresses, the extent of the interface between original substanceand reaction product alters and the rate of reaction thus varies ina complex manner.The shape of the curve representing the extentof reaction as a function of time depends upon the rate at whichfresh nuclei are formed relative to the rate of growth of existingnuclei. When the change spreads from a limited number of nucleifor each particle of the solid, the rate increases with time in an“ autocatalytic ” manner, and passes through a maximum. It ispossible by careful analysis of the form of the curves to draw con-clusions, on the one hand, about the rate of advance of the crystalface and, on the other, about the kind of nucleation process occur-ring. 58When the rate of advance of the new crystal face is known as afunction of temperature, it is possible to attempt a correlation ofthe absolute rate of reaction and the “energy of activation,” andso to test hypotheses about the mechanism by which the new phasegrows.The complete answer to the question of mechanism hasnot yet been found, but Topley 59 has recently made an interestingexploration of possibilities, and concludes that, for the dehydrationof copper sulphate pentahydrate to monohydrate, “ it appears thatit is just possible to account for the observed rate, if four degrees offreedom in the complex cation are taken into account, and regardedas strongly coupled through the central Cu” ion; in addition, avery rapid redistribution of energy inside the activated complex isrequired.”In a review 6O of chemical kinetics in 1927, reference was made tothe fact that a number of bimolecular reactions in solution proceed5 7 E.g., the silver nuclei in the system Ag,C,O, -+ 2Ag + 2C0, are“ poisoned ” by oxygen.5 s ~ €3.Topley and J. Hume, Proc. Roy. SOC., 1928, [ A ] , 120, 211 (for thedecomposition of calcium carbonate hexahydrate in contact with water) ;R. S. Bradley, J. Colvin, and J. Hume, ibid., 1932, [ A ] , 137, 531 ; A., 1094(for the same system and for the dehydration of potassium hydrogen oxalatehemihydrate).59 Proc. Roy. SOC., 1932, [ A ] , 136, 413; A., 702 (for further references, seethis paper).Go Ann. Reports, 1927, 24, 314UINSHELWOOD : CHEMICAL KINETICS. 43at rates very much smaller than those given by the expression,(number of collisions) x e--E'RT, which predicts the correct orderof magnitude for a considerable number of gas reactions dependingon collisions between fairly simple molecules.At that time thediscrepancy was thought t o be due to a deactivating influence ofsolvent molecules. There proves, however, t o be no such generaldeactivating influence. I n the first place, the decomposition ofchlorine monoxide 61 and the interaction of ozone and chlorine 62have been shown to occur a t newly the same rate in solution incarbon tetrachloride as in the gas phase : thus reactions dependingon the co-operation of two molecules are not necessarily interferedwith by the solvent. Secondly, it has been found that two reactions,namely, the combination of triethylamine and ethyl iodide, and theesterification of acetic anhydride by ethyl alcohol, both of whichare " abnormally slow " to the extent of many powers of ten inhexane or in carbon tetrachloride solution, do not take place anymore rapidly in the gas phase.63 (Indeed, even such reaction asthe vapours undergo may be confined to the glass surface of thevessel.) Thus again it appears that, whatever the anomaly maybe, it is not directly connected with solvent action.It also appearsthat the " abnormally slow " reactions in solution are not neces-sarily the most characteristic. Further investigation of the litera-ture 64 reveals the existence of a considerable number taking placeat about the rate predicted by the simple formula, and of a furtherclass in which the rate is many times greater. To account for theseIatter it is necessary to assume the participation of varying numbersof internal degrees of freedom in the activation mechanism, aswith gaseous reactions of rather complex molecules.What causesunderlie the wide variations on either side of what might be called" standard behaviour " of bimolecular reactions in solution is aninteresting problem, about which various views are possible. Butthe time is hardly ripe for discussing them.Many of the subjects discussed in these reports in the last fewyears are still rapidly developing, and it is impossible to do justiceto more than a quite arbitrarily selected few. H. von Hartel, N.Meer, and M.Polanyi have made an exhaustive study of the inter-action of alkyl chlorides and sodium vapour with the object offinding out how the ease of reaction varies with the structure of the61 E. A. Moelwyn-Hughes and C. N. Hinshelwood, Proc. Roy. SOC., 1931,[ A ] , 131,177.6z E. J. Bowen, E. A. Moelwyn-Hughes, and C . N. Hinshelwood, ibid., 134,211; A . , 2 5 .63 E. A. Moelwyn-Hughes and C. N. Hinshelwood, J., 1932, 230.64 E. A. Moelwyn-Hughes, Phil. Mag., 1932, [vii], 14, 112; A., 916; J.,1932, 95; A., 233; Chm. Reviews, 1932,10,24144 GENERAL AND PHYSICAL CHEMISTRY.chloride.65 As is well known, Polanyi found that in many reactionsbetween alkali metals and halogen compounds, nearly every col-lision led to reaction, ie., that the heat of activation is zero, or, inother words, that there is no " inertia." Later, he discovered thatthere is an increase in inertia as the series methyl iodide, bromide,chloride, fluoride is traversed.The following general rules now seemto emerge : there is a decrease in inertia with increasing length ofthe hydrocarbon chain, with passage from primary through secon-dary t o tertiary compounds, with increase in the number of chlorineatoms present, and with introduction of a carbonyl group. Adouble bond on the carbon atom bearing the chlorine hindersreaction, while one on the next carbon atom decreases the inertia.In another paper, N. Meer and M. Polanyi 66 make a comparisonof these structural influences in the gaseous reactions with thosefound for a variety of organic reactions in solution : in a generalway a parallelism appears, which is very suggestive.The number of known unimolecular gaseous reactions increasessteadily, as was only to be expected as soon as the idea of exploringthe unlimited field of organic substances arose.Perhaps the mostinteresting of these recently investigated is the decomposition ofethyl bromides6'The first of the organic unimolecular gas reactions to be foundwas the decomposition of acetone. There has always been somediscussion about the chemical step's in this reaction. The firstsuggestion was that carbon monoxide separates from the molecule,leaving two methyl residues, the interaction of which determines theother products. Subsequently, it has been maintained that thedecomposition must take place by way of keten formation.Itnow appears 68 that when acetone vapour is passed through a tubeat 800-1000", methyl radicals can be detected by the Panethmetal mirror method. It even seems that the temperature coeffi-cient of the rate of decomposition into methyl radicals is about thesame as that of the rate of the ordinary thermal decomposition.Thus the idea of a primary splitting into CO and 2CH3 seems, afterall, to have something t o be said for it.Some years ago Wulf and Tolman concluded, on energetic grounds,that the decomposition of ozone could not take place by the Jahnmechanism 0, =+= 0, + 0, 0, + 0 = 20,. Much more reliablevalues for the heat of dissociation of oxygen are now available, and,65 2.physikal. Chem., 1932, [B], 19, 139.66 Ibid., p. 164.67 E. L. Vernon and F. Daniels, J . Amer. Chem. SOC., 1932, 54,2563; A.,F. 0. Rice, W. R. Johnston, and B. L. Evering, ibid., p. 3629; A.,815.1108HINSHELWOOD : CHEM’ICAL KINETICS. 45in point of fact, are much smaller than was formerly supposed.Recalculation 69 using the newer values rehabilitates the Jahnmechanism as a t least an energetically possible one. It may besaid, in general, that the decrease in the accepted values for theheats of dissociation of the simpler diatomic molecules places anumber of kinetic problems in quite a new light, and some reorganis-ation of our views on molecular decompositions in thermal reactionsmay soon be occurring.From the nature of the method employed in its investigation,the dissociation of nitrogen tetroxide into the dioxide during thepassage of sound waves is specially interesting.According toW. T. Richards and J. A. Reid,70 the velocity constant a t 25” and260 mm. is about 4.8 x lo4, while P. D. Brass and R. C. Tolman 71give 2-8 x lo4 sec.-l at 25” and 1 atmosphere. The activationenergy appears to approximate to the heat of dissociation of thetetroxide, as would be expected.Finally, before we turn to the consideration of photochemicalreactions, brief reference may be made t o recent work on chainreactions, and in particular to the study of the remarkable phe-nomenon of explosive combination between two critical pressurelimits. The work of different investigators can be correlated muchmore easily if, in applying the branching-chain hypothesis, werecognise that the conditions necessary for the actual starting ofchains may be quite independent of those which govern theirpropagation through a gas mixture.72 There is in a rough way ananalogy between this and the phenomenon of change of state, wherethe presence of nuclei may be necessary, but where the rate of growthof the nuclei depends only upon the temperature and pressure orcomposition of the surrounding material.Sometimes the firstcentres from which a branching-chain explosion develops are formedon the wall of the vessel by a heterogeneous reaction.73 If the cata-lytically active parts of the wall are poisoned the chains cannotstart. The system is then in a ccmetastable” state.74 Given,however, that some chains do start, the condition for their branch-ing may be determined entirely by the temperature and compositionof the gas mixture, as it appears to be in the neighbourhood of“ upper limits.”The initiation of chains by surface reactions has been studied byH.W. Melville and E. B. Ludlam 75 for the case of phosphorus69 0. R. Wulf, J . Arner. Chem. Soc., 1932, 54, 156; A., 344.70 Ibid., p. 3014; A., 916. Ibid., p. 1003; A., 474.72 G. Hadman, H. W. Thompson, and C . N. Hinshslwood, Proc. Roy. SOC.,73 H. N. Alyea and F. Haber, see Ann. Reports, 1930, 27, 45.74 See (72). T 5 Proc. Roy. Xoc., 1932, [ A ] , 135, 315; A., 477.1932, [ A ] , 138,29746 GENERAL AND PHYSICAL CEEMITPRY.vapour and oxygen and by A.Ritchie and Ludlam for sulphur andoxygen. The initiation of explosion in hydrogen-oxygen mix-tures by the introduction of artificially produced hydrogen atomshas been studied by P. Haber and F. O~penheimer.~~ The influenceof inert gases on the diffusion of chain-carrying species t o the wallhas been further investigated by H. W. Melville,78 by A. Ritchie,E. R. H. Brown, and J. J. M ~ i r , ' ~ and by H. W. Thompson,8o andothers, the results being on the whole in agreement with whatmight be expected theoretically. The slow oxidation of moistcarbon monoxide has been studied by G. Hadman, H. W. Thompson,and C. N. Hinshelwood,81 who find evidence that chains of greatlength, initiated by hydrogen from the water-gas reaction, arepropagated.From a more general point of view, it should be mentioned thatalternatives to the chain theory of reactions showing explosionlimits are not being ignored.The problem of how far it wouldbe possible to construct a purely thermal theory of the whole groupof phenomena is being explored. Preliminary discussions of thismatter have been published.B2 On the whole, it appears t o thereviewer that a t the present moment the chain theory is the mostconvenient and satisfactory, though the alternatives are not con-clusively disposed of and may still prove to have important elementsof truth in them. (2. N. H.6. PHOTOCHEMISTRY.Technique.-The advent of the spectroscopist in the field ofphotochemistry has emphasised the need for more precise techniquein the examination of photoreactions, particularly in connexionwith the use of monochromatic illumination and very exact quantum-efficiency measurements. Thus, much attention has been given tothe construction of suitable light sources, monochromators, and tomethods of measurement.F. B. Bowden and C. P. Snow 83have used a simple type of large monochromator, constructed,however, of quartz crystal parts of a, size extremely difficult toobtain. F. Daniels and L. J. Heidt 84 describe a much more elabor-ate type of monochromator with optical parts of fused quartz, to be7 c Proc. Roy. SOC., 1932, [ A ] , 138, 635.7 7 2. physikal. Chem., 1932, [B], 16, 443; A., 576.78 Trans. Faraday SOC., 1932, 28, 308, 814; A., 701.T9 Proc.Roy. SOC., 1932, [A], 137, 511 ; A., 1093.Trans. Paraday SOC., 1932, 28, 299; A,, 701.Proc. Roy. Soc., 1932, [ A ] , 137, 87.*2 C. N. Hinshelwood, Trans. Paraday SOC., 1932,28, 184; see also (72).83 Nature, 1932, 129, 720; A., 656.8 2 J . Amer. Chem. SOC., 1932, 54, 2381, 2384BOWEN : PHOTOCHEMXSTRY. 47used in conjunction with a new type of mercury lamp of very highintrinsic intensity. 85 With such lamps and the monochromator theemission lines in the ultra-violet can be isolated with an intensityample for photochemical work, though the shorter wave-lengthssuffer through absorption by the fused quartz. Similar intensitieswithout such good monochromatism of the ultra-violet mercurylines can be obtained from an ordinary mercury lamp with con-denser-f3ters.8G Accurate calibration of such ultra-violet light isbest performed by actinometry,s7 for the surface thermopile has beenshown to be subject to large errors in ordinary use.S8 H.Klumband T. Haase 89 have shown that glass windows lop thick are astransparent as quartz to the ultra-violet, and can be made strongenough to be useful in photochemical work. The most suitablelight source for the region about 2000B. is the condensed sparkdischarge. describe a device forensuring the constancy of this source, for which monochromatismcan be obtained by means of “focal isolation.” 91 Very intenselight of shorter wave-lengths (1469-1295 A;) can now be obtainedfrom a new rare-gas lamp.92Predissociation and Photodissociation (see Ann.Reports, 1930, 27,21).-The most important photochemical problem of the moment isthe elucidation of the mechanism of the photoreactions of simplemolecules in the gaseous state by the correlation of photochemicaldata with spectral observations. It has generally been assumedthat a considerable change in the quantum efficiency of a photo-reaction, and possibly in the nature of the products formed, wouldoccur as the wave-length of the exciting light passes from one sideto the other of spectral thresholds (predissociational or photo-dissociational) .93 I n the case of nitrogen dioxide the spectralpredissociation threshold a t 3800 A. is associated with a veryG. S. Forbes and F. P. Brackett85 See also P. A. Leighton and F. E. Blacet, J . Amer.Chem. Soc., 1932, 54,For capillary lamps containing Bi, Cd, 3165; and R. H. Crist, ibid., p. 3939.Pb, T1, and Zn, see R. H. Hoffman and F. Daniels, ibid., p. 4226.86 E. J. Bowen, J., 1932, 2236; A., 1013.8 7 G. S. Forbes, G. B. Kistiakowsky, and L. J. Heidt, J . Anzer. Chem. SOC.,1932, 54,3246; A., 1013 ; W. G. Leighton and G. S. Forbes, ibid., 1930, 52,3139; A., 1930, 1260.8 8 P. A. Leighton and W. G. Leighton, J . Physical Chem., 1932, 36, 1882;A., 924.8g 2. Physik, 1932, 76, 322.s1 E. 0. Wiig and G. B. Kistiakowsky, ibid., 1932, 54, 1806; A., 705.92 P. Harteck and F. Oppenheimer, 2. physikal. Chem., 1932, [B], 16, 77.93 G. Herzberg, Trans. Faradccy SOC., 1931,27, 378 ; R. Mecke, ibid., p. 359 ;A., 1931, 1136; see also “ Discussion on the Critical Increment of Homo-geneous Reactions,” Chem.Soc., Dee., 1931, pp. 15-21? 50-61.J . Amer. Chem. SOC., 1931, 53, 397348 GENERAL AND PHYSICAL CHEMISTRY.striking photochemical threshold,94 but more recently examinedreactions have not shown such simple behaviour. The absorptionspectrum of chlorine dioxide exhibits a predissociation threshold a t3753 A., and though precise measurements of the rate of photo-decomposition in the gaseous state are difficult to make owing tothe variable effects of secondary reactions, there does not appear tobe a change in the quantum efficiency as the threshold is crossed.g5Experiments on chlorine dioxide in solution indicate that a photo-chemical threshold does exist on the long-wave side of the spectralone a t a distance from it farther than would be expected from themere influence of the solvent .96 Contrary to earlier expectation^,^^no marked photochemical thresholds associated with the spectralpredissociation limits have been €ound for the photodecompositionof aldehydes.Working with gaseous formaldehyde, which showsa predissociation limit at about 2750 pi., R. G. W. Norrish andF. W. Kirkbride 97 found no change either in the quantum efficiencyof photodecomposition or in the nature of the products in spectralregions on each side of the threshold. The products were found tobe H, + CO, and the quantum efficiency unity-facts which do notagree with the older view that the photoreaction is essentiallyH,CO + hv+ H,COx+ H + HCO. The results of P.A. Leightonand F. E. Blacet 98 are similar. They studied the photodecom-position of propionaldehyde in monochromatic light from 3130 to2537 A. This wave-length range brackets a spectral threshold atabout 3250 A. between a predissociational absorption spectrum anda continuous one.* They confirmed earlier work on aldehydes,that two photoprocesses occur, ( a ) decomposition, and (b) polymeris-ation; that the decomposition process is chiefly of the typeRHCO -+ RH + CO, accompanied by the formation of only a smallamount of hydrogen and the hydrocarbon R,; and that, while thedecomposition is unimolecular, the polymerisation is bimolecular.The quantum efficiencies of dissociation and of polymerisation wereseparately estimated ; the former, independent of pressure, variedfrom 0.5 to 1.0 between 3130 and 2537 B., while the latter, dependingdirectly on the pressure, reached values of 0.7 a t 200 mm.pressurein the same spectral range. At high pressures, therefore, the total* The threshold between the predissociational and fine-structure spectrum94 R. G. W. Norrish, J., 1929, 1158, 1604, 1611 ; A., 1929, 893, 1022.g 5 W. Finkelnburg and H. J. Schumacher, 2. physikaZ. Chem., BodensteinFestband, 1931, 740; A., 1931, 1210; J . W. T. Spinks, J . Amer. Chem. SOC.,1932, 54, 1689; A., 581.is unknown for this aldehyde.g 6 E. J. Bowenand W.M. Cheung, J., 1932,1200; A., 581.9 7 J., 1932, 1518; A., 706.g 8 J . Atner. Chem. SOC., 1032, 51, 3163; A., 1006BOWEN : PHOTOCHEMISTRY. 49quantum efficiency attains values well above unity, and further,fluorescence of the vapour was observed, indicating the productionof non-dissociating excited molecules.99 These facts go to showthat the original application of the theory of predissociation tophotochemistry was too simplified.In an important paper on thepredissociation of polyatomic molecules, J. Franck, H. Sponer, andE. Teller 1 provide an explanation of many of the difficulties. Inthe original theories of predissociation the following considerationswere not taken into account :(1) Certain apparent spectral predissociation limits are notassociated with unimolecular decompositions but are caused by theabnormal broadening of the rotational lines through collisions, i.e.,collisions cause the transformation of the excited molecules intoanother neighbouring state whose potential energy-distance curvedoes not cut that of the first.The so-called predissociation limitof sulphur dioxide at 2800-2600 A. is of this type, and this explainswhy this gas does not undergo photochemical change until the higherpredissociation limit a t 1950 A. is approached,2 and why fluores-cence is observed in it a t about 2000 A.(2) When account is taken of the vibrational and rotational energyof the products of the predissociation of polyatomic molecules, anexplanation is provided of the fact that in such cases the spectrallimit is not sharp ; e.g., for NO, the lower limit reaches from 4000 to3000 A. The exact value of a recorded limit thus varies with theexperimental ccnditions of its observation.(3) Predissociation can be induced or increased by collisions insome cases; e.g., deviations from Beer’s law occur in Br, and NO,vapour,3 andiodine atoms are detectable in I, vapour at wave-lengths less than 5100 A.if argon is present, the argon simultaneouslyquenching the fluorescence of the higher vibrational states of the I,molecule.4(4) Predissociational and photodissociational processes, and prob-ably, in general, non-dissociating and dissociating processes, ofactivation can interpenetrate one another, as in the case of iodinechloride.The sum total of these considerations shows that great care mustbe used in interpreting spectral limits, so much so that, instead of99 G.+ Herzberg and K.Franz (2. Physik, 1932, 76, 720; A., 896) have alsoobserved fluorescence of formaldehyde vapour.1 2. physikal. Chem., 1932, [B], 18, 88; A., 896.(Frl.) G. Kornfeld and E. Wecgmann, 2. Elektrochern., 1930, 36, 789; A . ,1930, 1383; K. Wieland, Nature, 1932, 130, 847.3 V. Kondrathev and L. Polak, 2. Physik, 1932,76,386; A., 791.* L. A. Turner, Physical Rev., 1932, [ii], 41, 627.W. G . Brown and G. E. Gibson, ibid., 40,520; A., 79150 GENERAL AND PBPSICAL CHEMISTRY.spectroscopy providing an easy answer t o photochemical problems,it now seems that the photochemist may be able through refinedwork to help the spectroscopist.A number of reactions of the dissociation type have been studied,and mechanisms proposed for the total change in different cases,including the photodecomposition of chlorine monoxide,6 of ozone inred and ultra-violet light ,7 the alkyl iodides,* hydra~ine,~ phosphineloand carbonyl sulphide.ll The mechanism of decomposition of theammonia molecule has been thoroughly investigated,12 the smallquantum yield being due to back reaction,13 and traces of hydrazinebeing also formed.l4Chain Reactions and Photosensitisation.-The photoreactionbetween hydrogen and chlorine continues to receive attention.The hydrogen-atom concentration during reaction has been estim-ated by making use of the two forms of hydrogen.15 Its temper-ature coefficient has been investigated.16 An important newobservation which explains certain of the baffling features of thisreaction has been made by R.W. G. Norrish and M. Ritchie.17By the use of a light-absorption technique for following thereaction, they have shown that the hydrogen chloride formedexerts a large inhibiting effect. New results fail to confirmearlier work on the inhibiting effect of drying.17a Calculationsbased on wave-mechanics indicate that when halogens are dis-sociated by light the free atoms combine with other moleculesW. Finkelnburg, H. J. Schumacher, and G. Stieger, 2. physikal. Chenz.,1031, [B], 15, 127; A . , 227.7 H. J. Schumacher and U. Beretta, ibid., 1932, [B], 17, 405, 417; A.,820.8 G. Emschwiller, Compt. rend., 1931,193, 1003 ; Ann. Chim., 1932, [x], 17,413 ; A., 29,706 ; W. West and (Miss) B. Paul, Trans. Faraday SOC., 1932,28,688; A., 1007.9 R.R. Wenner and A. 0. Beckman, J . Amer. Chem. SOC., 1932,54,2787 ; A , ,918.lo H. W. Melville, Nature, 1932, 129, 546; A., 479.11 W. Lochte-Holtgreven, C. E. H. Bawn, and E. Eastwood, ibid., p. 869 ;l a E. 0. Wiig and G, B. Kistiakowsky, J . Amer. Chenz. SOC., 1932, 54, 1806 ;13 H. W. Melville, Trans. Faraday SOC., 1932, 28, 885.14 G. R. Gedye and E. K. Rideal, J., 1932, 1160; A., 581.1 5 K. H. Geib and P. Harteck, 2. physikal. Chem., 1931, [B], 15, 116; A . ,l 6 E. Hertel, ibid., p. 325; A., 348.17 Nature, 1932, 129, 243 ; A., 348.17a W. H. Rodebush and W. C. Klingelhofer, Proc. Nut. Acad. Xci., 1932, 18,A., 820.A., 705.237.531 ; A. J. Allmand and H. C. Craggs, Nature, 1932, 150, 927BOWEN : PHOTOCHEMISTRY. 51giving, e.g., C13;18 a t the same time, the heats of activation of thereactions :C13 + H2+ (3, + HC1 + HH + C1, + H2-+ 2HC1+ HC1+ H2O + H2-> H a + H20 + Has estimated by the methods of wave-mechanics are such that noneof them is likely to occur in the hydrogen-chlorine photoreaction.19The photochlorination of tetrachloroethylene is strongly inhibitedby oxygen, and in presence of excess of the latter substancethe chief products are trichloroacetyl chloride and carbonyl chloride.20Further study of the chlorination of such hydrogen-free moleculesin the presence and absence of oxygen is likely to clear up manydifficult points in the mechanism of chlorination processes.Chainmechanisms for the photosensitised decompositions by chlorine fornitrogen trichloride21 and of ozone22 have been proposed toexplain the experimental results.Miscellaneous Photochemical Reactions.-A surprising observationof importance in theories of autoxidation is that illumination ofoxygen-free alkali sulphite solutions results in the liberation ofgaseous hydrogen.23 The photochemical decomposition of organicacids in the vapour state and in solution appears to be not a simpleprocess.24 In the photo-oxidation of aliphatic alcohols by acidsolutions of dichromate the photo-active ion is HCrO,’, and theprimary reaction probably gives aldehyde and quadrivalentchromium.25 I n marked contrast to this result, the photo-oxidationof quinine by dichromic acid is governed by the light absorption ofthe quinine molecule.26 Two reactions, whose rates have earlierbeen found to vary as the square root of the light intensity, can bysimplification of the conditions be made to obey the equivalence law.l8 G.K. Rollefson and H. Eyring, J . Amer. Chem. SOC., 1932, 54, 170; A.,l9 G. E. Kimball and H. Eyring, ibid., p. 3876.2o R. G. Dickinson and J. A. Leermakers, &bid., p. 3852.21 J. A. G. Griffiths and R. G. W. Norrish, Proc. Roy. SOC., 1931, [ A ] , 130,22 A. J. Allmand and J. W. T. Spinks, J., 1932, 599; A., 348.23 F. Haber and 0. H. Wansbrough-Jones, 2. physikal. Chem., 1932, [B], 18,24 L. Farkas and 0. H. Wansbrough-Jones, ibid., p. 124; A., 1006; W. C .25 E. J. Bowen and J. E. Chatwin, J . , 1932, 2081; A., 1006.26 G. S. Forbes, L. J. Heidt, and C. G. Boissonnas, J .Amer. Chem. SOC.,1932, 54,960; A., 480; R. Luther and G. S. Forbes, ibid., 1909,31, 770; A.,1909, ii, 632.348.591 ; 1932, [ A ] , 135,69; A . , 349.103; A., 1006.Pierce and G. Morey, J . A m r . Chem. SOC., 1932, 54, 467; A., 48052 GENERAL AND PHYSICAL CHEMISTRY.The photolysis of hydrogen peroxide solutions, normally complex,27becomes simple (quantum efficiency unity) in ultra-violet light ofvery high intensity,28 and by dilution with sufficient carbon tetra-chloride the chain reactions in the photobromination of cinnamicacid 29 also can be suppressed to give a quantum efficiency of unityto the reaction.30 The quantum yields of the photopolymerisationof acetylene 31 and of cyanogen 32 and of the photodecomposition ofpotassium persulphate solutions,33 of ethyl diazoacetate,w and ofchl~roform,~~ and of the photobromination of benzene 36 havebeen measured, and observations have been made relating tothe photochemical interaction of acetylene and water,37 of carbonmonoxide with ammonia and amine~,~* and of chlorine withbenzene.39The question of the production of formaldehyde and carbo-hydrates photochemically in vitro from solutions of carbon dioxide inwater 4O has received attention, and the consensus of opinion nowis that no procedure yet published enables the conditions for thereported formation of these substances to be reprod~ced.~~E.J. B.7. FLAMES AND THE MECHANISM OB CHEMICAL CHANGE.The subject of flames has claimed renewed attention in the pastfew years, and the inferences which can be drawn from the more2 7 F.0. Rice and M. L. Kilpatrick J . Physical Chem., 1927, 31, 1607 ; A .1927, 1154; A. J. Allmand and D. W. G. Style, J., 1930, 596, 606; A., 1030,715; M. Qureshi and M. K. Rahman, J . Physical Cheni., 1932, 36, 664.28 L. J. Heidt, J . Amer. Chem. SOC., 1932, 54, 2840; A . , 918.20 A. Berthoud and J. Bhraneck, J . CI~irn. physique, 1927, 24, 213; A . ,3 O W. H. Bauer and F. Daniels, J . Amer. Chem. SOC., 1932,54,2564; A . , 821.31 S. C. Lind and R. Livingston, ibid., p. 94; A . , 349.32 T. R. Hogness and L. Ts’ai, ibid., p. 123 ; A . , 349.33 R. H. Crist, ibid., p. 3939.34 E. Wolf, 2. physikal. Chem., 1932, [ B ] , 17, 46; A . , 706.35 D. G. Hall, J . Amer. Chem. SOC., 1932, 54, 33; A ., 349.36 E. Rabinovitsch, 2. physikal. Chem., 1932, [ B ] , 19, 190.3’ R. Livingston and C. H. Schiflett, J . Physical Chem., 1932, 36, 750.38 H. J. EmelBus, Trans. Faraday SOC., 1932, 28, 89; A . , 349.39 C . E. Lane and W. A. Noyes, J . Amer. Chem. SOC., 1932,54,161; A . , 349.40 Cf. Ann. Reports, 1927, 24, 39, 225.4 l J. Bell, Trans. Faraday Soc., 1931, 27, 771; A., 29; Nature, 1932, 129,170; A , , 237; G. Mackinney, J. Arner. Chem. SOC., 1932, 45, 1688; F. P.Zscheile, jun., ibid., p. 973 ; A . , 480 ; G. Mezzadroli and E. Vareton, Atti R.Accad. Lincei, 1931, [vi], 14, 347 ; A., 237 ; N. R. Dhar and A. Ram, Nature,1932, 129, 205 ; A., 349, 706 ; M. Qureshi and S. S. Mohammad, J . PhysicalChem., 1932,36, 2205 ; A., 1006.1927, 528THOMPSON: FLAMES AND MECHANISM OF CHEMICAL CHANGE.53recent lines of investigation, in particular with regard to the mechan-ism of chemical change, are already extensive, and promise tobecome more so.Essentially, developments have occurred in three directions.First, further data and hypotheses are available concerning themore purely physical properties of flames, such as their velocitiesof propagation and temperatures, and the function of chargedparticles detected in them ; whilst the conductivity of flames hasbeen studied both experimentally and theoretically. Secondly, theinvestigation of the so-called '' highly dilute " flames, such as areproduced when alkali-metal vapours are introduced into halogensa t low pressure, has led to a closer insight into certain elementaryreactions between atoms and molecules.This work is highlyimportant since modern theories of the forces between atoms andmolecules make a calculation of the heats of activation of suchprocesses a priori The manifold occurrence of " ele-mentary processes " in gaseous chain reactions, both thermal andphotochemical, has moreover made it the more desirable that theyshould be thoroughly understood. Thirdly, the radiation emittedfrom flames of various types has been examined with modern refinedtechnique by many workers, in the infra-red and also in the visibleand ultra-violet regions. Experiments on the infra-red emissionoffer a means of detecting any fundamental changes in themechanism of a reaction with alteration in conditions ; the examplemost studied in this way has been the oxidation of carbon monoxide.The examination of the visible and ultra-violet spectra has led tothe detection of " flame-carriers '' : in particular, the occurrence ofband systems indicates the existence of molecules, which, thoughnot capable of chemical isolation, are present transitorily at leastin excited states in the flames.These products are the activespecies essential for the continuance of the respective reactions,and can be identified with the intermediate products in chainprocesses. Inferences may thus be drawn about the mechanismsof those oxidation processes in which the flames have been studiedin this way. There are, however, almost always unavoidable com-plications which make this procedure questionable, although itappears likely to become very useful in the future.Evidence concerning the ionisation in flames and its bearing uponchemical reactions has been summarised in earlier reports.43 F.Haber,4* from a study of the deformation of the explosive zone and42 Cf.Ann. Reports, 1931, 28, 19.43 E. I(. Rideal, ibid., 1928, 25, 335; C. N. Hinshelwood, ibid., 1927,44 Sitzungsber. Preuas. Akad. Wiss. Berlin, 1929, 11, 162; A., 1929, 771.24, 31654 GENERAL AND PHYSICAL CHEMISTRY.the effect on the velocity of flame propagation when gaseousexplosive mixtures are passed through a wedge-shaped condenser,concludes that uncharged radicals and not electrical particles areresponsible for the process of combustion and especially for thepropagation of ignition.These uncharged radicals can be producedwith less expenditure of energy than the charged ones, and oiilyin the case of C-C and C-H, which have relatively low ionisationpotentials, is there an appreciable splitting into ions. A. E.Malinovski and F. A. Lavrov 45 have examined the influence of anelectric field on the velocity of propagation of the flame in explosivemixtures of various hydrocarbons with air, and find that thediminution in this speed which is observed in the vicinity of theregion of maximum conductivity is accentuated by increase in thecarbon content of the substances involved. According to theseobservers, this result agrees with Ilaber’s theory, the ionisation ofG-C and C-H radicals giving rise to the phenomena observed.Thefailure to obtain a positive effect of the field in hydrogen-oxygenmixtures was considered as substantiating evidence. W. M.T h ~ r n t o n , ~ ~ on the other hand, using methane-air mixtures, findsan increase in flame speed in the electric field, and suggests anexplanation based upon considerations of the internal energy ofthe “ molecular complexes ” said to be produced in the wave-front.Several series of facts are cited in support of the somewhat elaboratehypothesis, but the complications are rather serious. B. Lewis 47has also studied this question and emphasises the importance ofpositive ions in the maintenance of flames. He suggests a possibleexplanation of the discrepancy between the results of Thornton onthe one hand and of Malinovski and Lavrov on the other.H.A. Wilson48 summarises the data and discusses the variousmatters relating to the electrical conductivity of flames from atheoretical standpoint.Photographic measurements on the propagation of flame inelectric fields have also been made by E. M. Gu6nault and R. V.Wheeler.49 Some interesting results are described by H. F. Cowardand F. J. Hartwell 5o on the uniform movement of flame in methane-air mixtures using a series of vessels differing in diameter. Themaximum speed for uniform motion of the flame in a mixture ofgiven composition is markedly decreased with decreasing vesseldiameter. The relationship between the velocity V and diameter D4 6 2. Physik, 1930, 59, 690; A., 1930, 424.46 Phil.Mag., 1930, [vii], 9, 260; A., 1930, 708.4 7 J. Amer. Chem. Soc., 1931, 53, 1304; A., 1931, 689.4 8 Rev. Mod. Physics, 1931, 3, No. I, 156.49 J . , 1931, 195; A,, 1931, 313. J., 1932, 1996THOMPSON : FLAMES AND MECHANISM OF CHEMICAL CHANGE. 55is not simply of the type V = cD~, c and k being constants, but ismore complex. Several other determinations of flame speeds havebeen made,5I and a new method is described by C. Becker andK. Vogt 52 employing a system of rotating mirrors.Flame temperatures form the subject of several other papers.G. W. Jones, B. Lewis, J. €3. Friauf, and G. St.J. Perrott 53 haveemployed the spectral line reversal method to moist hydrocarbon-air mixtures, and find that the mixtures affording the maximumflame temperature contain less hydrocarbon than those affordingthe maximum flame speed of uniform movement.Employing theaccepted values for the specific heats of carbon dioxide and hydrogen,the degrees of dissociation of carbon dioxide and of water, and theheat of dissociation of the hydrogen molecule, G. Ribaud 54 calculatesthe flame temperatures in burning carbon monoxide or hydrogen.Finally, P. J. Daniell 55 obtains a theoretical connexion betweenvelocity of flame, velocity of reaction, specific heat, density, andconductivity of gaseous explosive mixtures.“ Highly diluted flames ” have been mentioned previously inthese Reports.56 Summaries of the work so far carried out, withdiscussions of its theoretical significance, have been published byM.Polanyi57 and G. Schay.58 The main point in the study ofthese “ cold ” flames is that they provide a means of investigatingreactions which proceed a t extremely high velocity, i.e., atalmost every collision of the reactants without requiring heat ofactivation.The view became generally accepted that atomic reactions haveno inertia; in other words, in the exothermic direction they haveno heat of activation. This conclusion was apparently confirmedin the reactions found to be the basis of the highly diluted flames.From measurements on the distribution of light and wall-precipitateand of the “light efficiency,” under different conditions of mixingof the reactants in the long reaction tube, the mechanism of theprocesses occurring was elucidated.The following are examples61 W. Payman andR. V. Wheeler, J., 1932, 1835; 0. C. de C. Ellis, J. SOC.s2 2. Physik, 1932, 75, 894; A., 701.53 J . Amer. Chem.Soc., 1931,53, 869; A., 1931, 572; cf. also A. L. Loomis54 Compt. rend., 1930, 190, 369; A., 1930, 418.55 Proc. Roy. Soc., 1930, [A], 128, 393; A., 1930, 424.5 6 E. K. Rideal, Ann. Reports, 1928, 25, 334; C. N. Hinshelwood, ibid.,5 7 ‘‘ Atomic Reactions,” London, 1932 ; cf. also Naturwiss., 1932, 20, 289 ;6 8 Hochverdiinnte Flammen,” Portschr. Chem. Physik, 1930, 21, 1.Chem. I n d . , 1931, 50,403; A., 1931, 1371.and G. St.J. Perrott, B., 1928, 881.1930, 27, 20; 1931, 28, 47, where detailed references are given.A., 582; 2. angew. Chem., 1931, 44,597; A., 1931, 99956 GENERAL AND PHYSICAL CHEMISTRY.of reactions which were found to occur a t every collision and areinertia-less :Na + X, --+ NaX + XNaX, + X+ NaX + NaNa + HgCl, + NaCl + HgClNa + HgCl + NaCl + Hg.More detailed examination of these reactions, however, and ofsimilar ones using other substances, has now shown that manyatomic processes involve a quite appreciable energy of activation.In particular, H.von Hartel and M. Polanyi 59 have found that thereactions between sodium and alkyl halides have heats of activationwhich increase uniformly from the iodide (about zero) to the fluoride.These experiments have been elaborately extended by H. von Hartel,N. Meer, and M. Polanyi,60 using different alkyl radicals.have studied the cases ofsodium vapour with cadmium halides and with zinc chloride.Herethe results are almost entirely similar to those originally obtainedwith the mercury halides, but the heats of activation are oftenappreciable.The inertia-less reactions of sodium vapour with the hydrogenhalides have been studied by G. &hay6, and H. von Hartel.63The calculation of heats of activation by methods arising fromthe results of molecular spectra and the new theories of valencyhave been reported elsewhere (Hinshelwood, this vol., p. 18). It issufficient to say that the calculat'ions lead to values which are ofthe same order as those observed.A series of measurements on the total infra-red radiation emittedby the carbon monoxide-oxygen and hydrogen-oxygen flames underdifferent conditions has been made by W.E. Garner and his colla-borator~.~* I n the case of hydrogen and oxygen the maximumradiation is observed with the mixture H, + 0,, and not with thestoicheiometric mixture 2H, + 0, ; from which the authors concludethat hydroxyl radicals are probably responsible for the emission.An examination of the effect of catalysts on the speed of the flameE. Horn, M. Polanyi, and H. Sattler69 2. physikal. Chem., 1930, [B], 11, 97; A., 1930, 174.6o Ibid., 1932, [ B ] , 19, 139.62 Ibid., 1931, [B], 11,291 ; A., 1931, 282. 63 Ibid., p. 316; A . , 1931, 282.64 With F. Roffey, Nature, 1928, 121, 56; A., 1928, 105; J., 1929, 1123;A., 1929, 973; with C. H. Johnson, J., 1928, 280; A., 1928, 375; with K.Tawada, Nature, 1928, 122, 879; A., 1929, 21; with D.A. Hall, J., 1930,2037 ; A., 1930, 1379 ; with D. A. Hall and F. E. Harvey, J., 1931, 641 ; A.,1931,576; with K. Tawada, Trans. Faraduy SOC., 1930,26,36; A., 1930,263;with C. E. H. Bawn, J., 1932, 129; A., 234; cf. also E. K. Rideal, Ann.Reports, 1928, 25, 343.Also this vol., p. 43.Ibid., 1932, [B], 17, 220; A., 680THOMPSON : FLAMES AND MECHANISM OF CHEMICAL CHANGE. 57of carbon monoxide-oxygen mixtures, on tAe infra-red emission,and on the ionisation, reveals the existence of a ‘‘ residual ” radi-ation in addition t o that given out in the explosion itself. Garnerand Johnson suggest that this residual radiation arises from therecombination of ions. The important result with carbon monoxideflames, however, is the existence of a “ step ” in the curve showingtotal radiation emitted against percentage of hydrogen added.Addition of hydrogen diminishes the radiation observed untilo.0470 is reached; at this point a break is observed, and withincreasing proportion of hydrogen the radiation again diminishes,continuously, but more slowly.It should be added that, whilstdiminishing the radiation produced, addition of hydrogen increasesthe flame speed. Garner and Roffey conclude that, in accordancewith the earlier ideas of Bone, there are two chemical mechanismsoperative in the reaction, one occurring below the step, the otherabove it. From further experiments it is concluded that excitedcarbon dioxide molecules are the origin of the radiation.Further experiments deal with the effect of vessel size, additionof inert gases, and other factors on the position and magnitude ofthe ‘‘ step.” The relationship pHn p(COfOa) = E , originally thought toapply a t this point, is later amended to pHa pco2 = k.The “ step ”is unaffected by changes in the vessel dimensions.Bawn and Garner have recently stated that carbon dioxide andsulphur dioxide effect an increase of the pressure at the ‘‘ step.”The visible and ultra-violet spectra emitted by flames were firstexamined many years ago by Kirchhoff and Bunsen. Subsequentlythe work was continued by Liveing, Dewar, Hartley, and others.65It nearly always led to the discovery of flame continua-continuousspectra, having no line or band structure.66 The origin of suchcontinua is still a matter of doubt ; it seems probable that they ariseas a result of processes of recombination of free radicals present inthe flame, although alternative hypotheses are possible. In manycases, however, it is now found that superimposed upon the continuaare lines or bands caused respectively by the excitation of atomsand of molecules.All authors are agreed upon the fact that this excitation has itsorigin in the energy liberated in the elmentary transformations.The implications of this are twofold : first, it compels us to find inthe reaction scheme some elementary process the heat evolution ofwhich will produce the excitation observed ; secondly, it enablesus t o infer the presence or absence of certain intermediate productsin the reactions occurring.65 Cf.Eder and Valenta, “ Atlas typischer Spektren,” 1911.8 6 Summary by W. Finkelnburg, Physikal. Z., 1930, 31, 158 GENERAL AND PHYSICAL CHEMISTRY.H. F. Bonhoeffer and F. Haber 67 identified the bands emitted bya hydrogen-oxygen flame with those due to hydroxyl radical, andfor this and other reasons suggested that hydroxyl occurs as anintermediate product in the reaction chain. The significance ofthis has been discussed elsewhere.68 It suggested the chainH, + 0, = 20H,H + 0, + H, = OH + H,O,OH + H, = H,O + H,which has been so much discussed in recent years.69V. Kondratbev 70 has re-examined the spectrum of the flame ofburning carbon monoxide. This has been studied by W. A. Boneand his collaborators for many years.71 Kondrateev's measurementsare confined t o the ultra-violet region, since in the visible, increaseddispersion still leaves the spectrum too complicated for analysis.In the ultra-violet the bands are arrangedin series having a frequencydifference of approximately 600 cm.-l; the corresponding infra-red and Raman frequency is 672 crn.-l.A variety of considerationslead to the conclusion that excited carbon dioxide molecules are theemitters of the bands. The evidence is, however, to some extentnegative in that the bands observed cannot be assigned to any othermolecule which might be present in the flame. The change infrequency difference in the two cases could be explained by theexcitation of higher vibration levels in the flame.Kondrateev also observed the flame of sulphur burning in oxygen,the spectrum consisting of two groups of bands-one in the visible,the other in the ultra-violet-separated by a continuous region.These can be attributed t o the S, molecule and to SO respectively.The phosphorescent flames of carbon disulphide and of etherwere also studied; in the latter case formaldehyde bands areprominent.The spectrum of the flame of carbon disulphide has been measuredby A.Fowler and W. M. Vaidya.', It is found that the mostcharacteristic bands of the ordinary flame, extending from theblue to the near ultra-violet, form part of the system already knownto be due t o S, molecules. The ultra-violet bands of S, appear in67 2. physikal. Chem., 1928, 137, [ A ] , 263; A., 1929, 11; cf.also Ann.Reports, 1928, 25, 342 ; 1930, 27, 46.W. L. Garstang and C. N. Hinshelwood, Proc. Roy. Xoc., 1931,134, [A],1 ; A., 25.*6g W. Frankenburger, Trans. Faraday Xoc., 1931, 27,431 ; A., 1931, 1136.' 0 2. Physik, 1930, 63, 322; A., 1930, 1332.'1 W. A. Bone and D. T. A. Townend, '' Flame and Combustion in Gases,"Longmans, 1927.Proc. Roy. Soc., 1931,132, [ A ] , 310; A., 1931, 996BOWEN: THE STRUCTURE OF SIMPLE MOLECULES, ETC. 59absorption but can be obtained in emission if a stream of oxygenis directed on t o the flame. Emission bands of SO are seen, and ifthe flame is enclosed in a chimney, absorption bands of SO, can alsobe obtained.Generally similar results were obtained in experiments on theflames of sulphur and hydrogen sulphide, the latter showing bandsof hydroxyl.The spectrum of the phosphorescent flame of carbondisulphide 73 was re-examined, and bands due to SO and CS found.Fowler and Vaidya discuss the significance of their results from thepoint of view of the mechanism of combustion. It is possible toreconcile all the spectroscopic data with the theory of peroxidationand with the results of kinetic measurements made on the reaction.The spectrum of the hydrogen-nitrous oxide flame has beenstudied by A. Fowler and J. S. Badami.74 These authors summarisethe relevant facts concerning the most, common “reference ” spectra-“ water vapour ” bands (OH), “ ammonia ’’ bands, “ third positivenitrogen” bands (NO). The results show that this flame is similarto that of ammonia burning in oxygen, each showing bands due t othe molecules NH, OH, NO, and the so-called #-bands of ammoniawhich may be ascribed to the NH, molecule.V.Kondrateev 75 has summarised the data at present available uponthis subject. The following extract from his paper serves to indicatethe types of result obtained :Flame. Molecule. Flame. Molecule.H2+02 OH NH, + 0 2 NH, NH,( ?), OH, NOCO + 0, co, CH, + 0, CHcs, + 0, so, s, a ~ $ ~ ~ d e ” ) + 0, C,, CH, OH, CO,, CH,O(CN), 3- 0, CN, c2, co H2 + N,O NH, NH,(?), OHs + 0, so,s, C2H2 + 0 2 CH, c,p4 + 0, PO(?)HCN+ 0, CN,C, CO + N20 co2H. W. T.8. THE STRUCTURE OF SIMPLE MOLECULES FROM SPECTROSCOPIC,X-RAY AND ELECTRON DIFFRACTION DATA.A number of improvements in the technique of obtaining molecularspectra have been recorded, and will be found in the work referredto below; in addition may be noticed improvements in gratingspectrographs 76 and far infra-red spectrographs.77 The question73 H.J. Emelbus, J., 1926, 2948.74 Proc. Roy. SOC., 1931, 133, [A], 326.7 5 Proceedings of Congress on Chemical Kinetics, Leningrad, Sept. 1930.7 6 A. L. Loomis and G. B. Kistiakowsky, Rev. Sci. Instr., 1932, [ii], 3, 201 ;7 7 H. M. Randall, ibid., p. 196; A., 592; R. B. Barnes, Physical Rev., 1932,A., 592.[ii], 39, 562 ; A., 44460 GENERAL AND PHYSTCATA CHEMISTRY.of the polarisation of Raman scattering from the point of view ofthe " spinning photon " has received attention.78 Accurate experi-mental results are difficult to obtain, and some confusion has beencaused by lack of satisfactory data.An outline of the methods by which the structure of a simplemolecule can be deduced has already been given.79 From X-ray orelectron-diffraction methods intramolecular distances are obtained.80The fine-structure, i e ., the rotational constituent, of absorptionbands in the infra-red, visible, or ultra-violet region, or of Ramanbands B1 provides values of the moments of inertia of the molecule,whence the interatomic distances and angles can be calculated.The vibrational frequencies of the molecule, also obtained fromabsorption band or Raman data, through a treatment of themolecule as a system of masses and springs, allow of calculations ofthe angular dispositions of the masses and of the force constants ofthe links.82 The spectroscopic methods naturally depend for theirreliability on the accuracy of the interpretation of the experimentaldata, that is, on the correct allocation of observed frequencies toparticular transitions.This would not be so difficult if everyimportant vibrational band were completely resolved into itsrotational constituents and selection rules applied.83 Owing, how-ever, to the elaborate technique necessary to overcome the experi-mental difficulties, there is a t present a lack of adequate data formost simple molecules, so that the selection of moments of inertia,and still more, of fundamental vibrational frequencies, often becomesa debatable rather than an answerable problem.Further diffi-culties arise in the question of the distribution of forces within themolecule, i . e . , whether the forces are associated only with chemical(Sir) C. V. Raman and S. Bhagavantam, Indian J . Physics, 1931 6,353 ;A., 107 ; Nature, 1932, 129, 22 ; S. Bhagavantam, Indian J . Physics, 1932, 7,79; A., 793; Nature, 1932, 129, 167; R. Bar, ibid., p. 505; A., 445; S.Bhagavantam and S. Venkateswaran, ibid., p. 580; -4., 445; S. Venkates-waran, Phil. Mag., 1932, [vii], 14,258; A., 898; J. Cabannes and A. Rousset,Cornpt. rend., 1932, 194, 79, 706; A , , 212, 320.Note: in theformu1,lc onp. 371 the unitsarenot accurately defined, and reference should be made to K. VC'. F. Kohlrausch," Der Smekal-Raman Effekt," Springer, Berlin, 1931.H.Gajewski, Physikal. Z . , 1932, 33, 122; A., 316; R. W. James, ibid.,p. 737; W. van der Grinten, ibid., p. 769.For rotational structure of Raman bands, see K. M'. F. Kohlrausch, op.cit., p. 5 0 ; A. Langseth, 2. Physik, 1931, 72,350; A. Carrelli and J. J. Went,ibid., 1932, 76, 236; A., 792.82 See R. Mecke, Z . physikal. Chenz., 1932, [B], 16, 409, 421; 17, 1; A.,559, 675.83 G. Placzek, 2. Physilc, 1931, 70, 84; A . , 1031, 893; D. M. Dennison,Rev. Mod. Physics, 1931, 3, 289; H. A. Kraus and G. P. Ittmann, 2. Physil:,1930, 60, 663.i9 Ann. Reports, 1931,28, 367BOWEN: THE STRUCTURE OF SIMPLE MOLECULES, ETC. 61linkages, and whether repulsions between non-linked atoms occur.84It is towards the solution of these difficulties that most of the workon the structure of simple molecules is a t present directed.As an illustration of the methods employed in correlating infra-red absorption-band data with Raman frequencies in order toobtain the energy levels of the molecule, reference may be made toA.Langseth and J. R. N i e l ~ e n , ~ ~ to P. E. Martin and E. F. Barker,86and to D. M. Denni~on,~' who examine the case of the molecule ofcarbon dioxide.88 This molecule definitely has a linear symmetricalstructure.89 The molecule of nitrous oxide is more complicatedand, though linear, has the unsymmetrical structure NN0.90 Thisstructure is also supported by other evidence of a very variedchara~ter,~l though it is not at present easy to reconcile this resultwith the very small dipole moment of the molecule.92The structure of the H,O molecule in the light of refined nearinfra-red absorption band measurements has been discussed byP.Lueg and K. Hedfeld,93 who conclude (from the calculatedmoments of inertia) that the molecule is an isosceles triangle of thefollowing dimensions : 0-H = 0.98 A.; H-H = 1.6 8.; angleHOH = 109". In this paper full references to earlier work will befound. Other new data for this molecule are presented by E. K.Pl~ler,~* I;. R. Weber and H. M. Randall,95 S. Rafalow~ki,~~H. Hul~bei,~' and H. Gajew~ki.~8Hydrogen sulphide appears to be a rectangular isosceles trianglewith S-H = 1.43 A. and H-H = 2-02 g.99 A. Dadieu andK. W. F. KohlrauschS9 from a general survey conclude that the0x0 angle in sulphur dioxide is 120".C. R. Bailey and A. B. D.84 H. C. Urey and C. A. Bradley, PhysicaZ Rev., 1931, [ii], 38,1969 ; A., 107.8 5 2. physikal. Chem., 1932, [B], 19, 35.8 6 Physical Rev., 1932, [ii], 41, 291.8 7 Ibid., p. 304; A., 982.8 8 See also A. B. D. Cassie and C. R. Bailey, 2. Physik, 1932, 79, 35.89 For X-ray results, see H. Gajewski, Zoc. cit. (ref. 80).E. K. Plyler and E. F. Barker, Physical Rev., 1931, [ii], 38, 1827; A.,1031, 108; A. Langseth and J. R. Nielsen, Nature, 1932, 130, 92; A., 897.91 K. Clusius, Nature, 1932,130,775; G. Herzberg, 2. physikal. Chem., 1933,[B], 17,68; A., 680; C. R. Bailey, Nature, 1932,130, 239; A., 997.s2 H. v. Braunmuhl, Physikal. Z., 1927,538, 141; J. W. Williams and C. H.Schwingel, Physical Rev., 1930, [ii], 35, 855; P.C. Mahanti, Physikal. Z.,1931,52,108; A., 1931, 287.93 2. Physik, 1932, 75, 512; A., 558.04 Physical Rev., 1932, [ii], 39, 77; A., 212.9 5 Ibid., 40, 835; A., 792 (far infra-red).9 6 Bull. Acad. Polonaise, 1931, [ A ] , 623; A., 792.O 7 Compt. rend., 1932, 194, 1474; A., 559 (Raman spectra).g8 LOG. cit. (ref. 80).90 A. Dadieu and K. W. F. Kohlrctusch, Physikal. Z., 1932,33,165; A., 32062 GENERAL AND PHYSICAL CHEMISTRY.Cassie from infra-red data show that there is a close similarity ofstructure between sulphur dioxide and chlorine dioxide. Theunpaired electron of the latter therefore takes no part in the linkagesof the molecule. According t o the assumptions made as to thedistribution of forces within the molecule, they show that twostructures can be deduced, the angles OSO and OClO being 60" for" central forces " and 122" and 140" respectively for " valenceforces." On evidence based on the as yet incompletely resolvedrotational structure they prefer the smaller angle, as the largerappears t o give too great interatomic distances.2 The chemist,however, would select the larger-angled solutions as having valencyforces and agreeing with the selection rules, and would regard thequestion of the linear dimensions of the molecules as still unsettled.Chlorine monoxide is probably a rectangular isosceles triar~gle.~The ozone molecule is reported on Raman spectra evidence to betriangular but not equilateral; its structure may possibly beanalogous t o that of sulphur dioxide.The vibrational structure of the near infra-red absorption bandsand of the Raman bands of ammonia has been carefully investi-gated, but entire agreement has not yet been reached as to themoments of inertia of the molecule. One of them is difficult t oobtain from spectroscopic data, but can be calculated by an applic-ation of wave-mechanics.' The original pyramidal form has beencodrmed, but the table below shows the structures deduced bydifferent treatments of the experimental data :Distances Dennison Langseth.&)and Luegand and (Dissolvedangles.Hedf'eld. Uhlenbeck. (Gaseous.) in water.)N-H 1.04 1.02 0.89 0.90H-H 1.72 1.64 0.92 0.93Height ofpyramid 0.3 0-7 1 0.73Angle HNH 110" 107" 62" 62"The HNH angle of about 110" is probably the most reliable;Langseth's results depend on the choice of a very small value for1 Nature, 1932,129,652 ; A., 888; Proc.Roy. SOC., 1932, [ A ] , 137,622 ; A.,1075.a Cf. R. Wierl, Physikal. Z., 1930, 31, 1028; A., 1931, 13.3 C. R. Bailey and A. B. D. Cassie, Zoc. cit. (ref. 1).4 G. B. B. Sutherland and S. L. Gerhard, Nature, 1932, 130, 241 ; A., 983.5 P. Lueg and K. Hedfeld, 2. Physik, 1932, 75,599; A., 674.6 A. Langseth, ibid., 77,60 ; A., 897 ; E. Amaldi and G. Placzek, Naturwisa.7 D. M. Dannison and G. E. Uhlenbeck, Physical Rev., 1932, [ii], 41, 313;8 R. RI. Badger and R. Mecke, 2. physikal. Chem., 1929, [B], 5, 333; A . ,1932, 20, 521 ; A., 897.A., 982; N. Rosen and P. M. Mor~e, ibid., 42,210.1929, 1363BOWEN : THE STRUCTURE OF SIMPLE MOLECULES, ETC.63one of the moments of inertia, but independently of the probableinaccuracy of this choice they serve to show how little the ammoniamolecule is deformed by dissolution in water.Pentatomic tetrahedral molecules have been examined by anumber of workers. J. G. Moorhead9 has calculated moments ofinertia of the methane molecule, and a discussion of the fundamentalfrequencies of the molecule is given by S. Bhagavantam.lo C. Schaeferand R. Kernll present accurate measurements of the infra-redabsorption bands of carbon tetrachloride and attempt to allocatethe bands to particular transitions in terms of the four fundamentalfrequencies.12 H. C. Urey and C. A. Bradleyl3 show that thefour fundamental frequencies of the tetrahedral molecules CCI,,SiCI,, SnCI,, CBr,, SnBr,, and TiCI, cannot be related to oneanother on the simple assumption of valency forces; an allowancemust be made in addition for the mutual repulsion of the corneratoms.New infra-red absorption bands of formaldehyde vapour havebeen measured,14 and G.Herzberg and K. Franz l5 find that themolecule gives a fluorescence spectrum with two characteristicfrequency differences identical with the Raman lines. Fromthe rotational structure of the ultra-violet absorption spectrum,G. H. Dieke and G. B. Kistiakowsky16 deduce the distances:C-0 = 1.19 B.; H-H = 1.88 A , ; C-H = 1.15 A.; angleHCH = 110".The identification of the vibrations of the acetylene molecule areat present uncertain; l7 provisional moments of inertia for theethylene molecule have been arrived at by R.M. Badger andJ. L. Binder.18It is remarkable that the angles obtained between the valenciesof the hydrogen atoms in the molecules H,O, H3N, (H,C), andH,CO are all close to the tetrahedral angle 109" 28'; H,S at presentappears to be an exception with an angle of 90". E. J. B.Physical Rev., 1932, [ii], 39, 83; A., 212.lo Nature, 1932, 129, 830; A., 675.l1 2. Physik, 1932,78, 609.la Cf. A. Langseth, ibid., 1931,72,350; A., 1931, 1363.l3 Physical Rev., 1931, [ii], 38, 1969; A., 107.l4 J. R. Patty and H. H. Nielsen, Physical Rev., 1932, [ii], 39, 957; A,,558; R. Titeica, Compt. rend., 1932, 195, 307; A., 897.2. Physik, 1932, 76, 710; A., 896.l8 Proc.Nat. A d . Sci., 1932, 18, 367.17 A. R. Olson and H. A. Kramers, J . A m r . Chem. SOC., 1932,54, 136; A.,320; W. Lochte-Holtgreven and E. Eastwood, Nature, 1932, 130, 403; A.,1075.l8 P h y s k l Rev., 1931, [ i i ] , 38, 1442; A., 6 ; see also H. H. Nielsen, ibid.,p. 1432; A., 664 GENERAL AND PHYSICAL CHEMISTRY.9. GENERAL STEREOCHEMISTRY.During this year the greater part of the new and comprehensivetextbook of Stereochemistry edited by K. Freudenberg l9 hasappeared. The earlier parts contain very thorough discussions ofthe physical aspects of the subject, by Mark, V. M. Goldschmidt,Mecke, Dadieu, and others, including a discussion of the newphysical theory of optical activity by Werner Ktthn. The moreorganic side is discussed in the later parts, by Freudenberg, Ebel,Richard Kuhn, Meisenheimer, and others.This book bringstogether for the first time the various physical and chemicalinvestigations bearing on the subject.W. H. Mills has published two important papers dealing withgeneral aspects of stereochemistry. In the first 2O he discusses theenergy relations of the cyclic compounds and the conditions oftheir formation. In the second21 he deals especially with themechanism of the racemisation of tercovalent atoms, and of thetransmigration in the Beckmann reaction ; he also gives the clearestand most thorough discussion which has yet appeared of the originof optically active compounds in living matter, and shows howthe growth of an organism must necessarily accentuate anydisproportion between the antimeric forms.Now that the normal arrangements of the valencies of multivalentatoms have been ascertained, we are in a position t o consider whatmodifications the molecule can undergo, how far it resists thesemodifications, and what are the forces that tend to bring themabout.The’ modifications are of three kinds :(I) Rotation of atoms with their attached groups about the lineof a single link : “ free rotation.”(11) Bending of the valencies, i.e., expansion or contraction oftheir angles.(111) Stretching or compression of the links : increase or diminu-tion of the distances between the linked atoms.The restoring forces exerted by the valency bonds themselvesagainst these deformations are for (I) zero, since no change of angleor distance is involved.lo ‘( Stereochemie : eine Zusammenfassung der Ergebnisse, Grundlagenund Probleme,” Leipzig, Deuticke, 1932; 5 of the 8 parts have now beenpublished, price RM.18 each.2 o Stkrkochimie des compos6s cycliques : Report of the Fourth ChemicalSolvay Conference, Paris, Gauthier-Villars, 1931, pp. 1-51.a1 Presidential Address to the Chemical Section of the British Association :in “ The Advancement of Science,” 1932, pp. 37-56. B. A. Report, 1932,p. 37SIDGWICK : GENERAL STEREOCHEMISTRY. 65For (11) they are given by the force constants derived from theabsorption or Raman spectra. These are much less easy to deter-mine for the bending than for the stretching, and are only knownin a few simple instances. For the C-H link the Raman spectraindicate 22 that a change ,of angle of 10" (about 0.1 B.U.) requiresabout 700 cals.per g.-mol. : for the linear molecule of hydrogencyanide and acetylene the spectrum givesZ3 similar values of 788and 772 cals. respectively. We may assume that this resistance ismuch the same for other atoms attached to carbon. As will beshown later, there is reason to think that for the valencies of oxygenand sulphur, and perhaps of all atoms with a covalency of lessthan four, it is very much smaller.(111) The resistance to stretching is much greater, and is givenby the force constants, which are known for a large number oflinks.24 The energy required for an increase of distance of 0.1 B.U.is on the average 3000 cals.for a single link; for G-C1 it is 2200cals.23The agencies external to the valencies which tend to deform themolecules are :1. The thermal impacts of other molecules : energy = IcT, or600 cals. per g.-mol. at 25".2. The dipole attractions and repulsions; 25 for two dipoles ofmoment 1 x e.s.u. at a distance of 3 A.U., the dipole potential-the work of complete separation of the dipoles-is about equal tothe thermal energy at 25".3. The van der Waals attraction between the atoms.26 Theimportance of this factor has only recently been recognised;and isstill somewhat doubtful. It seems, however, to be effective inethylene dichloride, accorqng to the recent observations of Kohl-rausch. The scattering of X-rays by the vapour of ethylenedichloride showed2' that the majority of the molecules had thechlorine atoms as far removed as possible (" trans-position "), butthe shape of the curves indicated that not all the molecules were inthis state.It was concluded that the trans- was the favouredposition, owing to the dipole repulsion, but that the thermalagitation, which for this molecule should be of the same order ofmagnitude as the dipole potential, disturbed the molecules from it22 See Ann. Reports, 1931, 28, 371, 401.23 H. A. Stuart, Physikal. Z., 1931, 32, 793 ; A., 1931, 1356.24 Ann. Reports, 1931, 28, 401.26 For a detailed discussion, based on wave mechanics, of this and the otherintermolecular and interatomic forces, see H. Eyring, J. Amer. Chm. SOC.,1932,54,3191; A., 996.27 P.Debye, Physikal. Z., 1930,31,142,419; A., 1930,400,843 : observeddistance, 4.4 & 0.1 k U . : calculated for trans-form, 4-25.25 Ibid., p. 390.REP.-VOL. XXIX. Cis GENERAL AND PHYSICAL CHEMISTRY.to some extent. This was confirmed by the measurement of thedipole moment, which was found to be considerable, though lessthan that required for t#he cis-form (the tyans- has no moment), andto increase with rise of temperature owing to the greater freedom ofrotation; 2* it was also found that in solution, where the dielectricconstant of the medium is larger, and hence the dipole potentialsmaller, the moment is larger than it is in the gas. It has now,however, been shown 29 that in the Raman spectrum of ethylenedichloride the line corresponding to the oscillations of the C-Cllink is double, one component being stronger than the other, andthe ratio of the intensities approaching unity as the temperaturerises. In cis- and trans-dibromoethylenc, which are distinct sub-stances, the C-Br Raman lines are not quite in the same position,indicating that the constant for the C-Br link is somewhat differentaccording as the second C-Br link is in the cis- or tr~ns-position.~~Kohlrausch concludes from this that ethylenc dichloride consists,nbt of molecules in or near the trans-position, but of a definitemixture of the cis- and the trans-form, with the latter predominating ;otherwise we should find one blurred line instead of two sharp ones.If so, there must be some force to hold the molecule for a time inthe cis-position, against the dipole repulsion, and this can only bethe van der Waals attraction of the chlorine atoms, which in thecis-position are about 2.7 A.U. apart, much like neighbouringmolecules of liquid or solid chlorine.The work required to separatethem against this force can be roughly estimated from the heat ofevaporation of chlorine. This is, a t the ordinary temperature, about4 kg.-cals. per g.-mol., or 2 kg.-cals. per g.-atom. If we supposethat in the evaporation of the liquid each chlorine atom has toovercome the van der Waals attraction of 4 or 5 neighbours, thiswould make the heat of separation of two atoms 400-500 cals.,which is of the same order as the dipole potential. The sameinfluence seems to be active in dichloroethylene, CHCKCHCL. Herethe cis- and the transform (b.p. 60.1" and 47.5") are stable at theordinary temperature, but change into one another at measurablcrates in the vapour a t 300"; and it has been found 31 that theequilibrium mixture, from whichever side it is approached, contains28 C, P. Smyth, R. W. Domte, and E. B. Wilson, J . arner. Chem. SOC.,1931, 53, 2005, 4242; A,, 1931, 786; 1932, 110; C. T. Zahn, Physical Rev.,1931, [ii], 38, 521; A., 1931, 1113.29 I<. W. F. Kohlrausch, 2. physikal. Chew., 1932, [B], 18, 61; A., 897.30 A. Dadieu, A. Pongratz, and K. W. I?. Kohlrausch, Monatsh., 1932, 60,31 L. Ebert and R. Bull, 2. p ? / y s i / a l . L'hem., 1931, [ A ] , 152, 451 ; A., 1931,For a discussion, sco H. A.Stuart, I'hysikal. Z., 1831,32, 793; A., 1932,221 ; A., 898.430.1356SIDGWICK : GENERAL STEREOCHXMISTRY. 67about 63% cis and 37% trans. Since the dipole repulsion mustcertainly favour the trans-configuration, we can only conclude thatthe van der Waals force is more effective in the opposite direction.4. Electron repulsion of non-linked atoms. The “ atomicradii” calculated from the distances between the nuclei of linkedatoms are now known to within a few hundredths of an A.U. Butthe least distance between two atoms which: are not linked is muchgreater than corresponds to these radii; and this fact, which is ofgreat importance in stereochemical phenomena, has been somewhatoverlooked. For example, the “radius” of a krypton atom canbe determined (1) from its spectrum, giving a value correspondingto the radius in a (2) from theviscosity of the gas,32 the “ collision radius ”; (3) from thecrystalline solid.The values are : spectroscopic 1.06, collisionradius 1.55, crystal radius 2.01 B.U. This shows that the distanceof nearest approach is in the crystal about 2 A.U. and in the gasabout 1 B.U. greater than in the link. For this greater distance inthe crystal there is much evidence. The densities of the diatomic“ permanent ” gases in the solid state, compared with those deducedfrom their internal radii, show that to fill up the space in the crystalwe must put an “ envelope ” about 1 A.U. thick round each mole-cule. In solid benzene hexachloride the minimum distance betweenthe nuclei of two chlorines belonging to different molecules is3-74 A.U.= This gives an external radius of 1-87, and if we subtractthe internal radius of 0.97 A.U., we are left with an envelope 0-90A.U.thick. So, too, Hendricks 34 has shown that in a whole seriesof solid organic compounds the nearest approach of two carbonatoms of different molecules is from 3.6 to 3.9 B.U. In graphitethe distance between the separate flat sheets, each of which is reallya giant molecule, is 3.41 A.U. These distances are due essentiallyto the electrostatic repulsion of the electrons, whose magneticmoments are already paired within the molecule. This force willgradually increase as the atoms approach one another, until itbalances the van der Waals attraction, which is due to polarisationand resonance.The chemist is more interested in molecules in the liquid or gaseousthan in the solid state, and here owing to their greater freedom ofmotion they will come nearer, and the “ envelopes ” will be thinner,its the collision radii show.The data for liquids and vapours are less32 For a very ingenious method of deducing the structure from the collisionarea, see R. M. Melaven and E. Mack, J . Amer. Chern. SOC., 1932, 54, 888;E. H. Sperry and E. Mack, ibid., p. 904; E. Mack, ibid., p. 2141 ; A., 563,566,904.link, the “ internal ” radius;33 S. B. Hendricks and C. Bilicke, ibid., 1926, 48, 3007; A., 1927, 98.94 Chern. Reviews, 1930, No. 468 GENERAL AND PHYSICAL CHEMISTRY.direct than for solids, and the distances will obviously vary with theconditions, and especially with the thermal energy.Good evidence of this repulsion is given by the measurements,from the scattering of X-rays by the vapour,35 of the distancesbetween the chlorine atoms in carbon tetrachloride, chloroform,and methylene chloride, which present several points of interest.As successive chlorine atoms are replaced by hydrogen atoms, thisdistance steadily increases :CCl, : C1-C1, 2.99 & 0-03 A.U.CHCl, : ,, 3-11 & 0.05 A.U.CH,Cl, : ,, 3.23 -J= 0.1 A.U.In carbon tetrachloride thc absence of dipole moment and thcspectroscopic data indicate that the molecule is symmetrical andhence the valency angle is 109" 28' ; the C-C1 distance must thereforebe 1.83 & 0.02 A.U.The distance between carbon and chlorine inmethyl chloride is given 35 as 1.9 & 0.1 A.U., but for a molecule ofthis kind the calculation of the distance from the curves is peculiarlydifficult, and the result may be in error by as much as 0.2 or 0.3 B.U.The '' internal " radius of carbon is known from many sources tobe 0.77, and that of chlorine, as measured in the gas, and confirmedby many of its compounds, is 0-97, giving the C-C1 distance as1.74 A.U. This is compatible with the results obtained for methylchloride, but in carbon tetrachloride, where the measurements aremuch more accurate, the distance is found to be nearly 0.1 A.U.longer.Now, if in carbon tetrachloride the chlorine atoms arecrushed together against their mutual repulsion, this must lead toa stretching of the link between them, and the observed excess of0.09 A.U.in their distance may well be due to this cause. It canbe shown that an extension of this order is to be expected. Thepotential energy due to the whole distortion in the carbon tetra-chloride molecule, the crushing and the stretching (there is nobending) can be found from the observed heat of formation. Theheat of formation from its atoms of the C-C1 link is 74.7 kg.-cals. inmethyl chloride, and 77.6 kg.-cals. in ethyl chloride. We may takethe mean value 76.2 as the heat of formation of the unstrained GC1link. Hence that of the carbon tetrachloride molecule, if therewere no strain, would be 4 x 76.2 = 304.8 kg.-cals. The observedvalue is 2904 kg.-cals., and the difference, 14.4 kg.-cals., mustrepresent the potential energy of the strain in the molecule in all itsforms.From the force constant for GC1 quoted above we cancalculate that to stretch the GC1 link by 0.09 B.U. needs 1.8 kg.-cals., or for the four links 7.3 kg.-cals. This leavcs 14.4 - 7.235 I?. Debye, 2. E'lektrochem., 1930, 36, 612 ; A., 1930, 1350SIDGWICK : GENERAL STEREOCHEMISTRY. 69= 7.2 kg.-cals. for the potential energy of compression of the chlorineatoms. The data used in this calculation, especially the thermaldata, are only approximate, and errors of 2 or 3 kg.-cals. are quitepossible; but the results are sufficient to show that the energyrelations are of the right order.This question of the length of the link is important when we tryto calculate the valency angles in chloroform and methylenechloride.If we take the length of the GC1 link to be 1.83 A.U.,the Cl*C-Cl angle in methylene chloride is 124" r f 6" : if we take itto be 1-74 A.U. the angle is 136" 6". I n either case it appearsthat the mutual repulsion of the chlorine atoms is sufficient toseparate them, against the resistance which the valencies offer tobending, to a distance of 3.2 A.U., which involves an " envelope ''rather more than 0.6 A.U. thick. It is, of course, to this atomicrepulsion that the " Thorpe-Ingold " effect is due.Another problem connected with atomic repulsion is that of theoptical activity of ortho-substituted diphenyl derivative^.^^ Thesuggestion of Mills and Kenyon that this is due to a steric inter-ference of the ortho-groups, preventing the rotation of one nucleusround the common axis of the two, has been fully confirmed by thework of W.H. Mills and K. A. C. Elliott,37 who found the samephenomenon with a 1 : 8-naphthalene derivative; and recentlyMills and J. G. Breckenridge 38 have shown that it occurs also with8-substituted N-alkylquinolines. Various attempts 39 have beenmade to determine what are the smallest groups or atoms which inthe ortho-position can inhibit the rotation. It was found that withfour ortho-methyl groups (I) racemisation practically does notoccur; 40 and that with fluorine and NH, on each ring 41 (11) theracemisation, though easy, is not instantaneous : it needs about36 For earlier references, see Ann.Reports, 1926, 23, 119; 1931, 28, 394.37 J., 1928, 1291.39 See e.g., R. Adams and co-workers, J. Amer. Chem. Soc., 1929-32 : E. E.40 W. W. Moyer and R. Adams, J. Amr. Chem. Soc., 1929, 51, 630; A.,4 1 E. C. Kleiderer and R. Adams, ibid., 1931, 53, 1575; A., 1931, 720.38 J., 1932, 2209.Turner and co-workers, J., 1929-32.1929, 43770 GENERAL AND PHYSICAL CHEMISTRY.20 minutes in boiling ethyl alcohol. These last are the smallestgroups which have yet been found capable of preventing racemis-ation. A model of o-fluoro-0‘-aminodiphenyl is given in Fig. 3 ;the radii adopted are : C 0.77 (C-C in the ring 1-42), N 0.71, F 0.68,H 0-37. It will be seen that if the hydrogen atoms of the amino-group are turned out of the way, the “inner spheres” of thenitrogen and fluorine atoms do not touch.The geometry of theortho-positions in diphenyl is very simple; if R is the radius of theatoms attached to the 0- and 0’-carbons, the nuclei of these atomswill be 2-19 - R A.U. apart; hence their inner spheres will be2-19 - 3R apart, and will touch if R is greater than 2.19 + 3,or 0.73 A.U. The radii of fluorine and nitrogen are just below thislimit, and it is impossible to explain, if we take account only of theinner spheres, why these two atoms should restrict rotation. Butif we admit that the repulsion extends beyond this range, we cansee that it may be effective, as is shown in the diagram, where thedotted line represents an envelope 0.5 -4.U. thick. It will be observedthat the envelopes of the unsubstituted hydrogen atoms on theleft-hand side of the diagram are not more than about 0-1 A.U.apart.The question of the racemisation of the diphenyl derivatives isvery different from that presented by the chlorinated methanes, inthat it is dynamic and not static. It is impossible to detect theoptical activity of a compound if its time of half racemisation ismuch less than one minute. Hence an effective steric hindrance isone which requires more energy to overcome it than that of theheaviest blow which the molecule receives in a minute. A moleculeof‘ a diphenyl derivative in dilute solution at 25” will make about1013 collisions a second with the solvent, the average energy of thecollisions being 600 cals. per g.-mol. The number of collisions ofhigher energy than the mean can be calculated by Boltzmann’sequation, which shows, e.g., that there will be one collision of 30times the mean energy (18,000 cals.) about every ten seconds.Only some of these collisions will tend to turn the molecule roundand cause racemisation; we may perhaps assume that 10% willbe effective. In that event, if the work required to overcome theresistance of the envelope-the heat of activation-is 18,000 cals.,the molecule will on the average be racemised in 100 seconds, whichmeans that its activity will last just long enough to be detected.This conclusion is confirmed by the observation of Mills and Elliottthat their 1 : 8-naphthalene derivative, which racemised with ahalf life of 16 minutes in chloroform a t 15”, had a heat of activation,as determined from the temperature coefficient of the velocity ofracemisation, of 18,500 calsSTDGWICK : GENERAL STEREOCHEMISTRY. 71FIG. 372 GENERAL ANT) PHYSICAL CHEMISTRY.Another group of phenomena in which the atomic repulsionSeems to be concerned is the valency angles as measured by meansof the dipole moments.42 This work has led to the remarkableconclusion that while the angle for carbon is not much greaterthan the tetrahedral (110-lZO"), for oxygen and sulphur it is farlarger, and usually about 140"; although, according to the wave-mechanical conclusions of Pauling, the angle for oxygen and sulphurshould be nearer to 90". This can only be understood by consideringthe actual compounds employed. In order to avoid complicationsdue to the mutual induction of dipoles, it is desirable to have theseremoved in the molecule as far as possible from one another. Hencethe method usually adopted is to compare the moment of diphenyl-methane, or diphenyl ether or thioether, with those of its mono-and di-substitution products containing polar groups (CH,, Br,NO,) in the para-position. What we really learn, therefore, is theangle of the valencies attaching carbon, oxygen, or sulphur to twophenyl groups.It is easy to see from the model that if the two rings are to becapable of rotating independently of one another, and so of passingthrough a plane phase, the valency angle of the central carbon oroxygen must be rather larger than the tetrahedral angle (about118") even if we disregard the envelopes of the hydrogen atoms inthe ortho-positions; if we take these into account it will be about140". In the dipole measurements we are concerned with theaverage value of the valency angle, and not with the result ofexceptionally severe blows. There is of course no necessity for thetwo rings to have the plane structure as one of their normal phases,but it is obvious that the thermal agitation will tend to promotethis, and will increase the vnlency angle to some extent. Theextent will depend on the resistance of the angle to deformation,of which we know the value for carbon, but not for any other element.Taking the energy of bending of the carbon valencies as 750 cals. forlo", we can see that if the whole 600 cals. of energy of the thermalimpacts was devoted to increasing this angle (which of courseis impossible), it would cause an expansion of 9". The dipolemeasurements indicate that for carbon the expansion is not morethan 10" a t the outside, but for oxygen and sulphur i t is about 30"(if we accept Pauling's view that the normal angle for a bicovalent42 E. Bergmann and co-workers, 2. physikal. Chem., 1930, [B], 8, 111; A . ,1930, 979; [B], 10, 397; A., 1931, 23; 1932, [B], 17, 81, 92, 100, 107; A . ,677; Ber., 1932, 65, 446, 457; A., 506, 507; 2. Elektrochem., 1931, 37, 563;0. Hassel and E. Nsshagen, 2. physikal. Chem., 1932, [B], 15, 417; A., 322;K. L. Wolf, ibid., [B], 17, 465; A., 794; C. P. Smyth and W. S. Walls, J.Amer. Chem.. SOC., 1932, 54, 1854, 3230; A., 794, 984SIDGWICII. : GENERAL STEREOCHEMISTRY. '73atom is a right angle, it is 50"). This strongly suggests that theresistance to bending of the valencies of a bicovalent atom is farweaker than with an element in which all the 8 electrons of theoctet are shared; indeed, since the energy is proportional to thesquare of the deflexion, it suggests that the value for oxygen orsulphur is not more than a thirtieth of that for carbon-say 30 cab.for 10" instead of 750. The Raman data for compounds like watershould afford evidence on this point, but it does not seem that thishas yet been obtained.This conclusion seems to be supported by the heats of formationof multiple link~.~3 It has been found that the relative values ofthe heats of formation from their atoms of single, double, and triplelinks of carbon to carbon are as 1 : 1.8 : 2-3, which is an indicationof the strain in the multiple links; but that for the links of carbonto nitrogen, oxygen, or sulphur the values are almost exactly as1 : 2 : 3, which shows that with these elements the strain is muchless. N. v. s.E. J. BOWENC. N. H~NSHELWOODN. V. SIDQWICKH. W. THOMPSONJ. H. WOLFENDEN43 Ann. Reports, 1931, 28, 387.c