1086 LEWIS STUDIES IN CATALYSIS. PART mf. XCV.-Studies in Catalysis. Part VIIL Thermo-chemical Data and the Quantum Theory. High Ten ipera t ure Reactions. By TVILLIAM CUDMORE MCCULLABH LEWIS. IT was shown in Part VII. (this vol. p. 457) that on the basis of the radiation theory the heat of a reaction is connected with the critical frequencies of the reactants and resultants by the relation : where N is the number of molecules in 1 gram-molecule h the Planck constant and v the critical frequency of any given molecular species taking part in the reaction. It has already been pointed out that this relation was first deduced by Haber (Ber. Bezct. physik~il. Ges. 1911 13 1117) who also attempted to verify it in three cases, namely the formation of potassium chloride potassium iodide and sodium chloride from their elements.I n the present paper it is proposed t o consider the experimental data available a t the present time with the object of obtaining if possible a wider experimental basis for the relationship. Incident-ally it. is necessary t o reconsider Haber’s calculations. F o r our present purpose it is convenient t o divide reactions into high tem-perature reactions and low temperature reactions respectively indi-cating by the former that the chemical clianges require quanta of great size correspondiiig with the visible and ultra-violet regions of the spectrum indicating by the latter that the reactions are such that quanta belonging to the short. infra-red region are sufficient to account for the critical increments involved.High Temperature Reactions. As examples of this class we are concerned mainly with the heats of formation of inorganic salts. To test the relation already given, i t is necessary to know the critical frequency of each of the sub-stances participating in the reaction. I n a large number of cases these frequencies have not yet been directly observed. Haber (Zoc. cit.) has suggested however a very simple relation which, although semi-empirical may be employed in this connexion. This relation which will be referred to as the square-root rule states that the characteristic infra-red frequency I+ of a substance that is, the frequency of the residual ray which is capable of accounting approximately for the specific heat of the substance is connecte LEWIS STUDIES IN CATALYSIS.PART VIII. 1087 with the characteristic frequency v, in the ultra-violet region in the following way : where m is the mass of an electron and M is the inolecular weight of the subst.ance. The ultra-violet frequency vv referred to is that which coi-responds with the maximum of the selective photo-electric effect. Employing the atomic weight f o r M in the case of a number of elements the alkali metals Haber has shown that the calculated and observed frequencies agree satisfactorily. Haber has extended the application of the square-root rule t o the calculation of the characteristic ultra-violet frequency of solid coin-pounds (salts). Thus in the case of sock salt Rubens and Asch-kinass have observed the characteristic infra-red band a t 51.2 p.Taking dl as 58.46 the normal molecular weight of sodium chloride, the ultra-violet wave-length thus calculated is 156.4 ,UP which agrees extremely well with the value 1 5 6 . 3 ~ ~ obtained by Martens from dispersion measurements. I n the case of potassium chloride the infra-red band occurs a t 61.1 p whence employing the normal molecular weight of the salt in the square-root rule Haber finds that the ultra-violet wavelength is 165.3 ,up whilst Martens obtained 160.7 pp from the dispersion. The values quoted are those given by Haber. So far as these data go they indicate the general applica-bility of the rule. Haber further points out that in addition to the characteristic ultra-violet f r squencies referred to in the above cases, the dispersion measurements indicate the existence of a still shorter wave-length.It is an interesting fact although not bearing directly on the present problem that these shorter wave-lengths may also be calculated with considerable accuracy by means of the squareroot rule provided we employ twice the molecular weight of the salt for the quantity 171. Thus in the case of rock salt the second ultra-violet absorption band is calculated to be 110.6 pp, whilst Martens’s value obtained from dispersion data is 110.7 pp. I n the case of sylvine Haber calculates in a similar manner that tlie shorter ultra-violet dispersional band should occur a t 11 6.7 pp, whilst Martens has calculated the value 115.3 pp. As already mentioned Haber has applied the square-root relatioil t o elements such as tho alkali metals and to iodine in which M is taken to represent the atomic weight with satisfactory results.In the case of iodine M obviously represents one-half of the molecular weight of the substance in the dissolved or gaseous state. I n general, tlierefore the term M may refer t o tlie normal molecular weight or to one-half this quantity. That the relation is largely empirical is evidenced by this lack of precision as to tht? significance of M 1088 LEWIS STUDIES IN CATALYSIS. PART VIII. especially when we consider that the investigation of the solid state by means of the X-ray spectrometer lias led t o a quite new concep-tion of the molecular weights of solids. It would appear that in the large majority of salts the term iil denotes the usually accepted value for the molecular weight.It will be shown later however. that one-half of the molecular weight appears to be the correct quantity t o employ in the case of the thallium haloids The significance t o be attached to M is not entirely arbitrary. The following considerations serve as a guide. If we restrict ourselves to the chlorides bromides and iodides of a given metal we would expect on general grounds t o find a certain sequence in the ultra-violet frequencies such 2s is found in the far infra-red region (com-pare Rubens and von Wartenberg Sitzzingsber. K . Aknd. Wiss. Berlin 1914 169). That is we would expect the bromide to occupy an intermediate position between the chloride and iodide. I n the cam of the thallium Ealoids using the nornial molecular weights, we obt ,in f o r the ultra-violet frequencies 15-52 x 1014 for the chloride 18.3 x 1014 for the bromide and 15-21 x 1014 f o r the iodide.Using the half -molecular weights the corresponding values are : 15.21 x 1014 12.93 x 1014 and 10.76 x 1014. I n the first case the sequence is broken in the latter it remains. We conclude there-fore that the latter values are more nearly correct. It will be shown later that ths conclusions here tentatively drawn are borne out from the point of view of the heat determinations. I n Raber’s consideration of the heats of formation of salts the process is regarded as involving the removal of electrons from certain atoms and their addition to others. Haber visualises the process in the following way for the union of a halogen with an alkali metal.Let us imagine an electric space lattice containing halogen atoms and atoms of the metal which have not yet reacted with one another to give the solid salt. The electric space lattice is supposed to possess properties which may be regarded as the mean of those exhibited by solid halogen and solid metal separately. This mean o r average state is then characterised by the single ultra-violet fre-quency (u1+v2)/2 where v3 is the frequency of the alkali metal by itself and v2 is that of the solid halogen. When transfer of the elec-tron has taken place the nature of the space lattice is altered the frequency being now that of the alkali salt. Haber then proceeds to determine whether the work % term Ziv involved in the removal of * Haber regards the quantum as measuring the \vork of removing nil It would appear more justifiable t o idcntify the quantum with the electron.total energy change involved in the transfer of the electron LEWIS STUDIES IN CATALYSIS. PART VIII. 1089 an electron from the alkali haloid salt space lattice is equal to the heat of formation reckoned per grnm-molecule together with the work term J t ( 0 . 5 ~ ~ + 0 . 5 ~ ~ ) . The first case considered by Haber is that of potassium iodide. The heat evolved by the union of the solid elements to produce the solid salt is 80,100 cals. per gram-molecule of the salt. Pohl and Pringsheim have observed the selective photo-electric effect of potass-ium the frequency being v,=0*685 x 1015. From measurements of the atomic heat of iodine it follows that the characteristic iodine frequency in the infra-red is 2-0 x 1012.Employing the square-root rule with M = 127 Haber calculates the ultra-violet frequency of solid iodine to be v1 = 0.9646 x 1015. Hence, N k ( 0 . 5 ~ ~ + 0 . 5 ~ ~ ) = 79,630 cals. The heat of union of K and 1=80,100 Hence for the salt NhvKI := 159,730 From this result Haber calculates the ultra-violet frequency of the salt to be 1.654 x 1015. Applying the square-root rule in the inverse manner Haber calculates from this value the characteristic fre-quency of the salt in the far infra-red region. The result expressed in wave-length is 100 p. The value observed by Rubens (Zoc. c i t . , 1914) is 94.1 p. Haber next considers the formation of sodium chloride.The lieat of reaction between solid chloride and sodium is taken to be 94,600 cals. The ultra-violet frequency of rock salt obtained from disper-sion measurements is 1.918 x 10'5 or A,= 156.4 pp. This corresponds with the value 185,200 cals. for NJLV~;,,:, the radiant energy re-quired to activate one grsm-molecule of the salt. Subtracting the heat of formation from this quantity we find the ~ i l u e l of ( 0 . 5 ~ ~ ~ + 0*5vX,,) namely 0.9382 x 1015 for half the sum of the frequencies of sodium and chlorine. On doubling this value and subtracting from i t the ultra-violet frequency of sodium which Pohl and Pringsheim have found by experiment to be vSn =0*947 x lO15,* we obtain the value vc = 0.9294 x 1015 for the ultra-violet frequency of solid chlorine.Haber uses this to calculate the density of solid chlorine, employing a relation of Lindemann and finds a number of the order which would be anticipated. This however is not a rigid test. Haber therefore considers the two following reactions simul-taneously K + C1= KCl and Na + Cl = NaCl. On subtracting the second equation from the first we obtain : ,, ,, The agreement is fairly good. K+ NaCl=KCl-+ Na. * The above value is that. quoted by Haber. The corresponding wave-length is 317 pp. Recent measurements by Pohl and Pringsheim however, give the value 340 pp for the maximum of the selective photo-electric effect of sodium (compare Hughes " Photo-electricity," p. 84). VOL. CXI. x 1090 LEWIS STUDIES IN CATALYSIS. PART VIII. The corresponding energy expressions are : which give on subtraction N'(VKC - V N ~ C I - Oa5VK f O*'v~a) = QKCI - QN~CI.If we now write vK =0*685 x 1015 vNRCl = 1.918 x 1016 vSa =0*947 x we can calculate the ultra-violet frequency of sylvine. The value thus obtained is 1.8683 x 1015 or ~ = 1 6 0 * 5 pp which is in excellent agreement with the value calculated by Martens from dis-persion measurements namely 160.7 pp. Reviewing Haber's treatment of the problem it is evident that considerable 'doubt exists as regards the mechanism whereby half the sum of the frequencies of the halogen and metal is introduced, although it is evident that the results obtained by this means are in good agreement with the observed values. On the basis of the expression for the heat of a reaction quoted a t the beginning of this paper we should have expected the sum of these two quanti-h s not half the sum.Haber's concept of the mechanism of union of the halogen atom with the atom of the alkali metal seems to involve a rather artificial mean stage which is itself regarded as the starting point of the process. An alternative view might be taken of the mechanism and this view has the advantage that it does not restrict us to the solid state only. If we suppose that the ultra-violet quantum corre-qmnding with the selective photo-electric effect breaks the bond between two adjacent atoms that is activates two atoms in a chemical sense then one quantum characteristic of sodium plus one quantum characteristic of chlorine serves to bring about the following reaction 2Na + 2C1= 2NaC1.Hence the heat of forma-tion 20 reckoned for two gram-molecules of the salt would be given by or the heat of formation of one gram-molecule is given by which is simply Haber's expression without any assumption beiiig made as t o a mean stage. [ 2 N h V N a C 1 - (NhVNa + VCJ]? [ N ~ v - 0*5Nh(~, + vc)], Dissociation of the Halogens. The dissociation of chlorine bromine and iodine may be con-sidered before the question of the formation of salts as the data are required for later calculations LEWIS STUDIES IN CATALYSIS. PART VIII. 1091 It will be observed that the relat,ion is identical with Q = (Eresultaiits - E,e.rctallt6). where E stands for the critical increment as defined i n previous papers. I n the case of gaseous iodine and bromine Evans (Astrophys.J. 1910 32 I 291) has fouiicl that on raising the temperature, the bands in the visible region finally disappear the lowest observed temperature of disappearance being 950O. The tempera-ture of disappearance of colour is a function of the pressure of the gas the greater the pressure the higher being the temperature of disappearance. I n view of this behaviour Evans has concluded that the disappearance of colour is due to dissociation into atoms, which evidently do not absorb in the visible region. The atoms must absorb either in the ultra-violet or the infra-red region. The heat of dissociation of the halogens is negative heat being absorbed in the process. I n order that Q may be negative the critical increment of the reactant (molecular form) must be greater than the increment of the resultant (atomic form).Hence on taking Evans’s results into account and applying the radiation expression we conclude that the critical increments of the atoms correspond with quanta .in the infra-red region. Further the heats of dissociation represent quantities of energy considerably greater than those obtainable from the infra-red region. It is obvious that in the case of gaseous dissociation the critical incre-ment of the reactant must exceed the observed heat of dissocia-tion. If however the critical increments of the resultants are small as in the present case the heat of dissociation cannot be very different from the critical increments of the corresponding tindissociated molecules. The observed heats of dissociation per gram-molecule a t a fairly high temperature that is at a temperature a t which the dissocia-tion becomes measurable are in round numbers as follow: chlorine - 113,000 cals.(compare Pollitzer Ahrens “ Sammlung,” 1912 17 434) ; bromine - 50,000 cals. (Bodenstein and Cramer, Zeitsch. Elektrochem. 1916 22 327) ; iodine - 36,860 cals. (Bodenstein and Starck ibid. 1910 16 961). The values in the case OF bromine and iodine are known with considerable exactness ; that for chlorine is a rough approximation only. From a consideration of the temperature range a t which these gas- dissociate sensibly i t is evident that we are dealing with high temperature reactions that is reactions which require larger quanta than those which correspond with the short infra-x x 1092 LEWIS STUDIES IN CATALYSIS.PART VIII. red region. Further iodine dissociates more easily than bromine and bromine more easily than chlorine. We woi-lld expect there-fore that the critical energy and hence the size of the correspond-ing quantum would increase in the order iodine bromine, chlorine. This sequence is also exhibited by the values of the respective heats of dissociation. To show that radiation in the visible region is capable of sup-plying quanta of the necessary size we may proceed in the follow-ing approximate manner. As indicated by its violet colour iodine absorbs largely in the red end of the visible spectrum. Assuming that the characteristic wave-length is of the order 700,up it follows that the critical increment per gram-molecule is 41,000 cals.in round numbers. This is slightly greater than the observed heat of dissociation. It is therefore a possible value. Similarly if we take the wave-length 500 ,up to be characteristic of bromine this wave-length corresponding with absorption in the green region we find the critical increment per gram-molecule t o be 57,000 cals. This quantity is somewhat greater than the observed heat of dis-sociation of bromine. Owing to the very extensive absorption of both iodine and bromine throughout the visible region i t is impossible at the present time to ascribe the critical increment t o ar,y particular band. The investigations of Hasselberg and of Konen (compare Konen Ann. Ph?ys. C'hen2. 1898 [iii] 65 257) show that iodine possesses numerous bands in the visible region.The same is probably true of bromine although a recent investiga-tion by Peskov (,7. Physicnl C'hem. 1917 21 382) indicates a broad maximum a t 436,up with considerable absorption down to 600pp. I n the case of chlorine a well-defined band has been measured by Brannigan and Macbeth (T. 1916 109 1277) in the near ultra-violet occurring at h = 327 pp. Peskov (Zoc. c i f .) places the maximuin a t 334 p,u. Taking Brannigan and Macbeth's value, i t is found that the critical increment of chlorine is 86,750 cals. per gram-molecule. This is considerably less than the value quoted for the heat of dissociation but it is to be remembered that the latter is a rough approximation and the quantity 86,750 is theoretically an upper limit for the heat effect.We require the critical increments of the halogens in the gaseous state in dealing subsequently with the formation of salts. For this purpose we shall employ the following average values chlorine 86,750 cals. per gram-molecule; bromine 57,000 cals. ; and iodine 41,000 cals. It may be mentioned that the process of dissociation of chlorine, bromine and iodine is one which requires larger quanta than are required for the decompositJon of the corresponding halogen hydr-acids. The only exact measurements available in this connexio LEWIS STUDIES IN CATALYSIS. PART VIII. 1093 refer to hydrogen iodide for which the critical increment per gram-molecule is 20,000 cals. a quantity which corresponds with the short infra-red region. H e a t o f F o r m a t i o n o f S a l t s Potassium Chloride.The characteristic ultra-violet freclilency of this salt as obtaiiied from dispersion measurements is 18.6 x 1014 or A,,= 160.3 pp. The value of the critical iiicrerneiit NhvKC is therefore 175,960 cals. per grain-molecule. As regards the critical increment of potassium the maximum of the selective photo-electric effect occurs a t A = 440 pp whence the increment’ is 64,517 cals. This amount of energy 011 the view already suggested represents the ainouiit required to activate two adjacent atoms of potassium. The stoicheiometric equation requires one-half of this quantity. Similarly the critical iiicreineiit of oiie gram-molecule of chlorine or two gram-atoms of chlorine is 86,750 cals. The total critical iiicremeiit of one gram-atom of each reactant is (64,517 + 86,750) 12, or 75,634 cals.Applying the equation it follows t h a t & = 175,960 - 75,634 = i- 100,330 caIs. in round numbers whilst & &served (Thornsen) = + 105,600 cals. Hack-spill (“Tables Aiinuelles,” 3 p. 588) gives the value 99,650 cals. for the heat of formation. The agreement between observed and calculated values is moderately good. It may be mentioned t h a t if the square-root rule had been employed with M=74.5 in the case of the salt and the infra-red frequency as determined by Rubeiis the critical iiicreiiient per gram-molecule would have bee11 164,000 cals. which is somewhat lower than t h a t obtained from dispersion measurements. As regards the observed heats of forma-tion of salts it may be pointed out that the values given are in general obtained indirectly so t h a t the result is liable to a certain amount of error.Potassium Bromide. The characteristic infra-red band as observed by Rubens (coni-pare Rubens and voii Wartenberg #itzungsber. Ii. A kad. Wiss., Berlitt 1914 169) occurs a t A-82.61“. Measurements of the molecular heat of the salt require the wave-length 82.4 p (Nernst, A72n. Physik 1911 [iv] 36 395) in the Nernst-Liiidemann formula that is v r =0.036 x 1014. Usiiig the squareroot rule an 1094 LEWIS STUDIES IN CATALYSIS. PART VIII. the normal molecular weight of the salt the ultra-violet frequency vv= 16.67 x 1014 or A = 180 ,up. Hence the critical increment, NhvKBr per gram-molecule is 157,700 cals.As before the energy required for two gram-atoms of potassium is 64,517 cals. For bromine the critical increment for two gram-atoms is 57,000 cals. Hence for the formation of one gram-molecule of the salt the t o t a l critical increment of the reactants is (64,517 + 57,000)/2 = 60,758 cals. Hence Q = 157,700 - 60,758= + 96,940 cals. The observed heat of reaction between liquid bromine and solid potassium is +95,310 cals. The calculated value refers to gaseous bromine so that it is necessary t o add the heat of vaporisation of bromine namely 3500 cals. t o the observed value thereby obtaiii-ing the quantity 98,810 cals. The agreement between calculated and observed values is moderately good. Sodium Chloride. The observed infra-red band of the salt occurs a t 52p.The value 51p is required to account f o r the molecular heat (compare Nernst loc. cit.). The infra-red frequency is therefore 0.0577 x 1014. Using the square-root rule and the normal mole-cular weight of the salt, the ultra-violet frequency vV= 19-27 x 1014, or A = 155 ,up which agrees excellently with the value calculated from dispersion measurements. It follows that the critical incre-ment NhvNaC, per gram-molecule of the salt is 182,290 cals. The critical increment of two atoms of sodium is obtained from the position of the selective photo-electric effect which occurs at h=340 pp or vxa =8-8 x 1014 the value of the increment being 83,250 cals. Hence the total critical increment of one gram-atom of sodium and one gram-atom of chlorine is (83,250+86,750)/2 or 85,000 cals.Hence, Q = 182,290 - 85,000 = 97,290 cals. Q (observed) =97,800 ,, The agreement is good. Potnssiunt Iodide. It has already been pointed out that Haber demonstrated the validity of the heat expression in connexion with this substance. Haber considers the reaction as taking place between the elements in the solid state. For iodine he makes use therefore of the square-root rule t o calculate the characteristic ultra-violet fre LEWIS STUDIES IN CATALYSIS. PART VIII. 1095 quency. On the other hand considering the reaction between gaseous iodine and solid potassium and employing therefore the value 41,000 cals. for the critical increment of two gram-atoms of iodine vapour the agreement between the observed and the calcu-lated heat effect is far from satisfactory.We are dependent of course upon the correctness of the infra-red characteristic fre-quency of the salt which has been observed to occur a t v?. =0*0319 x 1014. Using the square-root rule and the normal inolecular weight of the salt we obtain for the ultra-violet fre-quency the value 17.45 x 1014 or At.= 172 p p whence Nhv, = 165,077 cals. Employing the values already given for the critical increments of solid potassium and iodine vapour the calculated heat effect is 112,320 cals. whilst the observed is 83,100 cals. The discrepancy is very great. If we employ one-half of the normal molecular weight of the salt in the square-root rule we obtain, finally the value 63,680 cals. for the calculated heat of the reac-tion. This is now considerably less than the observed value.There does not appear to be any justification however for this mode of calculation in view of the results obtained in the case of the other alkali haloids in which the normal molecular weight of the salt is employed. The agreement obtained by Haber rests on the fact that in the case of iodine he applied the square-root rule to the infra-red frequency given by Lindeniann’s melting-point formula. The resulting value for the critical increment for solid iodine is 91,300 cals. The value which we have taken f o r gaseous iodine is widely different namely 41,000 cals. It may be pointed out however that> the value A,=172pp for the ultra-violet wave-length of the salt-a quantity which is employed by Haber and by the author-is almost certainly in-correct as it involves a breaking down in the expected sequence of the chloride bromide and iodide.Thus since hKcl = 160.7 pp and hRBr= 180 p p we should expect A, to lie somewhere in the region of 200pp. If we take the observed value for the heat of formation together with the critical increments of solid potassium and gaseous iodine already employed we can calculate the critical increment of the salt. Thea value thus obtained is 135,860 cals. per gram-molecule. It follows from this that the ultra-violet fre-quency of the salt is 14.4 x 1014 or A, =208 ~ p . This value occupies roughly the expected position with respect to potassium chloride and potassium bromide but a t the present time there is no means of further testing its accuracy.Taking this value to be correct and applying the squareroot rule in the inveres sense we find that the characteristic infra-red wave-length is 115 p 1096 LEWIS STUDIES IN CATALYSIS. PART VIII. Silver Chloride. The observed infra-red band of the salt occurs a t X-81.5p. Hence v,.=0'0368 x Using the square-root rule and the normal molecular weight' of the salt we obtain for the ultra-violet frequency ~ = l 8 - 6 6 x or A,= 160pp. That is Nhv,,, = 166,520 cals. For silver the infra-red frequency given by Biltz (Zeitsclz. E'ZektrocJwm. 1911 17 676) on the basis of the Linde-mann melting-point formula is lrl. = 0.0436 x l O I 4 (compare also Lindemann B e y . D e u f . physikrrl. G'es. 1911 13 1114). Using the squareroot' rule with M= 108 we obtain for the! ultra-violet frequency I!,,= 19-23 x or A,.= 156 pp. The corresponding value of Nhv, is 182,016 cals. for the activatioii of two gram-atoms. Hence the total critical increment of one gram-atom of each of the reactants is (182,016 + 86,750)/2 OK 134,383 cals. Hence Q = 166,520 - 134,383 = 32,140 cals. whilst Q observed (Fischer Zeitsch. Elektrochei~i. 1912 18 283) = 29,940 cals. The agreement is moderate. Silver Bromide. The observed infra-red band of the salt occurs a t 127~1 or v,. =0-0266 x 1014. Proceeding as in the previous case the ultra-violet frequency is 15-48 x 1014 or A,= 194 pp. Hence Nh,VAIIBr = 146,440 cals. From the data already given i t follows that the critical increment of the reactants per gram-atom of each is (182,016 + 57,000)/2 = 119,508 cals.Hence the heat of formation ($ = 146,440 - 119,508 = 26,930 cals. in round numbers. The observed heat of formation for liquid bromine and solid silver is 22,700 cals. Hence for the reaction involving gaseous bromine the observed heat is 26,200 cals. which is in good agreement with the calculated value. I n all cases the calculated heat effect is a relatively small diff ereiice between two large quantities. It is not to be expected in general that the result can be an accurate one. Silver Iodide. The characteristic iiifra-red band of this salt has not yet been measured. It is possible however to obtain a moderately exact value by comparing the observed values of the three thallium haloids with the two silver haloids all of which have been measured by Rubens.These are as follows TlCl 9 1 . 6 ~ ; TlBr 117-0p; TlI 1 5 1 . 8 ~ . For the silver haloids AgCl 8 1 . 5 ~ ; AgBr, 112.7 p. On plotting these figures the lines run approxim LEWIS STUDIES IN CATALYSIS. PART VIII. 1097 ably parallel aiid an extrapolation iiidicates h = 145 /L for silver iodide. This value is probably correct to k5 per cent. The infra-red frequency is therefore 0.0207 x 1014. Using the square-root rule and the normal molecular weight of the salt the ultra-violet frequency is 13-46 x 1014 or A = 223 pp Hence Nhv,, = 127,332 cals. Employing the values already obtained for silver and gaseous iodine the total critical increment of the reactants per gram-atom is (182,016 + 41,000)/2 =111,508 cals. Hence the heat formation = 127,332 - 111,508 = + 15,820 cals.in round numbers. The heat of formation of the salt. from the elements in the solid state has been accurately measured by Fischer (Zoc. c i f . ) the value being + 15,100 cals. Taking the heat of sub-limation of iodine to be 3000 cals. per gram-atom the observed heat of the reaction involving gaseous iodine is 18,100 cals. which agrees approximately with that calculated on the radiation theory. It will be observed that in the above calculation we have made use of the value 41,000 cals. for the gram-molecular increment of gaseous iodine. Had we employed the value 91,300 cals. obtained from the infra-red band by means of the square-root rule (which Haber has employed in the case of potassium iodide) the heat of the reaction between the solid elements calculated on this basis would have been a negative quantity namely -9300 cals.in place of the observed positive quantity + 15,100 cals. This further emphasises the difficulty met with in the formation of potassium iodide. The result serves to throw still further doubt on the value 172 pp as being the ultra-violet wave-length of potassium iodide. Q T hnl li u m Nnlo ids. T~c~ZZiwn C'liloride.-Direct measurement of the infra-red band of the salt gives the value A=91.6p or v,=0.0327 x 1014. Using the squareroot rule and the normal molecular weight the value obtained for the ultra-violet frequency is 15-52 x 1014 or A = 193 pp. Hence NhvTlc = 146,820 cals. For thallium metal, Biltz (lor. c i t . ) gives the value v,.=0*0184 x 1014. Using the squareroot rule the ultra-violet frequency v,.= 11.15 x or h,=269 pp. The value of Nhv, for two gram-atoms of the metal is therefore 105,480 cals. Hence the critical increment of the reactants per gram-atom is (105,480 + 86,750)/2= 96,115 cals. and the heat of formation Q = 146,820 - 96,115 = 50,700 cals. in round numbers. The observed heat of formation is 48,600 cals. The agreement is satisfactory. Thallium Broniide.-The infra-red band occurs at h = 117 p or v,. =0.0256 x Using the square-root rule and the normal x s 1098 LEWIS STUDIES IN CATALYSIS. PART VIfI. molecular weight we obtain for vv the value 18.3 x 1014 or A,= 164 pp. Hence NhvB = 173,120 cals. The critical increment of thallium and of bromine have already been given. The total critical increment of the reactants is (105,480 + 57,000)/2 or 82,240 cals.The observed heat effect for the reaction involving liquid bromine is 41,300 cals. and therefore for gaseous bromine 44,800 cals. The discrepancy is very great. Thallium Zodide.-The infra-red band occurs a t 151.8 p or vY = 0.0197 x 1014. Using the square-root rule and the normal mole-cular weight of the salt we obtain vv=15*21 x 1014 or A,=197ppu. Hence Nhv,, =143,890 cals. The critical increment of the reactants is (105,480 + 41,000)/2 = 73,240 cals. Hence Q = 143,890 -73,240=70,650 cals. whilst Q observed is 30,200 cals. As this refers to solid iodine the observed value for the reaction involving gaseous iodine is 33,200 cals. The discrepancy is even greater than in the case of the bromide.It has already been pointed out however that the values obtained for the ultra-violet frequencies of the thallium haloids suggests that the square-root rule should be employed in conjunc-tion with half the molecular weight of the salt in order to give the correct sequence in the ultra-violet frequencies of the +,hree salts. Carrying out the calculation we obtain the following results : Hence Nhv for the salt is 143,890 cals. and therefore Q=47,780 cals., whilst the observed value is 48,600 cals. I-Ience Nhv for the salt is 122,320 cals. and therefore Q=40,080 cals., whilst Q observed is 44,800 cals. Thallium Zodide.-v,, = 10.76 x 1014 o r A,= 278 ,up. Hence Nhv= 101,790 cals. and therefore Q = 28,550 cals. The observed value is 33,200 cals. All three thallium haloids exhibit satisfac-tory agreement between the observed and calculated heats of formation on the assumption that one-half of the molecular weight should be employed in conjunction with the square-root rule.This is scarcely likely to be accidental although no reason for the choice can as yet be given. Hence Q = 173,120 - 82,240 = 90,880 cals. Thallium Chloride.-v,,c = 15.21 x 1014 or A,,= 197 pp. Thallium Bromide.-v.r,,3 = 12.93 x 1014 or hv= 232 pp. Lead Chloride. The characteristic infra-red band of lead chloride has been observed by Rubens at Ar=91.0 p that is v,=OaO33 x 1014. Using the normal molecular weight we obtain for the ultra-violet fre-quency vv = 23.33 x 1014 whence the critical increment per gram LEWIS STUDIES IN CATALYSIS. PART VIII.1099 inolecule is 220,700 cals. The infra-red frequency for metallic lead is 0.0195 x 1014 (Neriist Zoc. cit.) whence the ultra-violet frequency is 11.9 x 1014 o r hv= 252 p p ; whence the critical increment of two gram-atoms is 112,574 cals. and the increment per gram-atom is 56,290 cals. The critical increment per gram-molecule (Cl,) is 86,750 cals. Hence the heat of formation of one gram-molecule of lead chloride is 220,700 - (56,290 + 86,750) = 77,660 cals. The observed heat of formation (involving gaseous chlorine) is + 85,570 cals. according t o Braune and Koref (Zeitsch. EZektrochem. 1912, 18 818) and 85,380 cals. according to Gunther (ibid. 1917 23, 197). The agreement is only approximate the discrepancy being due probably to error in the value taken for the critical increment of the salt.Assuming the observed value of Braune and Koref we can calculate a corrected ' value for the critical incre-ment of the salt namely 228,610 cals. By applying the square-root rule we find the infra-red frequency to be 0'034xlOf4 or A,. =89*2p7 which is not greatly different from that observed by Rubens (91.0 p). This illustrates how sensitive the final value for the heat effect. is to error in the infra-red frequency. Mercu~ic Chloride. The infra-red band of the salt occurs a t 95p. Employing t.he normal molecular weight the ultra-violet frequency is found to be 22-06 x 1014 or hv= 136 pp. The critical increment is therefore 208,690 cals. per gram-molecule. The corresponding quantity f o r one gram-molecule of chlorine is 86,750 cals.Lindemann (Zoc. (,it.> finds the infra-red frequency of mercury t o be 0.022 x 1014 whence the ultra-violet frequency is 13.2 x 1Ol4 or hv=227 pp. Hence the critical increment of mercury is 124,872 cals. for two gram-atoms, or 62,436 cals. per gram-atom. The heat of formation per gram-molecule of mercuric chloride is therefore 208,690 - (86,750 + 62,43$) = 59,504 cals. The observed heat of the reaction between liquid mercury and gaseous chlorine is 53,300 cals. Lindeniann's value for the infra-red frequency refers t o solid mercury. On correcting for the latent heat of fusion the calculated heat of the react'ion is 59,000 cals. Mer carotts C?L loride. Let us assume in the first place t,hat the molecule of the salt is represented by HgCl.The observed infra-red band is 98*8p or v,. =0.0304 x 1014. Using the normal molecular weight we find i t u = 19-76 x 1014 or A,= 152 pp whence the increment is 186,930 x x" 1100 LEWIS STUDIES IN CATALYSIS. PART VIIT. cals. per grani-molecule. The critical increinerit per gram-atom of mercury we have already taken to be 62,436 cals. the correspond-ing quantity per gram-atom of chlorine being 43,375 cals. Hence the heat of formation of the salt is 186,930-(43,375+62,436)= 81,120 cals. The observed heat of formation (Nernst Zeitsch. pJ~ysikal. Chptn. 1888 2 23) is 31,300 cals. The discrepancy is very great. Let us now assume that the salt is represented by the formula Hg,CI,. Using the square-root rule with this molecular weight we find v,=27.97 x 1014 or hV=107pp.Hence the increment is 264,600 cals. The reaction is now represented by 2Hg + C1 = Hg2Cl2 hence the critical increment of the reactanh is double the value given above. The heat of formation is thus calculated to be 264,600 - 211,620 =53,000 cals. in round numbers. As the observed heatl of reaction refers t o one-half the quantities here con-sidered it is necessary to calculate the heat effect per gram-atom of mercury namely 26,500 cals. This is in much better agreement with the observed value than the result obtained by the previous method. It appears therefore that the correct formula is Hg2C1,, and not HgCl a conclusion which is borne out by measurements on the salt' in the dissolved state. Employing the observed value for the heat effect we can calculate a ' corrected ' value for the increment of the salt namely 274,000 cals.in round numbers. Thence, calculating backwards we obtain the value v,.=0*0302 x 1014 or A = 101 ,u for the salt which is not very different from the observed value (98.8 p ) . The Reaction Pb + 2AgC1= PbCl 1- 2Ag. The' lieat of this reactlion per gram-atom of lead is according t o Magiius ( Z e i t s c h . ElektrochPrn. 1910 16 273) 24,590 cals. As we have already ohtained the critical increments for the substances participating i i i this reactioii it should be possible t o calculate the heat eflect. Thus: Jncrementr for two gram-inolec~iles of AgCl ... = 2 x 106,620 cals. - ......... Y S .. one grain-atom o f l e d 56,290 Henco total critical increment of re- - actants ......................................389,330 cals. - Increment for one grani-molecule of PbCl ... - 228,610 9 9 , two gram-atoms of silver - 182,016 - ...... Hence total critical iiicrement of re-sultnnts .................................... - - 410,626 cals. Hence Q = 410,626 - 389,330 = + 21,300 cals. in round numbers. This is of the correct order of magnitude and the result is satisfac LEWIS STUDIES IN CATALYSIS. PART VIJI. 1101 tory in view of the fact t h a t we are dealing with a small difference between two very large quantities. The I?eaction P b + Hg,Cl = PbCl -t- 2Hg. Proceeding as in the previous case we obtain : Increment for one gram-atom of lead ......... = 56,290 9 , gram-inolecule of Hg,Cl,. .. = 374,000 Hence total critical increment of re-actants ....................................- :1:30,290 cals. lncreiiiciit fur one gram-iiioleciilr~ of l’hC1 ... = 228,610 1 9 , two grain-atoms of inereury ... =124,870 Hence total critical iiicrement. of re-sultitilts .................................... = 363,480 C ~ S . Hence Q = 353,480 - 330,290 = 23,190 cals. Tlie value observed is 21,800 cals. approximately Giinther (loc. The agreement is satisfactory especially as the critical incre- ,.it.). ments are very large. LYji w r Cyun i d e . The heat of formation of this salt froiri silver aiid gaseous cyaiio-gen as determined by Thomsen is 1393 cals. per gram-molecule. This quantity i q so small t h a t it would be impossible to calculate it with any degree of precision by the method employed in previous cases.I n addition the question of the critical frequency of cyano-gen is in an involved state (compare Grotrian and Runge PAysikuZ. Zeitsch. 1914 15 545). We may use the available data t o calcu-late the critical frequency of cyanogen. Rubens and von Warteiiberg (Zoc. c i t . ) have observed the infra-red band of silver cyanide a t A,.=% p approximately. That is I!,.= 0.0323 x lo** and employing the square-root rule in coiljunction with the normal molecular weight of the salt as we have done in tlie case of the silver Iialoids we obtain 15.86 x 101.‘ for the ultra-violet frequency and A,= 189 ,up. Hence tlie critical iiicrement per gram-molecule is 150,000 cals. The stoicheioirietric equation considered is Ag+ CN=AgCN. We have already seen that the increment of one gram-atom of silver is 91,010 cals.The heat of formation being 1393 cals. the total critical increment of the reactants is (150,000 -1393) cals. On subtracting the value for one gram-atom of silver, we find t h a t the critical increment of the cyanogen group is 57,600 cals. or f o r one gram-molecule of cyanogen the value is 115,200 cals. Hence the frequency is 12.2 x 1014 or h,=246 pp. Tlie author is unaware whether any measurements have been carried out wit 1102 LEWIS STUDIES Ih’ CATALYSIS. PART VIII. cyanogen in this region of the spectrum. In the process considered. tlie energy term 115,200 cals. is t h a t required t.0 break the link between the two carbon atoms in the molecule (CN), thereby giving rise to two nascent groups of monocyanogen.This is quite distinct from the mechanism involved in tlie dissociation of gaseous cyanogen into carbon and nitrogen in which the carbon-nitrogen linking is broken. This would probably require a vory different amount of energy. Sumniury. 1. I n spite of tlie fact that. many of the available data are inac-curate and incomplete the foregoing consideration of liigh-tempera-ture reactions indicates t h a t the radiation expression is borne out in a fairly satisfactory manner. 2. The following table contains the observed and calculated values of the heat effects in those cases in which the necessary data are avaiIable to permit of the complete calculation being carried out. For the reactions considered positive t h a t is heat is evolved. Reaction.K+C1 - KC1 ........................... K+Br -. KBr ........................... Na+Cl -+ NaCl ........................ K+I 4 KI .............................. Ag+CI + AgCl ........................ Ag+Br - AgBr ........................ ;Ag+I -- AgI ........................... TI+Br - TlBr ........................ Tl+I - T1I .............................. Pb+C1 - PbCl ........................ Hg+CI - HgCl ........................ Hg+CI - &Hg,CI ..................... Pb+2AgC1 4 PbCI,+SAg ............ .ri+ci - ~ i c i ........................... Pb-tHg,Cl -t PhCI,+SHg ........ the heat effect is in all cases Heat effect per gram-atom of - Q observed. Q calculated. first reac t,a nt. 98,810 97,800 83,100 29,940 26,200 18,100 48,600 44,800 3 3,2 00 85,570 53,900 3 1,300 24,500 21,800 100,330 96,910 97,290 112,320 ? 32,140 26,930 15,820 47,780 40,080 28,550 59,000 26,500 21,300 23,190 77,660 I n a subsequent paper i t is proposed to consider the data avail-able in connexion with reactions which proceed a t a sensible velocity a t the ordinary temperature that is reactions which require quanta belonging to the short infra-red region to supply the energy neces-sary for the critical increments. MUSPRATT LABOBATORY OF PHYSICAL AND ELECTRO-CHEMISTRY, UNIVERSITY OF LIVERPOOL. [Received October 9 t h 1917.