PART I.-EINSTEIN’S LAW OF PHOTOCHEMICAL EQUIVALENCE.

INTRODUCTORY ADDRESS TO PART I.

BY PROFESSOR A. J. ALLMAND (KING’S COLLEGE, LONDON)

Received September 3 ~ d , I g 2 5 ,

I. Introductory.

The application of the quantum theory to photochemistry dates in practice from the enunciation by Einstein in 191 2 of the so-called ‘‘ photo- chemical equivalent law,” a law which, stated in its baldest terms, says that, in a photochemical reaction, one quantum of active light is absorbed per molecule of absorbing and reacting substance which disappears. This simple and attractive relation, put forward with the authority of Einstein, has proved a great stimulus to research in a somewhat neglected field of chemistry, and a field, moreover, in which an impasse seemed to have been reached in respect of such matters as the primary mechanism of photo- chemical change, the significance of the part played by the absorbed light, and the whole question of the classification of photochemical reactions. I n this sense then, the relation has proved itself a working hypothesis of great value. To what extent it can be regarded as a (‘ law ” will be dis- cussed in the course of this paper.

Before dealing with Einstein’s work, the writer would wish to emphasise particularly the degree of priority which is due in this field to Stark. This author published, four years previously to Einstein, two papers * which deal, in part, with the mechanism of photochemical change. In them are to be found, sometimes explicitly stated, sometimes only to be inferred, not only the photochemical equivalent relation, but also a clear distinction between the primary and secondary stages of a direct photochemical change, and an equally clear distinction between the mechanism of direct and indzrect (in- cluding semitised) reactions. Stark’s views undoubtedly did not receive from photochemists the attention they deserved-possibly because, as in- dicated, they were put forward more or less incidentally in the course of papers dealing mainly with other subjects ; possibly because they were clothed in qualitative language, and not given the dignity of a thermodyna- mical deduction ; perhaps because certain others of Stark’s views, with which they were bound up, immediately afterwards lost interest, in conse- quence of the development of new ideas on atomic and molecular structure by Bohr, G. N. Lewis, Kossel, and others. Whatever the cause, this neglect of Stark’s work has led to much misunderstanding as to the relations which

1 Pltysikal. Zcitsch., 9, 889, 894 (1908). See also Prinzipietz der Afom-Dynamik, II. , 207 (1911).

43 8

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PROFESSOR A. J. ALLMAND 43 9

can exist between the number of quanta absorbed in a photochemical re- action, and the final chemical effect.

11. Einstein’s Work.

In dealing with Einstein’s work on this subject, we will distinguish be- tween his thermodynamic “proof” of the law, and his subsequent quite different deduction ’’ of the same relation.’ The thermodynamic proof appeared first in the form of two German papers,2 and then, during the following year, with a slightly different treatment, as a single French paper.3 In this proof a gaseous reaction of the type-

XY + t - L X + Y, is considered. The dissociation takes place as a necessary consequence of and soZe4 by the absorption per molecule of XY of a m a n quantity t of radiant energy of frequency v-the recombination of X and Y takes place sole& with the simultaneous liberation of a m a n value of E units of radiant energy of frequency Y per molecule of XY formed. The reaction is thus a completely reversible one. The rate of decomposition of XY is assumed to be proportional to [XU] and to the radiation density (p) of fre- quency V. I t is assumed to be independent of [XI and of PI. The pro- portionality factor (A) entering into the rate of decomposition can depend on the temperature of the system (T), but on nothing else. The recom- bination of X and Y (and hence the liberation of radiant energy of frequency V) is assumed to take place according to the ordinary mass-action law, the velocity constant (A’) being dependent solely on temperature, and, in par- ticular, being independent of p. z, whether reckoned per molecule of XY formed or per molecule decomposed, is assumed to be independent of p.

If now p is the black body radiation density for frequency v at tempera- ture T, then we are simply dealing with an ordinary thermal equilibrium. As a general case, however, Einstein imagines an equilibrium in which the radiation density p corresponds, not to T, but to T,, where T and T, are different (T, will be the higher in practice). Such a pseudo-thermodynamic equillibrium * is clearly only imaginable in a closed space, the walls of which are internally completely reflecting, and under such conditions is stable. Einstein considers a small virtual change from this pseudo-equilibrium state, equates to zero the sum of the entropy changes in the gas, the radia- tion and the constant temperature reservoir which surrounds the gaseous system, and arrives at a connection between p and T,, which, provided that the conditions are in other respects those under which Wien’s radiation law is valid, leads directly to the identity-

t = h. (The Einstein Law.) I n the course of the proof, he shows that E, under such conditions,

On the other hand, in the early part of the 1913 must be ind@endent ofT.

The inverted commas are inserted by the writer to ernphasise the difference between the nature of Einstein’s treatment in the two cases-in the one, an exact mathematical proof of what will happen under the ideal conditions laid down, in the other practically a mere statement of what obviously will be the approximate result under another given set of conditions.

Ann. der Physik. (iv.), 37, 832 ; 38, 8Sr (1912). your. de Phys., 3, 277 (1913). Einstein’s terms are ‘‘ aussergewohnliche thermodynamische Gleichgewicht ” and

Such an equilibrium is not of course ‘‘ 6quilibre thermodynamique improprement dit.” to be confounded with the ordinary ’‘ stationary state ” of the photochemist.

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440 EINSTEIN PHOTOCHEMICAL EQUIVALENT LA\V

paper, he states that c may be dependent on T. (It should again be emphasised that 6 is the mean energy absorption per molecule decomposed.) Later, assuming, as happens in practice, that a whole range of frequencies is active in causing decomposition, and that the total decomposition is the sum of those caused by the single elementary frequencies, he shows that I / ,

in the above formula, is the frequency of the radiation, and has nothing to do necessarily with any characteristic frequency within the molecule. Finally, it may be noted that, although deduced for a particular type of truly monomolecular gas reaction, Einstein expressly states that the result is a general one, and can be extended to more complex gas reactions or to reactions taking place in dilute solution. I t is unfortunate, that in none of his papers does he deal with these more complex cases. The result has been, inevitably, to suggest that the photochemical equivalent relation is more applicable to dissociations of the XY + X + Y type than to other kinds of reaction; whereas a consideration of reactions of the second order would have made more clear the fact that the relation strictly applies to the formation of the primary product of photochemical change, whatever may happen subsequently.

This last point was first emphasised by Stark when putting forward a claim for priority in respect of the actual relation-

Energy absorbed = NE = Nh,,, per mol

and is, of course, of fundamental importance when dealing with attempted experimental verifications of the law.

Einstein’s deductim of the photochemical equivalent relation follows quite different lines. The absorbing (and reacting) molecule is regarded as a kind of generalised Bohr model, capable of existence only in a definite series of energy states (Bohr states), and passing from one state to another by absorption or emis ion of a quantum. H e considers two such states Z,, and Z,, of corresponding energy contents Em and En, where E,)E, and Em - E, = hv. After dealing with such a system in temperature equilibrium, lie takes the special case where T is such that p, the radiation density corresponding to frequency Y, is very low. Practicallyall the mole- cules will be in the 2, (lower) quantum state. H e further assumes that a molecule in the 2, state, besides reverting to the 2, state with emission of hv, can also, andfar more rapid&, undergo a different change analogous to a unimolecular reaction-say Z,+W. Clearly then, in such a system insolated with radiation of frequency Y from a source at a temperature higher than T, one molecule in the 2, state will be formed per absorbed quantum, and admost add will react further to give W, which corresponds to the PracticaZ vadidity of the law.

I t is of special importance here to note that theprimary and secondary reactions are clearly distinguished, which was not previously the case, and that the primary product, for the formation of which the law implicitly holds, is a higher quantum state. The process considered is, therefore, in appearance at all events, very different from that discussed in the thermo- dynamic proof.

1 A m . der Physik. (iv.), 38, 467 (1912). See also ibidem, 38, 888 ; 39, 496 (1912). Verh. d . deut. Physikal. GLS. , 18, 318 (1916).

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PROFESSOR A. J. ALLMAND 441

I I I. Warburg's Work.

Amongst the experimental researches which deal with the photo- chemical equivalent, those of Warburg,' published between the years of I 9 I 2- I g 2 I, occupy a very special position. This investigator was already, previous to 1912, engaged on a study of the energetics of photochemical reactions and was, further, in direct touch with Einstein. His work, henceforward essentially directed towards the testing of the Einstein rela- tion, is distinguished, not only by its experimental skill and accuracy, but also by the great acumen exhibited in the interpretation of the results obtained.

We further owe to him a nomenclature which derives naturally from the Einstein relation, and which will be briefly discussed. The funda- mental photochmical equivalent ( p ) is a magnitude based on the Stark- Einstein conception in its simplest form-i.e. on the assumption that a molecule absorbs a quantum and then decomposes. It is the num8e.r of gram-mols required f a r the absorption of one gram-calorie of radiant energy of frequency V, and consequent4 the number of p-am-mols primari4 decomposing per absorbed gram-caZorie. We have-

4.186 x 107 = ___ A mols * = Nhv 28470 (where X is expressed in microns, h is 6.554 x IO-~? , and N is 6.062 x 10~~). Corresponding top, the theoretical figure which is reached only when the Einstein law is implicitly obeyed, we have 4, the speczjfc photochmical f e c t or the efective photochemical equivalent. This has the same dimensions (mols per absorbed calorie), but is a purely experimental magnitude, ex- pressing the final results of an actual photochemical reaction, and therefore including the effects of all partial reactions, whether primary or secondary. The term e~ectjvep~otochemicaZ equivalent, when used, expresses the number of absorbing gram-molecules actual& decomposed per absorbed calorie, whilst the term spect$c photochmical e f e d may refer either to mols of absorbing reactant (disappeared) or of resultant (produced).

The equivalent radiant energy (I&) clearly represents the theoretical energy absorption in calories per mol of absorbing substance which dis- appears, calculated on the basis of one quantum absorbed per molecule. Finally, the quantum eJiciency (7) represents the number of absorbing molecules which have reacted per absorbed quantum. I t is given by the ratio +/p9 where + refers to the absorbing reactant, not to the resultant, is therefore the ratio of the efective to the fundamental photochemical equivalent, and becomes equal to unity if the law holds.

There is obviously an analogy between these magnitudes and those suggested by Faraday in connection with electrolytic decomposition. Thus, to the Faraday, which is 96,500 coulombs per gram equivalent, corresponds the equivalent radiant energy ( ~ / p ) ? which is 28,47o/A calories per absorbing gram-molecule. And whilst, in electrolysis, we have-

Fractional Current equivalents produced Efficiency = 96500 coulombs passed

Sitsb. Prezus. Akad. Wissett., 1912, 216 ; 19x3, 644 ; 1914, 872 ; 1916, 300, 1228; 1919, 960. Zeitsch. Elektrochem., 26, 54 (1920); 27, 133 (1921).

'3 Fundamen a1 has been chosen as translation of indiziertes. :{ Valenz-strahlung. Giiteverhaltniss.

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442 EINSTEIN PHOTOCHEMICAL EQUIVALENT LAN’

we have, in photolysis-

Quantum Efficiency = y = t+,@ - 28470 mols decomposed

x calories absorbed --

The magnitude I/P is, of course, simply Nhv expressed in calories instead of ergs. Analogy strongly suggests that the name of a Wal-burg might very suitably be given it.

This is not the place to go into the details of Warburg’s work, and in any case some of his numerical results will presently be quoted. It is interesting, however, to follow how his views evolved during the develop ment of his researches. His first work was done on NH3 decomposition. He tacitly assumed direct dissociation to be the primary effect produced by the absorption of radiant energy, the small values of + found being due to exothermic recombination of N and H atoms. His early work on ozonisation of oxygen confirmed the probability of the dissociation mechanism, as he found two molecules of O3 produced per absorbed quan tum, a result obviously easily explicable by the successive reactions-

His work on deozonisation, however, yielded results of great complexity, which could not be completely explained except by assuming that a part of the decomposition was due to impact between “ nascent ” 0, molecules of high energy content and O3 molecules. When he came to test the effect of wave-length on the reaction O2 3 O,, he found that the Einstein relation broke down, y becoming less at linger wave-lengths. This of course corresponds to general experience in photochemistry, which teaches us that, in practice, it is the shorter wave-lengths which are the more active, whereas the photochemical equivalent law, for equal quantities of absorbed energy, states the contrary; He further drew attention to the point that, if the Einstein law is valid, and the decomposition of a molecule results from the absorption of a quantum, the amount of decomposition per calorie of absorbed radiant energy will increase with wave-length up to a point, and then suddenly become zero when I/” no longer exceeds q, the energy necessary for the decomposition of a gram molecule. This of course does not happen, and Warburg consequently suggested that absorbing molecules should no longer be regarded as identical kith decomposing molecules

one should write$ = ___ .f(A,P) where and that, instead off = ___

f (A,P) represents the fraction of the absorbing molecules which decomposes (I? is gaseous pressure).

Considering further the relations between p and I/? he concluded that whilst the primary reaction in the case of 0, +03 may still possibly be 0 , 3 2 0 , decomposition directly to N c 3H is impossible in the case of the NH, molecule. His work on the decomposition of HBr and HI gave him the best agreement with the Einstein relation hitherto recorded, by him or any other worker, and at this stage he tended to distinguish sharply between the primary reaction in cases where the absorbed quantum is sufficiently large to decompose the molecule, and cases where this is not so. The latter type of photochemical change cannot be made the subject of quantitative prediction, the primary result of the absorption of a quantum being merely the formation of an ‘‘ activated ” molecule, which will sub- sequently, as the result of molecular collision, bring about chemical

x A 28470’ 28470

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PROFESSOR -4. J. ALLMANI) 443

change. Fruitless collisions between activated ” and ordinary molecules are assumed to occur. The mechanism of NH, decomposition and possibly of the ozonisation of oxygen is supposed to be of this nature.

In a later paper he dealt with the photolysis of aqueous K N 0 3 solu- tions. Very low quantum efficiencies were obtained, and he ascribed them to the fact that much of the absorbed radiant energy was degraded by solvent molecules during the process of $absorption, and before the real photochemical action could set in. The wide absorption bands shown by solutions were referred to as evidence of such ‘‘ damping.” The larger the quantum and the smaller q, the more likely is the law to be obeyed. When, however, the reciprocal transformations of aqueous inaleic and fumaric acid were studied (small value of q) very low values of y were still got.

Up to the end of his work, Warburg still assumed that a molecule was bound to decompose as the result of absorbing a quantum greater in size

than -, provided that none of the energy was lost during absorption by

molecular impact or damping. N

IV. Summary of Experimental Data.

In the following summary of data (pp. 444-5), only those researches have been noticed in which determinations of absorbed energy were actually carried out at the time-estimated quantum efficiencies, even those in Bodenstein’s well-known I 9 I 3 paper, are excluded.

For the sake of completeness, data on solid reactions are inserted, as also are data on sensitised reactions, although the Einstein relation cannot of course be applied in its ordinary form to the latter. Gaseous reactions are given first, solid reactions last.

V. Discussion of Experimental Data.

Cases iiz which the Eiltsfein Law Holds.-Included under this heading are all reactions in which the absorption of N quanta (a) within reasonable limits of error, causes the decomposition of a single gram-molecule; (b> causes the decomposition of less than one gram-molecule, the figure however extrapolating to unity for the first stages of the reaction; (c ) causes the decomposition of a larger number of gram-molecules, the number being readily explicable on the basis of straightforward stoichio- metric secondary reactions; (d) brings about the formation of N “acti- vated ” molecules, which then react stoichiometrically.

The reactions thus provisionally grouped together are (a) Gaseous- decomposition of HBr, HI and C1,O; ozonisation of 0, by zogpp; bromination of C6H,, ; sensitisation of ozone decomposition by C1, : (b) Liquid-decomposition of uranyl formate and oxalate, of C1,O and of C10,; hydrolysis of CH,Cl. COOH; oxidation of Fe” ions by iodine; chlorination of CC1,Br ; sensitisation of CC1,Br oxidation by means of Br2: (c) Solid-the three quoted in the table. I t is not proposed to discuss these reactionsin detail, as that would raise the subject of reaction mechanism in its widest aspect. I t may, however, be stated that examples of apparent agreement with the Einstein law in its strict sense (molecular decomposition following quantum absorption) are comparatively few, and in several cases are perhaps rather better explained by assuming primary

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444 EINSTEIN PHOTOCHEMICAL EQUIVALENT LAW

Reaction.

Gaseous.

H B r decomposition.

HI decomposition.

0, -> 0,.

C&O decomposition.

Br, + C,HI2.

0, + 0,.

NH, decomposition.

c1, + so,. CI2 + co.

C1, + H,.

Sen sitised Gascous.

0, + 0, [Cl,].

0, 0, [Br,].

Liq u a d. Uranyl formate de-

composition (in H,O]

Uranyl oxalate decom position (in H,O)

C10, decomposition

C1,O decomposition (in CCl,).

(in CCI,).

Author and Date.

Warburg, 1916.

Warburg, 1918.

Warburg, 1912-21.

Bowen, 1923.

Pusch, 1918. Noddack, 1921. Warburg, 1913.

Warburg, 1911-12.

Kuhn, 1923-24.

Bonhoeffer, 1923.

Bodenstein, 1922.

Bonhoeffer, 1923. Bodenstein & Dux, 1913.

Bon hoeffer, 19 23.

ao.

Hatt, 1918.

Biichi, 1924. Buchi, 1924.

Boll, 1913-14.

Bowen, 1923.

do.

Quantum. Effici- ency, t.e. y.

2.1 - 2 3 f o r

About I t o r 460 P.E.C.

470 t+* For 253 PP- 0.28 in 0, mix-

1-07 in N, mix-

1.7 in He mix-

tures.

tures.

tures.

0.23 for 209 ,up.

0-45 for 202- 214 pp at 20' C. ; 3 at 500' C, 0.1 for 206.3 p~ at 20' C.

About 2-3 for 420 up.

For 436 1000-1500 wit1 ordinary or moist gases ; 10-150 with very dry gases 2700 for 420 ,up. About 0.5 x I O ~ for white light.

About 2 mole- cules of 0, for 420 PP-

About 31 mole- cules of 0, for 420 pp.

0.4 for 420 pp

0'7 1, 420 11

1'07 I , 420 9 ,

jo molecules of H2C,0, for 254 p,u- 0.74 - 0'92 for 445 PP. 0-83-1'02 for 445 P,u-

Remarks.

Independent of P H B r be- tween 10-400 mm.

At 47.5 atm. Louer values with 125 and 300 atm.

At 47.5 and 125 atm. <I with 300 atm.

Limiting values of y for dilute 0, '' solutions 'I.

For strong '' solutions " in 0, and N,, y can amount to 3.5 and 2'6 respectively. It is also much greater in moist gases.

Practically the same figure over a pNHn variation of 50 : I (N, + H, present).

Pressure has no effect be- tween 5-900 mm. Excess of hydrogen nullifies effect of rise of temperature.

y increases with increasing [Cl,]. Traces only of 0, present. Larger amounts retarded reaction and CO, formation took place.

I per cent. O2 present. Ordinary moist gases -

trace of 0% present.

Practically independent of

ditto.

COJ

Probably tn iiiimtr nt values of y.

Reaction of zero order.

Very dilute solutions-air present.

Concentration variation 10 : I had RO effect.

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PROFESSOR A. J. ALLMAND 445

0.32 - 0.35 at 254 PP.

1 for 579 pp.

1360 for 230 pp.

~

Reaction.

27'5 for 405 pp.

25 for blue light.

NCl, decomposition (in CCl,).

KMnO, decomposition (in H,O).

K,Co( C,O,), decom- position (in H,O).

H 0 decomposition $n ,H,O).

KN 0, decomposition (in H,O).

Maleic Acid 3 Fu. mark Acid (in H,O),

A c i d + Maleic Acid (in

Decomposition of H20 solutions of ferric salts of organic acids

Hydrolysis of chloro- platinic acids.

Fumaric

H2O)-

H y d r o l y s i s o f CH,CI . COOH.

H y d r o l y s i s o f CH,Br .. COOH.

Fe" + I, (in H,O).

Hydrolysis of Acetone,

Cl, + zCBrC1, in CCl, and in SiCl,

C1, + Toluene.

I, -t- K,C,O,(in H,O),

Sensifised Liquid. 0, + zCBrC1, (in CCI,)

Maleic Ester + Fu- CBr&

maric Ester (in CCl,) CBr2l.

Solid. AgBr decomposition.

o - nitrobenzaldehyde 9 o-nitrosobenzoic acid.

Sensitised Solid. AgCl decomposition

CAgl.

Author and Date.

do.

Rideal and Norrish,

Vranek, 1917. 1923.

3enri and Wurmser 1913.

Kornfeld, 1921.

Warburg, 1918.

Warburg, 1919

do.

Winther and Oxholt- Howe, 1914.

Boll, 1914.

hdberg , 1924.

do.

aideal and Williams

Henri and Wurmser 1975.

1913. Ncddack, 1921. Griiss, 1923.

Book and Eggert,

Berthoud and Bel- 1923.

lenot, 1924.

Griiss, 1923.

Eggert & Borinski, 1923.

Eggert and Nod- dack, 1923.

Bowen, Hartley, Scott and Watts 1924.

Weigert, 1921.

Quantum Effici- ency, Z.C. y.

5 for 238 pp changing con- tinuously to 0'004 for 546 PP.

I molecule of 0, for 420 pp.

680 for 365 pp. 560 9 , 436 1 ,

430 3 , 557 9 ,

0.75-1.08.

About I for violet light.

I for 436 pp.

Remarks.

Practically independent of Concentration.

Light between 214-298 pp -mean about 230 py.

} Monochromatic light. Depends on concentration,

acidity, etc. For N/3 KNO,. Smaller

values with lower con- centrations.

For 0.01 M. solutions. y increases at lower con-

For 0.01 M. solutions. y decreases at lower con-

centrations. Dependent on time, A, and

concentration. Used 313-436 pp. Arbitrary concentration. y

is less at lower concentra- tions. Thus, for 254pp, 4 at 2 x 10-7 mo1s.lc.c and 0.3 at 0'2 x 10'; moIs./c.r.

centrations.

Solutions far weaker than with CH,Cl. COOH.

y became less than unity when [CBrCl,] became too low.

At - 80" C.

Independent of [O,].

Only slightly dependent on concentration.

For 365, 406 and 436 yp. Became less as reaction proceeded.

Became much less a s re- action proceeded.

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446 EINSTEIN PHOTOCHEMICAL EQUIVALEN‘T LAW

formation of an L L activated ” molecule, which does not subsequently necessarily react stoichiometrically. That is, certain cases of agreement may simply be coincidences.

Thus, Stern and Volmerl suggest this even in the case of HBr decom- position; the quantum corresponding to 209pp may not be big enough to dissociate an 0, molecule into atoms;, the data on C1,O decomposition as gas and in solution necessitate different secondary reactions in the two cases if decomposition to C1, and 0 is regarded as the primary reaction; although the sensitisation of O3 decomposition by C1, can be explained by a simple stoichiometric mechanism, this is not the case with the same reaction sensitised by Br,; if the low value of y for CH,Br . COOH hydrolysis compared with the value for CH,Cl. COOH hydrolysis has anything to do with the low concentration employed in the former case, as seems possible, a simple stoichiometric mechanism cannot hold ; the chlorination of CC1,Br may very well be the result of the primary forma- tion of an activated chlorine molecule;* in the sensitisation of the oxidation of CC1,Br by means of bromine, the disappearance of one molecule of oxygen per absorbed quantum may well be a coincidence. The best support at present available for the view that the primary process in a photochemical change is molecular dissociation is perhaps contained in the papers of Bodenstein and Liitkeme~er,~ Berthoud and Bellenot,6 and Dhara7

Reactions with Low Quantum EBciencies.--But few have been actually measured. They include the decomposition of weak ‘‘ solutions ” of O3 in 0,, of NH, at low temperatures, of KNO, and KMnO, solutions; the hydrolysis of the chloro-platinic acids by light of long wave-length and of brom-acetic acid at the concentrations worked at by Rudberg; the trans- formations maleic acid

Reactioits with Nigh Qziaiztum Eficie?zcies.-These are more numerous. In particular, as will be seen by reference to the tabular summary, many reactions involving the halogens, whether as reactant or as sensitiser, have high values of y. Other well-marked cases are the decomposition of aqueous solutions of H,O, and of organic acid ferric salts, the hydrolysis of acetone and the decomposition of dilute solutions of uranyl oxalate in presence of air by 254pp.

Efect of Wave-Length.-According to the law, one should have one molecule decomposed per absorbed quantum, independently of the size of the quantum. This latter is directly proportional to the frequency of the light and inversely proportional to the wave-length. For a given energy absorption therefore, the number of molecules decomposed should be proportional to the wave-length, the quantitative relation being given by the equation-

fumaric acid in aqueous solution.

This requirement of the law is well fulfilled in the cases of the decom- position of gaseous HBr and HI, and, less accurately, in the case of the decomposition of solid AgBr. But these are the only instances investigated

1 Zeitscli. Wiss. Pliot., 19, 275 (1920). Warburg, loc. c i t . (1914, 1916, 1921).

3 Nernst and Noddack, S i t z b . Prezcss. Akad. Wiss., 1923, 110. 4Nernst and Noddack, lor. c r f .

Zettsch. Plijlsikal. C h e w , 114, 208 (1924).

Trans. CIitm. So:., 123, 18 56 (1923). ‘ H H E ~ v . Chim. A d a , 7, 307 (1924).

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PROFESSOR A. J. ALLMAND 44 7

in which y is independent of X No case is known in which y increases with A, if we omit the irregular changes shown in the maleic acid fumaric acid transformations investigated by Warburg. In fhe majarity of cases, y increases as X decreases, corresponding to the universal tendency towards increased photosensitivity at shorter wave-lengths.

As y = +/p, and as p decreases when A decreases, a conconiitant decrease in 4 should take place, if y is to remain independent of A. I n certain reactions 4 is found to be independent of A-that is, the absorp- tion of a certain amount of radiant energy causes the same amount of chemical change, whatever the wave-length of the light. Such is said to be the case for example in the decomposition of H,O, solutions by short wave-length light,’ and in the transformation of maleic ester into fumaric ester when sensitised by bromine., In these circumstances, y increases with increasing frequency. Still more so is this true, whn + acfzcally in- cnases as A decreases, i.e., changes in the opposite sense to that demanded by the Einstein Law. This is the type of behaviour observed, for example, in the ozonisation of oxygen, the hydrolysis of the chloro-platinic acids, and the decomposition of aqueous solutions of KN03 and K,CO(C,O~)~ In respect fhrpfore of fh efect of wave-length, the Einstein law holds bad& in practice.

E f e c t of Concentration of Absorbing Substance.-Omitting sensitised reactions, we find first of all a number of cases in which y is independent of concentration over a considerable range. Such are, for example, the photolysis of HBr, NH,, U02C204, K,Co(C,O,), and C10, (in CCI, solu- tion). In the reactions 02+ 0, and maleic acid+fumaric acid, y becomes lower as the concentration increases. Whilst in many cases, y increases as the concentration of the absorbing substance increases-eg., COC1, formation ; the decomposition of 0,, of H20, and of KNO, ; the hydrolysis of the chloro-platinic acids ; the transformation fumaric acid+ maleic acid.

E@ct of Zmperature.-The only work on record is that of Kuhn3 dealing with the decomposition of ammonia gas. y increases with rising temperature.

y then increases very rapidly with U.

None of them shows a high value of y.

VI. The Conditions of Validity of the Einstein Law.4

The above discussion will have made it amply clear that the ‘‘ law ” seldom holds when applied, as is usually done, in connection with the complete reaction. I t will be equally obvious, from what has been said, that the reason is very often the occurrence of one or more secondary reactions, the nature of which remains obscure. The subject of such secondary reactions is closely bound up with the subject of the mechan- ism of photochemical change and for that reason will not be considered here. Quite apart however from this, th quantum rehution should strictZy on& be ajpZied to theprimary reaction, a point, as we have seen, first made clear by Stark, and afterwards insisted on by Warburg. The question which then arises is-does the law hold for all primary photochemical reactions, and if not, for which ? Einstein’s ‘‘ deduction ” deals with one kind of primary

Why is this?

1 Henri and Wurmser, C.R., 157, 126 (1913). 2 Eggert and Borinski, Physikal. Zeitsch., 24, 504 (1923). 3C.R . , 178, 708 (1924). 4 Good recent papers dealing with the photochemical equivalent relation are those

of Warburg, Zeitsch. Elektroch., 26, 54 (1920) ; Nernst and Noddack, loc cit . ; Weigert, Zeitsch. f a r Phjis., 14, 383 (1923).

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448 EINSTEIN PHOTOCHEMICAL EQUIVALENT LAW

reaction only, the production of a higher Bohr state. Other kinds are presumably possible. So we will take for consideration Einstein’s thermo- dynamic proof. Not only is it more comprehensive in respect of possible primary reactions, but, as has already been hinted, much of the confusion which has arisen in connection with the interpretation of the law is due to the fact that no clear distinction is made in the proof between theprimary and the compZete reaction.

The equation arrived at by Einstein is-

where T, is the temperature of the radiation of frequency v and pTs the corre-

e is the average quantity of radiation absorbed per molecule of XY reacting

N and R have their usual significance ; a is an integration constant 1 and independent of temperature ; A’ is the velocity constant of the reverse reaction :

sponding radiation density ;

to give X + Y;

x + Y+XY + €

and is dependent on temperature on& ; A is the ordinary ‘‘ intensity formulation ” photochemical reaction velocity

constant (the ‘‘ photochemical susceptibility ” of Boll and Henri) and is dependent on temperature only.

As now pTs and T, are functionally connected in a way independent of the temperature of the system (T), and as, further, AT, is sufficiently small

A a for Wen’s law to be obeyed, both - and c must be independent of T A under the conditions Zaid down 6y Einstein in his proof; whilst the relation E = hv follows directly. (As has been pointed out, Einstein states in one of his papers that E can depend on temperature, and seems conse- quently to be contemplating cases in which the law cannot strictly hold, even for the primary process.)

That the law cannot be expected to hold in practice for a complete photochemical reaction in which Nr is identical with the total energy increase per gram-molecule transformed,z can easily be shown. For then, as a is independent of temperature, and as, according to Einstein, both

A’a A A and A‘ are functions of temperature, if - is to be independent of

dA and dA‘ must be identical. I n actual practice, x ’ n A ” d T temperature, I

this is very unlikely to happen. .,4’, being an ordinary chemical reaction velocity constant, will certainly vary with temperature more rapidly than A,

A’ A [XI [Yl I For-consider the case in which T, =T. Then p = -a. c RT. But - ~

A A‘ - [X Y ] N E

N € Q _ - RT

= KT. Hence KT = ae

Hence a = C and Q = Nc.

and I ~ z K T = h a - KT. But ZUKT = - R~ f ZUC.

See previous foot-note.

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PROFESSOR A. J. ALLMAND 449

a photochemical reaction velocity constant. There is no doubt however that, in the Einstein proof, Q is equal to Nr.

We are therefore dealing with a type of process in which the complete reaction and the primary reaction are identical, a process in which represents equally the average total energy increase per molecule ultimately transformed and also the average energy of acfivatzon or criR’CaZ increment

per molecule, a process moreover in which both E and - are independent

of temperature. I t would seem then that Nhv or NE is fundamentalh the molar energy of activation involved in the primary photochemical process, and only under the particular conditions assumed by Einstein in his proof is it identical with the total energy change, and the primary process identical with the complete process.

A’ A

Let 4 be the gram molecular energy of activation for XY-x + Y,

x + Y-XY. and q’ the same for

Then, generally, we shall have

and, in the present case, as Q = q, we have 4’ Hence the state X + Y is fundamentally

state XY. Further, as E is independent of T, T, = r q -

= 0. unstable with respect to the we can write (putting again

where K = ApT, k’ = A’ and c and c’ are integration constants. We get at once that k‘ = 6’-that is, that A’ is independent of temperature.

If, however, A‘ is independent of temperature, so must also be A, the photochemical reaction velocity constant. The causes which can affect the temperature coefficient of photochemical reactions are discussed in an im - portant paper by Tolman,l who deduces the equation-

dink, : - z -= - aT kTL9

where 2 is the average energy before activation of all molecules which can pick up a quantum and react, E is the average energy of aZZ molecules, and K , is identical with our coefficient A. The fact then that A must be inde- pendent of T under the conditions assumed in the Einstein proof means that 2 and E are identical, and that all molecules must equally be in a posi- tion to react on absorption of a quantum. All molecules are therefore at the same energy level, no molecule requires preliminary activation before it can react as the result of absorbing a quantum, and the critical increments of the separate molecules are equal to one another.

1 your. Amer. C h e m Sx. , 45, 2285 (1923).

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4.50 EINSTEIN PHOTOCHEMICAL EQUIVALENT LAW

Th &4e ofphotochmical change then for which t h Einstein thrmodyna- mic proof rZgidZy holds is one in which (a) all reacting molecules are at the same energy Zevel before reacting and are hence equally reactive ; (b) the re- activi9 of th absorbing molecules under a given radiation dens@ is inde- pendent of temperature ; (c) the amount of energy absorbed per absorbing mobcute is the same in every case and is independent of temperature; (d) the product after the absorption of energy is fundamenfa@ unstable with respect to the ortginal absorbing system, and will revert to th latter spontaneoudy at n rate independent of temperature. The whole process is identical for all the molecules.

I t is interesting to note that these four conditions are all fulfilled by the change 2, + hv -3 Z,, the passage from a lower to a higher Bohr state which forms the primary reaction in the Einstein 1916 deduction, and it is clearly of importance to know whether other primary mechanisms which have been suggested in connection with photochemical reactions also fulfil these c0nditions.l Apart from such generalised terms as “ activation ” of the molecule or a rise of the same to the ‘( critical energy level ” (Perrin, W. C. Lewis, Winther, Weigert), following on the absorption of a quantum (by molecule, group, atom or electron), suggested mechanisms can be grouped as follows :-

1Mechanism. Limiting Case. ~ Actual loss of electron Loosening of valency electron

Polarisation of molecule

Wide separation of constitutents ~ Breaking of bonds or dissociation

(Stark, Volmer, Bodenstein) (Winther, Bodenstein)

(Baur) . negative ions

(War b u r g )

Ionisation into positive and +

(Einstein, Warburg, Nernst).

I t would appear that the ideas here indicated are not sufficiently well- defined to enable them to be discussed satisfactorily from the present point of view, although it would certainly seem that the above conditions would not be fulfilled in the ‘‘ limiting cases ” referred to. Thus it might be ex- pected that a photochemical reaction in which the primary process were dissociation of a molecule would not obey the Einstein law, however simple any secondary reactions. Presumably also there is a connection between the rate of return of the activated product to its original state and its in- herent instability. I f consequently primary activated products were found with lives considerably longer than the I o - second characteristic of the higher Bohr state, one might anticipate that reactions in which these took part would not follow the Einstein law.

Assuming, however, that an activated molecule does always have the properties of a higher quantum state and obeys stipulation (d), it may be of interest to discuss briefly why, even then, the Einstein relation may fail in practice when applied to the primary stage of a reaction.

we get K

Consider the equations on page I 2. Remembering that KT =

at once that C = and hence that A’ = 5 C’ Remembering also2 that

1 Stern and Volmer (loc. c i t . ) , prefer to regard Bohr states as primary products in all cases.

2 P. 448.

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PROFESSOR A. J. ALLMAND 45 1

u = C , the basic Einstein equation becomes-

where -4 and E must be independent of temperature if the law is to hold. I n practice, however, A does increase slightly with temperature, and some- times appreciably so. This is doubtless in part due to the fact that it is actually determined for the complete reaction, whereas the primary reaction is now under consideration. But we should hardly be justified in conclud- ing that the temperature variation is entirely due to secondary reactions. E represents the average molecular critical increment and this, in practice, one would expect to decrease with rise of temperature. In fact, as pTs and T, are functionally connected independently of temperature, A and E, if they vary with temperature, are bound to do so in opposite senses and to com- pensating degrees. Under such conditions, E and hv cannot be equated, even if Wien’s law holds, and hence the Equivalent Law can, at the best, only be approximately true.

Clearly the approximation will be the closer, the smaller the degree of de- pendence of A and E on temperature. In a case where secondary reactions of a chemical nature have a negligible effect, a high temperature coefficient must mean ( I ) that E rapidly becomes less and y greater as the temperature rises (2) that the Einstein law will not be obeyed. A normal value of y at low temperatures becoming abnormally high with rise of temperature would suggest secondary reactions-in the present case one would rather expect an abnormally low value of y and a high temperature coefficient at low temperatures, y becoming normal and the temperature coefficient be- coming unity (dA/dT zero) at higher temperatures. The writer has compared existing data on y and on temperature coefficient, but the results are not il- luminating-the relations looked for, if they exist, are obscured by secondary reactions.

Tolman’s work on the significance of photochemical temperature co- efficients has already been mentioned. Suppose that the absorbing substance can exist in three quantum states Zl, Z,, and Z,, of which Z1 is the lowest, and Z3 an ‘‘ activated ” state. The ordinary substance consists of a mixture of 2, and 2, molecules, the proportion of 2, increasing with temperature rise. A positive photochemical temperature coefficient means that partial activation is required before the full quota of activated molecules is formed in the light field. In principle, this can happen in two ways. ( I ) AZZ ab- sorbing moteczdes react, but molecules in the 2, state cannot absorb. A temperature rise, therefore, increases the number of absorbing molecules, reacting molecules and amount of absorbed energy-aZi in the same ratio. Hence, whilst A increases, c (or y) remains unchanged. This would corre- spond to an experimental case in which an increased rate of photochemical action at high temperatures was entirely due to increased absorption. (2) AZZ absorbing mokcuZes do not react, but only those in the 2, state, the number of which is increased on raising the temperature. A temperature rise therefore increases the number of reacting molecules but not the total amount of absorbed energy-2.e. A increases and e diminishes. This would appear to be the real practical case, for, so far as is known, increased ab- sorption usual.ly accounts for but little of the increased rate of reaction ob- served at higher temperatures. I t is also in agreement with the requirement, mentioned above, of simultaneous change of A and c with temperature. I t

1 P. 448.

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452 EINSTEIN PHOTOCHEMICAL EQUIVALENT LAW

further accounts for the well-known results of Padoal on the effect of 011

the temperiture coefficient of photochemical reactions, for the smaller the active quantum, the greater must clearly be 2, and hence also the tempera- ture-coefficien t.

VII. General Conclusions.

One may say then that, in practice, there are the following reasons why the Einstein relation generally does not hold.

(I) The secondary reactions (not considered in this paper) are not coupled stoichiometrically with the primary reaction as assumed in the 1916 deduction.

(2) The absorbing molecules are not all “activated ” as the result of absorption. This may be due (a) to the quantum being too small to raise the particular absorbing molecule to the critical energy level, in which case, as we have just seen, the yield of primary product will be affected by temperature or (b) to loss of energy by “damping” during absorption (Warburg), even although the quantum would be large enough if it could be completely u tilised.

(3) Possibly the primary process may result in the formation of a pro- duct which is not essentially unstable with respect to the absorbing mole- cules, i.e., Q and q are not equal.

(4) Again possibly, though not at all likely, the conditions may not be those of Wen’s law, or the product AT, may be too high. A simple calculation will show however that, for example, with radiation of wave- length 300 U P , T, may reach 2ooooo C. and Wen’s law still approximately hold.

Under the conditions laid down in the 1916 deduction and implied in the 19 I z proof, the law is of course bound to hold, though it would seem also, from the fact that is the mean energy absorption per molecule and in one paper is referred to as being a function of temperature, that the author has had in mind “ practical ” cases of approximate validity. I f the “ deduction ’’ had preceded the thermodynamic proof in point of time, much misunderstanding of the relation would have been avoided. It was particularly unfortunate that a chemicul dissoczatioiz appeared in the proof both as primary and as complete photo-reaction.

From the practical standpoint, owing to the far-reaching results of secondary reactions, we are left simply with the idea of absorption of light as quanta, after which very little can be said as to what will happen. But the introduction of the simple and definite quantum conception was in irself a great advance. I t clarified our ideas on the classification of photo- reactions, reconciled the conflicting (‘ intensity ” and “ absorption ” formula- tions of photochemical change, settled (at all events for the time being) the questions of threshold intensity and photochemical extinction, and thrust into the background speculations on the existence of photochemical, as distinct from thermal, absorption bands-all this quite apart from the valuable new ideas which followed in its train. And whatever the value of the ‘‘ photochemical equivalent law ” in itself, there is no doubt of its formu- lation by Einstein having been the most potent factor in securing due and rapid recognition by photochemists of the Quantum conception.

University of L o d o n , King‘s College,

August, I 9 2 5 .

E g . , Linc. R ~ i t d i . , 25 (II.), 215 (1916).

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