396 TRANSACTIONS OF SECTION B. 



that Einstein does not take up the question of the temperature coefticient. Further, 

 Kriiger, in dealing with the plienomena of solubility, electrolytic dissociation, and 

 solution pressure already alluded to, makes the assumption that the magnitude of 

 these eiiects depends directly upon the energy density of the infra-red thermal radia- 

 tion existing in the system. 



Again, it is known that radiation density is a well-defined function of temperature, 

 increasing as temperature increases, so that its introduction into the expression 

 representing active mass has at least the advantage over that ordinarily employed in 

 that it leads one to regard reactivity as itself a function of temperature, a conclusion 

 which is borne out by experiment. We have now to substitute for U„ its value as 

 given by the theory of quanta. This may be written — • 



1 



constant x n^ x ^ — 7,-m' 

 /ic/feT 



e -1 



where the constant contains the frequency term v, multiplied by a pure number, 

 n stands for the refractive index of the system for this frequency, h is Planck's 

 constant, T abs. temperature, and k the gas constant per molecule = E/N, where 

 N is the number of molecules in one gram molecule. 



Now, it has been pointed out by Mr. Lamble and the writer that the significant 

 range of wave-lengths for the present purpose lies in the short infra-red between 

 1 and 5/j; and this has been supported by some preliminary measurements made in 

 the writer's laboratory by Mr. Callow upon the infra-red absorption spectrum of 

 hydrochloric acid in aqueous solution, which shows a marked band in the region 1.55^. 

 For this range of wave-length and at ordinary temperatures it may be easily shown 

 that 



^.^rj, simplifies to e-'"'/iT_ 



e- 1 



Hence the velocity equation (1) becomes 



= A(a — x) >. C, X constant x n^ xe ~ ''"''T 

 = k„{a - a;)C.7v'e-''W'.T (2) 



Since the effect of temperature is now explicitly allowed for in the final term, it 

 is fair to assume that fc„ is practically independent of temperature. fe„, or rather A, 

 which is included in fc,„ appears to stand for the proportionality factor involved in 

 the probability of a molecule of the reacting substance meeting a molecule of the 

 catalyst— either added catalyst such as HGl, or in other cases a molecule of the 

 solvent itself — and hence its maximum variation would amount to 2-3 % for 10° rise 

 in temperature. That this is the significance of the constant A becomes more certain 

 when one remembers that the catalytic effect considered is due to the emission of 

 quanta (7i.c) from the catalyst particles, which quanta are absorbed by the molecules 

 of the reacting substance, and it is clear that this transfer would take place most 

 easily when the two kinds of molecules were in close juxtaposition, the disturbance 

 of collision being also a very favourable circumstance for the emission of the quantum 

 and its absorption. 



It may be pointed out that at constant temperature and constant concentration of 

 catalyst, which latter defines the numerical value of the refractive index n, that 

 equation (2) reduces to the usual mass action expression — 



dx/dt = k'{a - x). 



Again, on integrating equation (2) at constant temperature and catalyst concentra- 

 tion we obtain 



^ log kfiiii'c 



t a - X 



But - log = ^"observed = velocity Constant experimentally observed. 



Hence 'fobserved = k^Ciiv'e " (3) 



We have now to consider the variation of ^observed with temperature. As a first 

 approximation we may regard n as constant for not too great changes in tempera- 



