LEWIS. — FREE ENERGY AND EQUILIBRIUM. 33 



where h is the sum of all the fj terms, and ( (7„i — C^.^ and h have the 

 same value regardless of the nature of the solvent. If the total change 

 in the number of molecules be n, then the quantity r will occur to the 

 power of n, and 



(I'l - b^yh . . . J T, 2 



Only in the case of equilibrium between gases is P K considerable, for 

 other cases P Vmaj be neglected. For equilibrium in liquid phases, if 

 we represent by k the equilibrium ratio with the volume corrections 



/>T Q (J 

 "' „ — - dT by y) 



then {R Tlnr'^k) + U + fT= 0, (52) 



or (R Tin k)=-R Tin r" - U-fT. (52a) 



We are now iu a position to answer the question how equilibrium is 

 influenced by the nature of the solvent. If we write for equilibrium in 

 two solvents two equations of the form of (52 a), 



(R T\a k') =-RT\n /" - U' -fT, 



(R Tin k") =-RTln /'" - U" -fT, 



and subtract, we obtain, since _/ is the same in the two solvents, according 

 to the assumption made on page 28, 



In V77 = — « lu ^ — 

 fc r 



( u' - n"\ 



and we find that the condition of equilibrium depends on the values of 

 r and the heat of the reaction in the two solvents. Ordinarily when tlie 

 solvent does not enter into the reaction, the values of {i\ — b^), etc. may 

 be replaced by v^, etc., and k, the corrected equilibrium ratio, may then 

 be replaced by K, the ordinary equilibrium ratio. If we are dealing 

 with reactions in which the original and final number of molecules is the 



/ 



same, or with any case where n In -j-, is negligible, the equation becomes 



lnK'-lnK-= ^ ^ ^^ . (54) 



In such cases the difference between the logarithms of the equilibrium 

 ratios in any two solvents at a given temperature is equal to the differ- 

 ence in the heats of the reaction divided by the gas constant and by the 

 absolute temperature. I know of no case in which the experimental 



VOL. XXXV. — 3 



