RICHARDS. — ENERGY OF PHYSICO-CHEMICAL REACTION. 473 



Cancelling the unnecessary powers of R T, we have 



d (R Tf* + "'»•-.- »i ~ *J pi »i p '«\ . . . U 



n „ »,«' «', — TT^a* ( 2 ) 



rfT pfif/j**... ~ RT 



Let us consider for the sake of argument a case in which 



(« 2 + n\ • • • — w i — n '\) = -W 



is positive, that is, a case in which the total number of gram-molecules in 

 the product is greater than that in the reacting mixture before the reac- 

 tion took place. The expression then becomes 



d^ (R T)* Pl ip\*\ . . ■ _ _U_ 

 dT p»* P '/*... ' RT*' K) 



From this pressure-equation at constant volume we may omit din R, 

 because R is a constant. Thus 



ji Pi *P 1 l • • • ■* 



«ln — t—, ^ 



p^p'o'"- ■ ■ ■ U (4) 



dT ~ 'RT 2 ' 



Here two cases may arise. If iV = 0, that is, if the osmotic or gas 

 pressure (or total number of molecules) does not change during the 

 reaction, the pressure remains constant. Mathematically, T y becomes 1 

 and hence disappears. On the other hand, if jV^ 0, T N becomes a 

 serious factor in the equation, affecting immensely the temperature coeffi- 

 cient of the " mass-law constant." 



The numerator of the second term of this modified equation of van't 

 Hoff still consists merely of U ; hence if the equation is to be used with 

 data obtained under constant pressure, the observed heat of reaction must 

 be corrected for the work done during expansion. For this reason its 

 prototype has been called the " reaction isochor " by Nernst ; it repre- 

 sents immediately the observed conditions only when the reaction takes 

 place in constant volume. The introduction of the correction causes an 

 interesting simplification. 



At constant pressure the heat evolved during the reaction would be 



less than U, because the work N R T is done against constant pressure ; 



N R T N 

 hence we shall be obliged to subtract n _ , = -=. from each side of 



the equation in order that the numerator of the second member may 

 truly indicate the actual conditions. But 



