DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
507 
duces A and B. Then, if £ 77 , £, e, be the number of equi valents of A, B, C, D, respec¬ 
tively, p, q, r, s, the number of molecules in these equivalents, w the mean potential 
energy of the mixture of the reagents, 6 the absolute temperature, we have 
|vy/ 
— CQ r+s ~i , -v e 
dw 1 
d£ K0 
(57) 
where Q is the volume of the solvent, and C and K are constants; we must not, 
however, assume without proof that the value of K is the same as that of the 
quantity denoted by the same letter for gases. 
The same conclusions as to the coincidence of this law with that of Berthelot at 
the zero of absolute temperature, and the close approximation between the two at 
ordinary temperatures in those cases where a very large amount of heat is developed 
in the reaction, hold in this case as well as in that of the gases. 
We will now apply this formula to some cases which have been experimentally 
investigated. The one to which most attention has been directed is that of a mixture 
of dilute solutions of nitric and sulphuric acids, sodium nitrate, and sodium sulphate. 
Here the reaction is represented by the equation 
H,SO, + 2NaN0 3 = 2HN0 3 + Na 2 S0 4 , 
and equation (57) becomes 
= £y, 
where y depends upon the temperature, but not on £ 77, £, or e. Here £ 77, £, e, are 
respectively the number of equivalents of sulphuric acid, sodium nitrate, nitric acid, 
and sodium sulphate. In order to fix the values of p, q, r, s, we must know whether 
the molecules of sodium nitrate and nitric acid in the solution are to be represented 
by Na 3 NoO G , H 2 N 3 O 0 , or by NaN0 3 and HN0 3 ; if the first supposition is correct, then 
p = qz=r = s= 1 ; if the latter, p = 1 , q — 2 , r = 2, s = 1 . In the first case the 
equation is 
y£e = £>7 ; 
in the second, 
y l C 2 e — I 77 3 . 
Thomsen”' has determined the state of equilibrium when solutions of nitric acid 
and sodium sulphate are mixed together in varying proportions. I have calculated 
from his results the corresponding value of y and y. In the following Table n is the 
ratio of the number of equivalents of sodium sulphate to the number of equivalents 
of nitric acid before chemical combination commences. 
* Thomsen, ‘ Tliermocliemisclie Hntersncliungen,’ I., 112. 
3 T 2 
