Chemistry. — “Pressure- and temperature-coefficients, volume- and 
heat-efjects in bivariant systems.” By P. H. J. Hoeren, S.J. 
(Communicated by Prof. SCHREINEMAKERS.) 
(Communicated at the meeting of Sept. 27, 1919). 
In a previous communication’) we developed a general law (of 
which the so-called Bracy’s law is a particular case) giving a relation 
between the pressure- and temperature-coefficients of the solubility 
of several solid substances, with which a solvent is saturated, and 
the heat of solution and volume increase accompanying the solution 
of these substances. In the present communication we shall attempt 
to find a similar relation for arbitrary bivariant systems. 
{. Heterogeneous Equilibria. 
1. With m components we have a bivariant system in the usual 
sense of the term, when there are 7 coexisting phases. In this case 
there are two independent variables, e.g., pressure and temperature. 
We can, however, even when there are fewer than 2 phases present, 
retain only these two as independent variables, if we subject all 
variations in the system to the condition that the composition of 
the whole remains constant. Then, no matter how many phases we 
have, provided the number is not more than mn, pressure and tem- 
perature alone remain the independent variables. 
There must thus be a relation among all the systems. Such 
systems differ greatly from bivariant systems in the ordinary sense 
of the term, i.e. from systems with 2 phases, in that in the latter 
case the composition of the phases is separately independent of the 
composition of the system as a whole. This is not the case with the 
systems which are only “bivariant with constant total composition.” 
We shall illustrate the above by a consideration of the equilibrium 
equations. We assume that we have 2 components in / phases. 
Let the composition of the phases be as follows: 
1E MESS GAS Was Zoest 
DEAN EE eee eect 
{th 55 Da U lb 33 3.6 
1) See the preceding communication in these Proceedings. 
