Page:Scientific Papers of Josiah Willard Gibbs.djvu/463

Rh In the above case of dissociation the formula would be For a coexistent solid phase of the solvent we have for constant pressure  $$m_{\text{S}}$$ being for convenience taken the same in both phases.

Then In integrating for small values of $$\gamma_{\text{D}}$$ we may treat the coefficients of $$dt$$ and $$d\gamma_{\text{D}}$$ as constant. This gives or if we write $$Q_{\text{S}}$$ for (the latent heat of melting for the unit of weight of the solvent), we have  This may be written  According to Raoult, the first member of this equation has a value nearly identical for all solvents and solutes (supposed definite compounds). This would make the second member the same for all liquids of "definite" composition, when we give $$M_{\text{S}}$$ the value for the molecule in the liquid state. I should think it more likely that these properties should hold for the two members of the equation which are pure numbers (of no dimensions in physical units). In this form it has a certain analogy with van der Waals' law of "corresponding states."

With a coexistent vapor phase of the solvent, we have