THERMODYNAMICAL SYSTEM OF GIBBS 139 



brane, i.e., if the pressure on the solvent remains constant, the 

 pressure on the solution must be such that the potential of Si 

 in the solution is /xi". The variation of mi with pressure, accord- 

 ing to (158), is 



fdfjA 

 \dPjt. 



Vi. 



Therefore, if P is the pressure on the solution for osmotic 

 equilibrium, 



.0 . _ r 



Ml -Mr = - h-dP. (183) 



By (166), we may write 



At 



— i,.o — 



^'~ ^' ~ M:(«> 



log (pi/pi"), 



where pi" and pi are the partial vapor pressures of Si over the 

 solvent and the solution at a total hydrostatic pressure Po, and 

 Mi^^^ is the molecular weight of Si in the vapor. If we regard vi 

 as constant, we have 



At 

 P -Po = - J^^^ log (Pi/Pi«),* (184) 



where P — Po is the osmotic pressure. 



* Differentiating equation (183), we obtain 



dm = — vi-dP, 



and since midfii + m2dii2 = 0, this becomes .dn2 = dP, which is similar 



rriiVi 



to (138), rriiVi (the partial volume of Si in the solution) being substituted 

 for the total volume of the solution. Assuming that Vi is constant, this 



At ?«2 



becomes for dilute solutions which obey (136), P — Po = TnTi) 



niiVi M2 



which may be regarded as a more exact form of (139). This equation 

 was obtained by G. N. Lewis, /. Amer. Chem. Soc, 30, 668 (1908). 

 Equation (184) was derived by Berkeley, Hartley and Frazer, and by 

 Perman and Urry from A. W. Porter's theory, Proc. Roy. Soc, A, 79, 

 519 (1907). 



