of Chemical Potential to the Theory of Solutions. 35 



Equation (16) of Part II., which gives the value of the 

 solvent potential lowering in terms of vapour-pressure data, 

 may be written in the form * 



r n <> Cp re 



A (s 9 p, 6) = \ V(#, 6)dx - P (s, *, 6)dx+\ v (0, x, 6) dx. 

 Jn J n Jn 



Hence we have • • • • w 



s (s, P , e) ={V(n, e) -p„(s, n, e)}^ + r^Po(«, «, *)<**• 



I. . . . (8) 



If we substitute this value in equation (6) we obtain 

 Duhem's t expression for the concentration gradient. 



Equation (15) of Part II., which gives the value of the 

 solvent potential lowering in terms of osmotic pressure data, 

 may be written in the form 



Po+Q(s, p Q ,Q) 



\ Po(*,*,0). 



Po + V 



&0&P, 0) = ( P («, #, 6)dx + f »(0, .t\ 0)d#. 

 Hence we have % 



(9) 



f . . , (10) 



If we substitute this value in equation (6) we obtain an 

 expression for the concentration gradient in terms of osmotic 

 pressure data. If in this expression we make p = p + £l, we 

 obtain the expression given by Berkeley and Burton §. As 

 these writers point out, a differential coefficient of the osmotic 

 pressure with respect to the concentration may be measured 

 experimentally even when the pressure on the solution is so 

 low that equilibrium with the pure solvent is experimentally 



* This equation applies only to a solution of an involatile solute. 

 The more complicated problem of expressing the solvent potential 

 lowering in terms of experimental data relating- to the equilibrium 

 between a solution of a volatile solute and the vapour phase, will be 

 considered in a later communication. 



t Loc. cit. 



X This expression and the preceding one may readily be obtained by 

 differentiating the respective equilibrium equations with respect to the 

 concentration. The values of S thus obtained will not correspond to 

 the pressure p. It will be readily seen that the first terms in the above 

 two expressions are the values derived from the equilibrium equations, 

 and the second terms the pressure corrections. 



§ Phil. Mag. vol. xvii. p. 508, April 1909. 



D 2 



