II. OSMOTIC PRESSURE MEASUREMENTS 47 



AFi = RT In (/,//i°) = RT In {P,/Pn = RT In ay 



The partial molar free energy change for such a process is related 

 also to the partial molar heat content change, A7?i, and the partia 

 molar entropy change, AS'i, by the Gibbs-Helmholtz equation: 



AFi = A^i - T^S^ (1) 



For "perfect" or "ideal" solutions, the mixing of the components (in 

 the liquid state) will have occurred without any deviation from addi- 

 tivity in heat content or in volume, i.e., the heat of dilution is zero 

 and the partial molar volumes will not change with concentration. 

 The total change in free energy will be due to an entropy of mixing 

 that, in cases in which the molecules of the components are of com- 

 parable dimensions, will approximate an "ideal" entropy of mixing 

 in that the activity of a component in the mixture will be changed 

 from its activity in the standard state in a manner proportional to its 

 mole fraction. This relationship is illustrated in Raoult's law, which 

 states that: 



(Pi° - Pi)/P:° = n^/ini + n^) = N^ or 



Pi/Pi° = n,l{n, + n^) = N, (2) 



where Pi° and Pi are the vapor pressures of the solvent in the pure 

 liquid and in the solution, respectively, rii and Hi are the moles of 

 solvent and of solute in the solution, respectively, and Ni and N2 are 

 the mole fractions of solvent and solute in the solution. Under these 

 circumstances : 



^F = RT In .Vi = RT In Oi (3) 



Then, in ideal solutions: 



ttFi = -RTlnNy 



In very dilute solutions, most of which approach "ideality," the 

 partial molar volume, Vi, approximates closely the actual molar 

 volume, Fi, and we can write: 



ttFi = -RT\n Ni (4) 



and since A^ + A^2 = 1 : 



xFi = -RTlnil - Ni) 



