436 Dr. F. Tinker on Osmotic Pressure. 



solution irreversibly, and without the performance of external 



work, in two ways : 



(i.) It can be allowed to diffuse into the phase in question 

 first, to then expand inside the phase from the pressure 

 p l to the pressure pi', and lastly allowed to diffuse from 

 the phase into the solution. The total heat given out 

 b} this process is dAi + U, where U is the diminution 

 in the internal energy of the solvent during the 

 expansion f rom p x to /?/• 

 (ii.) It can be added directly to the solution, with a total 

 heat evolution Q, where Q is the heat of dilution. 



Hence, since the total heat effect is independent of the 

 path traversed, we have ^A^U^Q. 



For the vapour phase proper, ;it any rate, we can neglect U 

 so that dAx = Q (approx.). 



Equation [9] can thus also be written 



£. 

 Pi 

 If the heat of dilution of the solution is small compared 

 with RT (as it usually is) the equation becomes 



Pi 



V 



Equation [10] and its approximate form (equation 11) 

 are the general equations for the vapour pressure of a 

 solution of any non-volatile solute at any concentration, it 

 being assumed that neither the solvent nor the solute is 

 associated or dissociated. 



For the dilute solution the equation becomes * 

 Pl _N-W Q\ 



l i+ RT/ 



eat of dilution of the solution is small compared 

 s it usually is) the equation becomes 



Pl _ f N + n n( Y 2 -b 2 + e \ \( Q\ f - 



5?"!"^" n^ 1 Y 1 -b l 'JjV + mJ' LilJ 



pi 



N 



Pl ~ N + // V RI7 L J 



(c) Ideal and Xon-Ideal Solutions. 



The ideal solution may be defined as one whose partial 

 vapour pressure under ordinary conditions is given by the 

 equation 



P± = * T + 

 Pl N + n 



IT ' N 



* Supra, the approximate equation — = ^ given on p. 433. 



t Cf. Willard Gibbs, ' Nature,' Ix. p. 46 (1897) ; Van Laar, Zeit. Phys. 

 cWxv. p. 457 (1894). 



