FUNDAMENTAL EQUATIONS OF IDEAL GASES 373 



represent the heat of vaporization of the pure solvent, the heat 

 of dilution is obtained at once for the case where the vapor, of 

 volume vi, may be taken to be an ideal gas, and the liquid 

 volume V2 is negligible. We find 



X. - X. = AX = a.^.P ^-^^\,: (93) 



Taking the temperature as constant in the general equation, 



n TYi f 

 assuming that v = — — — {m,' is the mass of vapor of solvent), 



V 

 we drop the accent in a" and r". This gives 



dr AiU aamst 



Integrating the last equation there is obtained 



/, 



— = log = - 7, r. (95) 



p.at. V P'at. asMst 



But psat. — p may be put equal to Ap, and w/ may be taken to 

 be numerically equal to ilf / the molecular weight of the vapor, 

 whence 



^=i^'- (96) 



p,ai. at nis 



Raoult's law in dilute solution may be expressed in the form 

 ^p/Ps = Ui/n, when Ui is small relative to n«. By comparison 

 we find 



\dmjp, t. 





which is constant at constant temperature and depends only on 



ilf, _ „ , . 



the molecular weight ratio vr. Fmally we obtam 



M.2 



[2 



Ms 

 M2 



/X2 = —-^Rt log rris + /(p, t, nh) 



for the relation between ^2 and the masses of solvent and dis- 

 solved substance. 



