324 SCHREINEMAKERS art. h 



and pressure. Also let (mi)o denote the free energy (poten- 

 tial) of 1 mol of pure liquid A" under the same conditions. 

 Then (/i:)o — Mi = total diminution of free energy resulting 

 from the transference of 1 mol of X from the pure liquid 

 state (as above defined) to an infinite mass of liquid of 

 composition x (as above defined). It is easy to show that 

 /•(pOo 



(mi)o — Ml = / vdp, where v = volume of one mol of the vapor 

 J pi 



of X at the given temperature. Now y is a function of p, and 

 for X = 0, pi = 0, and v = + co . Hence when x = the 



ripih 

 value of / vdp becomes + oo , so that (mi)x=o = — °o. From 

 J pi 



the preceding results it follows therefore that 



\dx/t 



= — 00. 



Hence the f-curve touches the line WW at the point W. Sim- 

 ilarly the f-curve touches the line XX' at the point X'. 



From the preceding analysis it is also evident that at the 

 minimum point of the f-curve, mi = M2 = (f)inin. 



An analytical and a graphical treatment of solid-liquid phase 

 equilibria in binary systems was given by A. C, van Rijn van 

 Alkemade {Verhand. Akad. Wetensch. Amsterdam, 1, 1 Sec, No. 5, 

 (1892); Zeitsch. f. physikal. Chemie, 11, 289 (1893)), who based 

 his discussion on the properties of Gibbs' f -function. In his 

 graphical treatment van Alkemade employed a ratio instead of a 

 fractional composition parameter, so that the part of the dia- 

 gram referring to one pure component is situated at infinity. 

 The method employed by Schreinemakers avoids this defect, 

 and is therefore much more general. 



It may be remarked in conclusion that the preceding analysis 

 establishes very simply the geometrical method for determining 

 the point on the f-curve which corresponds to a liquid in 

 equilibrium with a pure solid phase, say pure solid W, for 

 example. Let Piiti, ^1) and ^2(^2, X2) be two points on the 

 ^-curve. The equation of the straight line P1P2 is 



^2 ~ r _ ^2 ~ Ti 



Xz — X X2 — X]' 



