5i6 



N. L. BOWEN 



heat of anorthite from a point on the upper portion of the deter- 

 mined curve. If now we do this for the diopside curve, that is, cal- 

 culate the latent heat of diopside from a point on the upper portion 

 of its solubility curve, we find a latent heat of 23,420 cal. per mol 

 or 108 cal. per gram.^ Calculating the further course of the 

 curve with the use of this value we obtain the dotted curve. This 

 calculated curve also lies above the determined curve at points dis- 

 tant from pure diopside. There is one factor which can cause such 

 a deviation of the freezing-point curve from the theoretical curve of 

 the above equation, viz., a heat of mixing of the liquids, and Van 

 Laar has developed an equation which enables one to calculate the 

 differential heats of mixing involved. The equation is 



1+ 



a(i — x)^ 



T^T, 



{i-\-r{x~x)Y 



2T0 



Q 



Inx 



where a and r are coefficients from the Van der Waals equation of 

 state for binary mixtures. The numerator gives the number of 

 times the solution heat, at the concentration x and temperature T, 

 is greater than the melting heat Q, and the difference between this 

 and Q is the differential heat of mixing.^ From this equation we 

 find the following values of the differential heats of mixing per 

 mol iq). 



TABLE I 



MOLAL DliTERENTIAL HeATS OF MIXING IN AnORTHITE-DiOPSIDE MIXTURES 



For anorthite {j-^-i^-j; 



For diopside [^'^^^^^-^ 



0.7 

 120 



o-S 

 600 



0.65 

 340 



0.4 

 1 100 



0-3S 

 1250 



Now these differential heats of mixing are the heats of mixing of one 

 mol of liquid with a very large amount of solution of the various 

 concentrations referred to. These in themselves have no particular 



'A direct determination by W. P. White gave 106='= 15 cal. 

 Vol. XXVIII (1909), p. 486. 



^Z. physik. Chem., Vol. VIII (1891), p. 188. 



Amer. Jour. Sci., 



