HETEROGENEOUS EQUILIBRIUM 



267 



of phenol is so much lower than that of KNO3 that the vapor 

 pressure of the solutions probably decreases, without first rising 

 to a maximum. 



V. Application of Equation [97] to Systems of Three Components 



24. Transformation and Interpretation of Equations. Prob- 

 lems involving a greater number of components may be solved 

 by the same analytical method of treatment, but it will not be 

 possible to elaborate the discussion for systems of more than 

 three components, or to give a complete treatment of ternary 

 systems. *When equation (6) [129] is applied to a three- 

 component system it becomes 



H' mi m2 mz 



dp 

 dt 



H" mi" 



m^" W 

 W2'" ms'" 



V mi' 

 V" mi" 

 Y"' m^" 



mi mz 

 W2" mz" 

 nh"' mr 



IV IV 



vrh mz 



in which the composition of the phases is represented by the 

 actual masses of the components, mi, m^, and W3, and the 

 volume and entropy refer to the total mass. By setting 

 mi + m2 + mz = \, X = mi/inii + W2 -|- W3), 

 y = mn/{mi + 7^2 + mz), we getj 



* From this point to the end of section (28), and again from (30), 

 third paragraph (p. 281), to the bottom of p. 291, the text is taken, 

 with some omissions, alterations and additions, from the article of 

 G. W. Morey and E. D. Williamson, Jour. Am. Chem. Soc, 40, 59-84 

 (1917). 



t This equation has been used in the form of a determinant because of 

 the great convenience of that form of notation. For those not familiar 

 with determinants it may be said that this constitutes a shorthand 

 method of indicating the familiar operation of elimination by cross 

 multiplication. When dealing with systems of more than three com- 

 ponents such a notation becomes almost indispensable. 



