HETEROGENEOUS EQUILIBRIUM 251 



magnitude of 0.1 cc, or 0.0001 liters. The value of dp/dt is 

 thus about —0.012/0.001, or 120 atmospheres per degree; the 

 curve will be almost vertical. In other words, pressure, as com- 

 pared with temperature, has, as a rule, but little effect on the 

 equilibrium temperature and composition, 



13. Derivation of an Equation in Which the Argument Is 

 Pressure, Temperature, and Composition. It will be of interest 

 to correlate the solubiUty (t-x) curve more closely with the 

 p-t curve.* The p-t curve gives the change of vapor pressure 

 with temperature along the three-phase curve, representing 

 coexistence of vapor, liquid (saturated solution), and solid, and 

 the equation used in its discussion contained pressure and 

 temperature as expressed variables. The t-x curve repre- 

 sents the change with temperature of the weight fraction x 

 of the second component in the saturated solution along the 

 same curve, and for its discussion it is useful to have an equa- 

 tion containing temperature and composition as expressed 

 variables. Applying (1) [97] in the form of equation (7) to two 

 coexisting phases, denoted by single and double accents, and 

 eliminating dm, gives 



[v'(l - x") - v"{\ - x')\dp = h'(l - x") - 'n"{l-x')]dt 



+ (x' - x")diJL2. (9) 



But /x is a function of pressure, temperature, and composition, 

 so we may write 



From the equation 



de = tdR — Vdp + midm + miduz . . . + w„c/ju„, (11) [12] 



it follows that 



dn2 dV dfjii 9H 



T~ = :; — . and "77 = — 7 — . 

 dp dnh dt dm2 



* Cf. footnote on page 257. 



