250 MOREY AET. Q 



relation; whenever any two phases in a binary system have the 

 same composition the pressure-temperature relations become 

 those of these two phases, without reference to the composition 

 of the other phase present. 



11. The Equilibria, Ice + KNO^ + Vapor, and Ice + KNOz + 

 Solution. The preceding univariant equilibria have been 

 formed from the invariant equilibrium, ice + KNO3 + solution 

 + vapor, by the disappearance of ice or of KNO3, respectively. 

 Two others can be obtained, by the disappearance of liquid or of 

 vapor. In case the liquid disappears, we have left ice + KNO3 

 + vapor, and the p-t curve of this equilibrium will coin- 

 cide with the vapor-pressure curve of ice, and from the 

 invariant point will go to lower pressure and lower temperature. 

 In case the vapor disappears we have the condensed system, 

 ice + KNO3 + liquid, and the curve gives the change in eutectic 

 (cryohydrate) composition with pressure. The equation of this 

 curve* is 



dp _ ^^ ^ ^ a:'^^"' - x' ^^ ^ ^ 



and since x'" = 0, a;"''**" = 1, and x^ = 0.021, this becomes 



(„.ce _ I) t ^1^ („^NO. _ ,) 



dp ^^ ^ ^ ^ 0.979 ^^ ^ ^ 



Here again the entropy and volume changes of the water are the 

 predominating factors; since the entropy difference is positive 

 and the volume difference, in the exceptional case of water, 

 negative, the p-t curve of this equilibrium has a negative slope. 

 But in this case, as in all condensed systems, the slope is very 

 steep; the numerator is of the order of magnitude of 0.3 cal. or 

 0.012 liter-atmospheres; the denominator is of the order of 



* This is the equation of the tangent to the curve; but it is convenient 

 to refer to it as the equation of the curve itself, and need not cause 

 confusion. 



