THERMODYNAMIC AL SYSTEM OF GIBBS 137 



Now, if we write t = to —A/, where A^ is the lowering of the 

 freezing point, and represent xt and x< as functions of the 

 temperature by means of the equations 



x: = x; - Co -At, 

 x: = x- - c.-At, 



(179) 



where Co and C, are the specific heats of the pure solvent and of 

 the solid at constant pressure, we have 



'°H^°Jrj. Tit^^' ''^'•(i»* 



Here Mi^'^^ix]^ — x'J is the heat absorbed in the melting of the 

 molecular weight of the solid solvent at ^o- For ice and water in 

 the vicinity of 0°C., G. N. Lewis and M. Randall* have used 

 the values 



Mi^^"^ ixl - X') = 1438 calories, 



iWi^^^ (Co - C.) =9 calories, 



and integrating the right hand member of (180) in series have 

 obtained the expression 



log (pi/pi") = - 0.009696 At - 0.0000051 Af, (181) 



which they consider accurate up to 20 or 30 degrees from the 

 freezing point. This equation gives log ivi/v^) or log aj at the 

 freezing point of the solution. 



Table III gives a comparison of the values of log(pi/p]°)t for 

 aqueous mannite solutions, as calculated by (181) from the 

 freezing point depressions, with the values determined directly 

 from the vapor pressures by Frazer, Lovelace and Rogersf 

 at 20°C. 



The small differences between the two sets of values are to be 

 ascribed to the difference between the temperatures to which 



* Thermodynamics, p. 283 (1923). 



t J. Amer. Chem. Soc, 42, 1793, (1920). 



