Freezing-points, Boiling-points, and Solubilities. 411 



values of q seems to be much greater than at lower tempera- 

 tures. This may bo due not so much to the fact that q 

 actually decreases with the rise of temperature to such an 

 extent, as to the difficulty of getting reliable data for the 

 solubility curve, especially at too high temperatures*. 

 Indeed, from the run of the existing solubility and boiling- 

 point curves of C10 3 K it appears that the curves cut each 

 other at T^^IC^'S, but in reality much higher concentra- 

 tions than that belonging to 103 o, 8 have been observed for 

 the boiling-point curve. When the value of T /// is found 

 quite independently, namely, by a determination of the point 

 where the saturated solution boils in the presence of an excess 

 of salt, it at once becomes evident that the solubilities as 

 found by the present methods give, especially at higher tem- 

 peratures, too low values. This point T /// is found to be for 

 OIO3K at 105° (Gerlach), not at 103°'8. 



Again, from the equation for the freezing-point curve 



<y_ ( T °-gp-™ (non-electrolytes) and C'= (T ^g^ 



(electrolytes) we get for the temperature T / (point of cutting of 

 the solubility and freezing-point curves) and any temperature 

 T", if we assume that \ remains the same for all temperatures, 

 (C) T -T" , ., ,, , - .(C) (T -T")t; 



TT = Frf-^r- (for non-electrolytes) (II.) and v; = v ° ;./ 



(for electrolytes) (11/). 

 Connecting (I.) and (II.), and (F.) and (11/), we get : — 



1 _Csol_ = -q ( 1 _1\ , T Q -r 

 lg (C)fr.p. 2 x 2-3026 VT sol. T y / g T -T7 

 (for non-electrolytes) (A), and 



I. csoi. __ - g / 1 _i\ lff ( vn/ A 



(C) fr. p. i x 2 x 2-3026VT sol. TJ g (T -T y )*„ { )u 



Here vanH HofF's i / belongs to T„ i" to T". These equa- 

 tions give the connexion between the concentration of the 

 freezing-point curve, taken at any temperature T" the concentra- 

 tion of the solubility curve at any other temperatureT, the heat of 

 solution q, which we here assume to remain constant, and the 

 temperature T„ which is the point of cutting of the solubility 

 and of the freezing-point curve, the concentration at T, remain- 

 ing unknown, T y is found experimentally when we start 

 with an oversaturated solution, cool it in the presence of 



* See my paper " On Real and Apparent Freezing-points, Solubilities. 

 &c," Phil. Mag. xlv. p. 204 (1898) and August 1902, p. 270. 



