﻿36 Messrs. W. J. Jones and J. R. Partington on a 



concentrations of the solute when spherical particles of radii 

 r l and r 2 respectively are in contact with the saturated 

 solutions. If r 2 is intinite, the corresponding value of s 2 is 

 equal to the ordinary " solubility/'' which may be called the 

 " normal solubility," and denoted by s^ . The normal solubility 

 is therefore the concentration of a solution in equilibrium 

 with a plane surface of the solid solute. The difference 

 between the solubility of spherical particles of radius r and 

 the normal solubility is therefore given by the equation 



M l0 ^ = P T < 3 > 



Hence we find the value of s for any value of r in terms 

 of s n : 



2M<7 . 



For log e 5oo we can substitute the expression* 



log, s m = — g| + glog c T + const., 



where \ = A, + «'T is the heat absorbed when a gram-molecule 

 of the solid dissolves in the nearly saturated solution ; X and 

 a! are constants. Thence 



/2M(7 X n *' \ 



S = A S^~™ * ^ ) W 



Over a small range of temperature, p is a linear function 

 of temperature ; a closer approximation is given by the 

 equation 



l m dp 

 P 



The value of p is practically independent of r. 

 As a first approximation a is also a linear function of 

 temperature f, and hence we may assume that the equation 



— .- jrv =j3 (a constant) (6) 



represents a closer approximation: a is also practically inde- 

 pendent of r. 



We have now to consider how the radius of the particles 

 in equilibrium with a given supersaturated solution (i. e., a 

 solution which contains more solute than corresponds with 

 the normal solubility) alters with the temperature, when the 



* Hardman and Partington, Trans. Ohem. Soc. xcix. p. 1769 (1911). 

 t Frankenheim, Lehre von der Kohasion, 1836. 



^p— « (a constant) (5) 



