﻿Theory of Super saturation. 37 



amount of dissolved substance remains constant. If we 

 consider a supersaturated solution of given concentration at 

 a temperature T, then equation (3) shows that there is a 

 particle of definite radius r which will be in equilibrium with 

 this solution. The size of this particle we will call the 

 equilibrium-size. Towards particles of greater radius the 

 solution behaves as supersaturated, i. e. the introduction of 

 such particles into the solution would bring about crys- 

 tallization. Towards particles of less radius the solution 

 behaves as unsaturated, i. e. if such particles are introduced 

 into the solution they dissolve. These results have been 

 confirmed experimentally by Ostwald and by Hulett (loc. cit.). 

 Now let the temperature be raised to (T + ST). The equi- 

 librium size will also be changed, and the alteration may be 

 calculated as follows. Let (r + 8r) be the new equilibrium 

 radius, and (a + Sa), (p + Sp) the corresponding values of the 

 surface energy and density. Since the concentration remains 

 practically constant, 



s (T+§T) =Sr F ' ( 7 ) 



We have at the temperature T + ST, 



r 2.M.(<r + &r) Xo_ ,a_' ,.v /rn.iSmN.T.I 



S (T+OT )= A. *LB<p+ap)cr+aT)(r+ar) e(t+oT)^r- g.u+n.M-*| ^ 



The exponents in equations (4) and (8) are therefore equal; 

 T jl £T 

 and if we expand log- — ^- in a series, and assume 6T to be 



infinitesimally small, we have: 



AtI _ X 4- X ° ' P ' r 4- "' -P- r \4- d(T - d P — dr -0 f<» 

 di \ T + 2 fc T.M.cr- 77MTcrj + T p r ' {J) 



It is, however, known by experiment that a is approxi- 

 mately equal to ft *, i. e., 



da _ dp 



= 0, .../.. (10) 



p 



or — = const: (11) 



cr 



Thence we find from equation (9): 



<rr (- * + * T r -+h. .)-' / ;=o > . • • (12) 



where 



* Partington, ' Thermodynamics,' p, 483, 



