22G Dr. S. W. J. Smith on the Weston Cell 



§ 14. The application of the phase rule to admium amal- 

 gams. — The considerations given at the beginning of § 12 

 were introduced in order to explain a method of regarding 

 the effects of surface energy. They also supply a means of 

 interpreting the "equilibrium curves" of fig. 1. As in § 12, 

 if two homogeneous phases containing components A and 

 B can coexist in equilibrium we must have not only equality 

 of temperature and pressure, but also two other equalities 

 which we may write p /a = jjb a ' and (A b — p<b - 



To determine completely, at given and p, the state of 

 any mixture of A and B, we require to know how these 

 " potentials " vary with c, the percentage of B in the 

 mixture. 



It is conceivable that the substances can form a series of 

 mixtures in all proportions and that any one of these can be 

 entirely fluid or entirely solid at the temperature 6. For a 

 homogeneous mixture, at constant temperature and pressure, 

 we must have 



l )n a tlpLa + m b d/Ab = 0. 



Considering all-fluid mixtures first we may suppose, 

 following Gibbs*, that, when c approximates to zero, p. b must 

 have a very large negative value, whilst fju a is finite and 

 dfjia/dc has a finite negative value. Similarly, when c 

 approximates to 100, fjb a must have a very large negative 

 value, while p b is finite and d/j, b /dc has a finite positive 

 value. 



The curves connecting the variations of p, a and p b with c 

 may no doubt be complicated ; but, in the simplest cases, 

 they may (from what precedes) take forms like AM and BN 

 of fig. 5. 



We may assume that analogous relations, represented by 

 the curves A'M' and B'N', hold for the all-solid mixtures. 



If, as in fig. 5, a temperature is chosen which is below 

 the freezing point of B, but above the freezing point of A, 

 we shall have fi b >p. b for the phases of pure B, and hence B 

 will lie above B' ; but fjb a f >^ a for the phases containing pure 

 A, so that A' will be above A. 



The conditions for coexistence of a fluid phase containing 

 x per cent. B and a solid phase containing y per cent. B are 



[P>a]c=x = W]c=y 



and [p>b'\c=x — [.M&']c=y. 



* L. a. p. 194. 



