310 PROCEEDINGS OP THE AMERICAN ACADEMY. 



In this equation p' indicates the true concentration effect or " thermal 

 pressure " * of the pure metal, and z represents an imaginable pressure- 

 effect of the affinity (called the " physicochemical potential " in a recent 

 paper on driving energy f). The expression R Tlnz indicates of course 

 the outside work C — P capable of being done by the affinity, and may 

 be indicated by A' for the sake of brevity, according to the equation 

 on p. 305. Then 



n7re Q = RTln^- + A'. 

 V 



When the heat capacity is unchanging -p = and A' = (& = £7" and 

 the equation reduces to the result found by Cady. 



With the help of this equation it is possible to understand many 

 relationships which would otherwise be inexplicable. 



p' 

 In solutions of equal ion-concentration, R Tin — would be nearly the 



P 



same for all metals. It is true that we are as yet uncertain concerning 



the true value to give p r , for the so-called "mass-law" often does not 



apply to concentrated material ; but a large change in p' would not 



cause a serious change in its logarithm. Considering the five metals 



already treated, if we assume the pressure to be inversely proportional 



to the volume, and suppose that a normal solution of the sulphate of each 



metal is about one quarter ionized (four liters containing about a gram- 



p r 4000 



ion), the value of R Tin — will range from R Tin in the case of 



p b.7 



nickel to R Tin . ■ in the case of magnesium. At 20° these values 

 1 o.o 



become 2.43 In 600 = 15.6 kilojoules and 2.43 In 300 = 13.8 kilojoules. 

 Thus the range between the extremes is only 2 kilojoules, an amount not 

 greater than a possible error in the heat of reaction in some cases. On 

 the average, the concentration energy (or the pressure energy) of a 

 metallic electrode in a normal solution of its sulphate is probably about 

 15 kilojoules per gram atom. 



The only satisfactory actual data known to me concerning this concen- 

 tration effect are those of Richards and Lewis t published in the paper 



* Lewis, These Proceedings, 36, 145 (1900) ; Z. phys. Chem., 35, 343. 



t Richards, These Proceedings, 35, 477 (1900). In this paper the relation 

 between c and p is dwelt upon. It is by no means certain that anything is gained 

 either in the present equation or in that of Nernst by assuming this chemical 

 energy as a simple function of the temperature. 



1 Richards and Lewis, These Proceedings, 34, 87 (1898) ; Z. phys. Chem. 28, 1. 



