the Theory of Solutions. 591 



Furthermore, the concentration can be stated as a function 

 of pressure, temperature, and density, If the temperature 

 is always kept constant, 



7 dc Be 7 



dc = =— - dp -;- _— dp. 



If the values of dp and dp are substituted, 



7 /ac3 P i , -de v bu. au- au \ 

 \B/oa«K ^) r A3^' By J b~ / 



We must also be able to express it thus : 



(/c= — (/ ( i'+ — rfw 4- - rf:. . . . (2a) 



And since both the terms for dc must be identical, and 

 & } y, z are independent variables, 



■bx 



b'u - 



bo 



Bv 



~bu- 



_3c 

 -K- 



-bx 



Bi/ 



'bz 





is are 



inserted in (2a) 



dc: 



= - 







(26) 



From this equation it appears that dc = when dU = 0. 

 From this we conclude, that in the state of equilibrium the 

 concentration must be constant along a potential surface and 

 must have the greatest slope in the direction of the force. 

 U and K are given quantities. The only thing we now have 



to determine is ^— ; or, as we might call it, the concentration 



gradient. This must be determined by help of the thermo- 

 dynamic equilibrium condition, which we shall briefly 

 mention. 



If at constant temperature a system suffers a change from 

 a state to a state 1, the amount of heat that the system dis- 

 engages during the change can, as is well known, be expressed 

 as follows : 



Q =1(80-80+1?. 



Here T means the absolute temperature, S the entropy, 

 T(S — Sj) the amount of heat that the systems would have 

 disengaged if the process had been carried out reversibly. 



