EDING8 OF Till: AMERICAS ACADEMY. 



BolutioD is qow in equilibrium with tin' Bubstanoe in the second state, 



Let the substance pass reveraibly ou1 of the ideal solution into 



the second state. In the first Btep a, a = — Uv. In the second, 



ii' 

 _y,v = //'/In In the third, A, a = 1 1'/'. Since by equation III 



the activities are proportional to the o motic pre Bures in the ideal 

 solution, and since Uv = QV, the total increase in free energy is, 



Aa= //'/'In • XXV 



i 



This is a general equation for the change in free energy in the p 

 of oneinol of a given Bpecies from one Btate to another when the spe 

 itself does not change. 20 When we aTe dealing with the m< era! 



of chemical reaction, when a mols of A. b mols ofB, etc., combine 

 to form o mols of 0, p mols of P, etc., the total i in free energy 



will obviously be equal to that which accompanies the transfer of the 

 factors of the reaction from the original system to another system 

 where there is equilibrium, and the transfer of the products from this 

 equilibrium system to the original system. By a combination, there- 

 fore, of equations XXIII and XXV, we find, 



&% = BThi\ --//7'ln A'. XXVI 



B ' ' ' 



Here A,"v is the increase in free energy in any reaction when $ A , $g, 

 etc., are the activities of the factors, $ 0j £p, etc., those of the produi 

 and K is the equilibrium ratio. 



Electromotive Foitn Bqi ltion& 



The change of free energy of a reversible galvanic cell is a dir< 

 measure of the electrical work of the cell. If E is the electromotive 

 force of the cell, and /•' is the Faraday equivalent, then, 



A,\ = -„,/•'/;, 



where i i number of Faraday equivalents which pass through the 



cell during the reaction in question, and in the direction in which the 

 electromotive force A' tends to .-end the current. 



20 [t would havi 1 ublcal the beginning to define the activity by ineani 



of this equation, and this would hare led to a development of our set <>f equations, 

 which from a mathematical standpoint would have been simpler than the one 

 I adopted. 



