290 PEOCEEDINGS OF THE AMERICAN ACADEMY. 



solution is now in equilibrium with the substance in the second state. 

 (3) Let the substance pass reversibly out of the ideal solution into 

 the second state. In the first step A^^- = — Uv. In the second, 



A2(^ = BT In —. In the third, Aog = n'y'. Since by equation III 



the activities are proportional to the osmotic pressures in the ideal 

 solution, and since ILv = IL'v', the total increase in free energy is, 



A5 = i?rin|- XXV 



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

 of one mol of a given species from one state to another when the species 

 itself does not change.^*^ When we are dealing with the most general 

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

 to form mols of 0, p mols of P, etc., the total change 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, 



AS: = ET\n ;°:f' - ET\n K XXVI 



Here A^^ is the increase in free energy in any reaction when i^, ^s, 

 etc., are the activities of the factors, ^o. ^p, etc., those of the products, 

 and K is the equilibrium ratio. 



Electromotive Force Equations. 



The change of free energy of a reversible galvanic cell is a direct 

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

 force of the cell, and F is the Faraday equivalent, then, 



A^- = - mFE, 



where m is the number of Faraday equivalents which pass through the 

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

 electromotive force E tends to send the current. 



20 It would have been possible at the beginning to define the activity by means 

 of tliis equation, and tliis would liave led to a development of our set of equations, 

 wliicli fi-om a mathematical standpoint would have been simpler than the one 

 here adopted. 



