UNION OF ANTIBODY WITH ANTIGEN 131 



dF= - {nRTdP)/P 



Integrating, we obtain 



F^ - f., = _AF = nRT\n{Pi/P2) (20) 



Spontaneously, a perfect gas can only expand ; it cannot spontaneously 

 contract. In other words, the pressure can only decrease. From this 

 we see that in a spontaneous reaction AF will be negative. The larger 

 the negative value of AF, the greater the tendency of the process to 

 go. 



Strictly, equation (20) applies only to a perfect gas. But it also 

 applies without serious error to many real gases. If we replace Po 

 and Pi by the thermodynamic activities, which for the dilute solu- 

 tions used in immunochemistry do not differ appreciably from the 

 molar concentrations, we may apply this equation to antibody and 

 antigen solutions. 



Free Energy and Equilibrium 



We now proceed to derive an important relation between AF and 

 the equilibrium constant of a chemical reaction. Let us suppose we 

 have a reaction between two perfect gases A and B, to give two 

 other perfect gases, C and D. Then if we represent the numbers 

 of moles involved by lower case letters, a, h, c, and d. the initial 

 pressures as Pa and Pb, and the final pressures as Pc and Pd> we 

 have to write 



aA{PA) + bB{PB) -^ cC(Pc) + dD(P,>) + AF (21) 



where AF represents the change in free energy which accompanies 

 the reaction. In order to compare free energy changes, and therefore 

 tendencies of reactions to take place, we need free energy changes 

 where the starting and stopping points are always the same ; in 

 other words, all reactants must start at a standard state and finish 

 up in a standard state. In the case of gases the standard state is 

 atmospheric pressure. In the case of dissolved substances, which we 

 mostly deal with in immunochemistry, the standard state is unit 

 activity. 



We can find the free energy change, called the standard free 

 energy change and represented by AF°, which would result if the 



