UNION OF ANTIBODY WITFI ANTIGEN 127 



spontaneity of a chemical reaction.* The more spontaneous a reac- 

 tion, the stronger the chemical bonds formed. But before we can dis- 

 cuss free energy we must introduce the second law of thermody- 

 namics. 



Entropy 



Going back to equation (3), we may rewrite it as follows: 



dQ = (IE -\- dW (6) 



If the pressure on a system remains constant, any work done is the 

 product of the change in volume times the pressure, thus 



dQ = dE -\- PdV (7j 



Since we know that £ is a function of P and V, we have, by an ele- 

 mentary and purely formal application of the calculus 



dE = {dE/dV) dV + (dE/dP) dP (8) 



where g indicates partial differentiation. Substituting in equation (6), 

 we obtain 



dQ = (dE/dV + P) dV + (dE/dP) dP (9) 



Since dQ is not an exact differential, equation (9) cannot be inte- 

 grated as it stands. It is shown in the calculus (e.g., Osgood 1925) 

 that, whenever you have an equation of the form 



dQ = XdV -\- YdP (IC) 



where X and Y are functions of the variables P and V, there is al- 

 ways an integrating factor B = j(P,V), in fact a number of such 



*A reaction may be spontaneous and, nevertheless, not take place at any- 

 appreciable rate of speed under ordinary conditions. For example, the reaction 



2H2 -1- O2 ^ 2H..0 



has a large negative \H and is also spontaneous by the free energy criterion 

 (see below). Nevertheless, mixtures of gaseous hydrogen and oxygen can be 

 stored indefinitely at ordinary temperatures and pressures. The reaction is 

 spontaneous, however, as is clear from what happens when an electric spark 

 is passed through the mixture. 



