132 INTRODUCTION TO IMMUNOCHEMICAL SPECIFICITY 



reacting gases shown in equation (21) started at atmospheric pres- 

 sure and the products ended up at atmospheric pressure. We simply 

 systematically add to equation (21) a series of equations, each one 

 of which carries one of the gases from the standard pressure to the 

 partial pressure Pa, Pb, etc., actually observed, adding also each 

 time the free energy change which such a change in pressure entails. 

 For instance, the first equation we add is 



aA{PA = 1) -^ aA{PA = Pa), AF = oRT\n{PA/\) (22) 



After performing all these additions we combine the logarithmic 

 terms and obtain 



AF° = AF+ RT\n[(PAy(PB)W{Pcy{PDy] 



AF° = AF - RT\n[{Pcy{PDY/{PAY{PBy] (23) 



If the amounts a, b, etc., and the pressures Pa, Pb, etc., are those 

 found at equilibrium, the free energy change AF in the reaction 

 shown in equation (21) is zero, and the term AF drops out. And 

 since we see that the expression whose natural logarithm appears 

 in (23) is in that case simply the equilibrium constant K, equation 

 (23) reduces to 



AF° = - RT In K (24) 



which is the relation we were seeking. Again we see that when 

 there is a strong tendency for the reaction as written to go to the 

 right (K is large), AF° will be large and negative. 



The equilibrium constant of a reaction is a measure of the extent 

 to which a reaction goes to completion. The standard free energy 

 change, which can be calculated from it, is thus a proper measure 

 of the strength of the chemical bonds that are formed, and broken, 

 during the reaction. Whenever the equilibrium constant of a reaction 

 can be measured, we can calculate the standard free energy change. 

 If we know AF°, we can calculate the entropy change A^"", if 

 AH° is known from calorimetric measurements, by using equation 

 (14) in the form AF° = AH° — T A5"°. A//° has been measured 

 directly for only a few immunochemical reactions. When it cannot 

 be measured it can often be calculated from van't Hoff's equation 



