21 : 3/ Thermodynamics and Biology 391 



If the system, instead of being isolated, is maintained at constant 

 temperature, then 



dA = -8W because dT = 



At equilibrium, in this isothermal system 



dA = (A is a minimum) 



If this system starts out other than at equilibrium, the Helmholtz free 

 energy in excess of the equilibrium minimum value is the maximum 

 work obtainable from the system. 



Most biological changes occur with external restraints which main- 

 tain not only the temperature but also the pressure approximately 

 constant. Under these conditions, Equation 12 shows that 



dG = -8W (13) 



and equilibrium corresponds to a minimum of G 



dG = (14) 



If one starts with reactants in a nonequilibrium condition, the excess 

 of the Gibbs' free energy above this minimum is the work (other than 

 pdV) available from the system. 



In a system which is restricted by its surroundings to isobaric, iso- 

 thermal conditions, and in which hW consists only of chemical work, 

 one may write 



dG = 2niRTd{\n Ci ) (15) 



In this case, it is possible to integrate dG, providing all the n i are held 

 constant. A useful quantity, for chemical thermodynamics, is the 

 partial molal Gibbs' free energy, G t . This is the Gibbs' free energy 

 per mole of i, which the system possesses because of the presence of 

 substance i. From Equation 1 5, one finds readily that 



dG i = RTd{\n Ci ) (16) 



This is simple to integrate from a standard concentration c\ 0) to the 

 actual concentration, since the factor T is constant because the system 

 is isothermal. Integrating and rearranging terms, one may write 



G t = Gf + RT In (cJcW) (17) 



The term Gf is the value of G t when the concentration is c\°\ We 

 may choose the latter as unit concentration and rewrite Equation 1 7 as 



G t = Gf + RTlnct (17') 



It is important in (17') to realize that c K represents, not the concentration, 



