392 Thermodynamics and Biology /2I :4 



but really a dimensionless concentration ratio, because one cannot take 

 logarithms of numbers with dimensions. This problem may be avoided 

 by using activities or fugacities in place of c, but these are also meaning- 

 less unless one specifies the standard concentration. 



The term Gf will depend on T, p, and the standard concentration of 

 substance i. It may also depend on the concentrations of the other 

 molecular species. To uniquely define Gf, it is necessary to state all 

 of these standard (or unit) concentrations. This group of standard 

 concentrations is called the standard state. To recapitulate, the quantity 

 Gf is the Gibbs' free energy per mole of substance i, due to the presence 

 of substance i, when the system is in its standard state at absolute 

 temperature T and pressure p. 



The standard state need not be a real state. For instance, one might 

 use 1 mole per liter for the concentration of catalase in the standard 

 state. A concentration of 1 millimole per liter is a large one for catalase, 

 and 1 mole/liter is physically unrealizable. In this case, Gf means the 

 value of the partial molal free energy obtained by extrapolating from 

 infinite dilution to the standard state under the hypothesis that the 

 solution acted as an ideal one. Even though this hypothesis is obviously 

 absurd, the term Gf is a useful one for thermodynamic calculations. 



From Equation 10, one sees that it is possible to write 



Gf = H? - TSf (10') 



Changing the standard state by decreasing c\ 0) by a factor of 10 3 will 

 decrease Gf by an amount RT In 10 3 . Because the partial molal 

 enthalpy, in the standard state Hf, is not dependent on c\°\ this change in 

 Gf must be an increase in Sf of R In 10 3 . Statistical mechanics inter- 

 prets this increase as the equivalent of saying a mole of substance i can 

 be distributed 10 3 times more ways at 10 ~ 3 of the original concentration. 

 In order to assign meaning to Sf, it is necessary to have a zero for 

 entropy. This is provided by the second statement of the third law of 

 thermodynamics as the entropy of a simple single crystal of a single 

 substance at 0°K. By varying the standard state concentration, it is 

 possible to change even the sign of Sf. Thus, no significance per se 



can be attached to either the magnitude or sign of Sf ; it is a useful 

 mathematical construction only. 



4. Equilibrium Constants 



The concepts of thermodynamics, and particularly the Gibbs' free 

 energy, may be applied directly to the enzyme kinetic rates discussed in 



