176 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS 



chemical potential. These are both energies. Force is energy change per unit 

 distance, £, along some reaction path; eg., dF/di~. Since this quantity can- 

 not be determined for chemical reactions, it is usually tucked away (and for- 

 gotten) in a proportionality constant. In diffusion, heat conduction, and 

 other physical processes, however, it can be evaluated, as will be seen in the 

 next chapter. 



The Free Energy Released During the Drive Toward Equilibrium 



Internal energy, U, enthalpy, H, entropy, S, and free energy, F, all refer 

 to 1 mole of the substance or system under consideration. In any real system 

 the value depends upon the amount of substance present. During the drive 

 toward equilibrium, as a reactant, A, begins to decompose to product B, the 

 concentration (1 — x) of A at any time, t, becomes less than the original con- 

 centration, while the concentration, x, of B builds up. Hence the free energy 

 difference decreases toward zero as equilibrium is approached, and the posi- 

 tion of equilibrium will be determined by the concentrations, x and 

 (1 - x) eq , at which AF = 0. Thus, 



K = —^3 



" (1 - *) eq 

 The relation between K and AF per mole can be derived from funda- 

 mental principles, and is simply stated here: 



-AF = RT\nK eq 



Strictly speaking this "thermodynamic equilibrium constant," K is a 

 ratio of activities, which are defined as effective concentrations, it being remem- 

 bered that the hydration of a molecule, the splitting of salt into ions, etc., 

 makes the effective concentration somewhat different from that determined 

 from the composition. In terms of activities, a, then, at equilibrium: 



-AF = RT\n(a B /a A ) 



which separates out to 



-AF = -AF° + RT In (a B /a A ) 

 if AF° refers to the standard state in which the activities are 1 mole/1, and 

 the second term corrects for deviations from an activity ratio of unity. 



More generally, a B is replaced by the product of the activities of the prod- 

 ucts, and a A is replaced by the product of the activities of the reactants. Fig- 

 ure 7-4 indicates how the position of equilibrium can be quite different for 

 different processes. 



ATP: The Mobile Power Supply 



An ubiquitous wanderer and a molecule of unrivalled versatility is adeno- 

 sine triphosphate (ATP), a condensation product of adenine with a pentose 



