In chemistry, the standard state for a solution is 1 M (see Table 18.2). This means that each solute concentration expressed in molarity is divided by 1 M. In biological systems, however, we define the standard state for the H1 ions to be 1 × 10-7 M because the physiological pH is about 7. Consequently, the change in the standard Gibbs free energy according to these two conventions will be different involving uptake or release of H1 ions, depending on which convention is used. We will therefore replace ∆G° with ∆G°9, where the prime denotes that it is the standard Gibbs free-energy change for a biological process. (a) Consider the reaction
A + B→C + xH+
where x is a stoichiometric coefficient. Use Equation (18.13) to derive a relation between ∆G° and ∆G°9, keeping in mind that ∆G is the same for a process regardless of which convention is used. Repeat the derivation for the reverse process:
C + xH+ → A + B
(b) NAD+ and NADH are the oxidized and reduced forms of nicotinamide adenine dinucleotide, two key compounds in the metabolic pathways. For the oxidation of NADH
NADH + H+→ NAD+ + H2
DG° is -21.8 kJ/mol at 298 K. Calculate ∆G°9. Also calculate ∆G using both the chemical and biological conventions when [NADH] = 1.5 × 10-2 M, [H1] × 3.0 × 10-5 M, [NAD] 5 4.6 × 10-3 M, and PH2 = 0.010 atm.