Many important biological reactions involve electron transfer. Because the pH of bodily fluids is close to 7, the “biological standard potential” of an electrode, E*, is measured at pH = 7.

(a) Calculate the biological standard potential for (i) the reduction of hydrogen ions to hydrogen gas; (ii) the reduction of nitrate ions to NO gas.

(b) Calculate the biological standard potential E* for the reduction of the biomolecule NAD⁺ to NADH in aqueous solution. The reduction half-reaction under thermodynamic standard conditions is NAD⁺(aq) + H⁺(aq) + 2 e^– → NADH(aq), with E° = –0.099 V.

(c) The pyruvate ion, CH₃COCO₂ ^–, is formed during the metabolism of glucose in the body. The ion has a chain of three carbon atoms. The central carbon atom has a double bond to a terminal oxygen atom, and one of the end carbon atoms is bonded to two oxygen atoms in a carboxylate group. Draw the Lewis structure of the pyruvate ion and assign a hybridization scheme to each carbon atom.

(d) The lactate ion has a similar structure to the pyruvate ion, except that the central carbon is now attached to an —OH group: CH₃CH(OH)CO₂^–. Draw the Lewis structure of the lactate ion and assign a hybridization scheme to the central carbon atom.

(e) During exercise, the pyruvate ion is converted to lactate ion in the body by coupling to the half-reaction for NADH given in part (b). For the half-reaction pyruvate + 2 H⁺ + 2 e^– → lactate, E* = –0.190 V. Write the cell reaction for the spontaneous reaction that occurs between these two biological couples and calculate E* and E° for the overall reaction.

(f) Calculate the standard Gibbs free energy of reaction for the overall reaction in part (e).

(g) Calculate the equilibrium constant at 25°C for the overall reaction in part (e).