Muscle cells need energy to contract. One biochemical pathway for energy transfer is the breakdown of glucose to pyruvate in a process called glycolysis. In the presence of sufficient oxygen in the cell, pyruvate is oxidized to CO₂ and H₂O to make further energy available. However, under extreme conditions not enough oxygen can be supplied to the cells, so muscle cells produce lactate ion according to the reaction

where Δ_rG°′ = −25.1 kJ/mol. In living cells, the pH value is about 7. The hydronium ion concentration is constant and is included in ΔG°, which is then called Δ_rG°′ (Applying Chemical Principles 18.1 Thermodynamics and Living Things). (This problem is taken from the problems for the 36th International Chemistry Olympiad for high school students held in Kiel, Germany, in 2004.)
(a) Calculate Δ_rG° for the reaction at 25°C.
(b) Calculate the equilibrium constant K′. (The hydronium ion concentration is included in the constant. That is, K′ = K ∙ [H₃O⁺] for the reaction at 25°C and pH = 7.0.)
(c) Δ_rG°′ is the free energy change under standard conditions; that is, the concentrations of all reactants (except H₃O+) are 1.00 mol/L. Calculate Δ_rG′ at 25°C, assuming the following concentrations in the cell: pyruvate, 380 μmol/L; NADH, 50 μmol/L; lactate ion, 3700 μmol/L; and NAD⁺ ion, 540 μmol/L.

Transcribed Image Text:

00 H₂C-C- CO+NADH + H+ pyruvate OH O lactate dehydrogenase, H₂C-C-C-0- + NAD+ H lactate