The relationship of free-energy change (ΔG) to the concentrations of reactants and products is important because it predicts the direction of spontaneous chemical reactions.Consider, for example, the hydrolysis of ATP to ADP and inorganic phosphate (P_i) .The standard free-energy change (ΔG°) for this reaction is −7.3 kcal/mole.The free-energy change depends on concentrations according to the following equation:
ΔG = ΔG° + 1.42 log₁₀ ([ADP] [P_i]/[ATP])
In a resting muscle, the concentrations of ATP, ADP, and P_i are approximately 0.005 M, 0.001 M, and 0.010 M, respectively.At [P_i] = 0.010 M, what will be the ratio of [ATP] to [ADP] at equilibrium?

Question

Quizplus · Accepted Answer

First, we need to find the value of ΔG at the given concentrations: ΔG = ΔG° + 1.42 log([ADP][P_i]/[ATP]) ΔG = −7.3 + 1.42 log((0.001×0.010)/(0.005)) ΔG = −7.3 + 1.42 log(0.2) ΔG = −7.3 − 0.669 ΔG = −7.969 kcal/mole Since ΔG is negative, the reaction will proceed spontaneously in the forward direction (i.e. ATP will be hydrolyzed to ADP and Pi). At equilibrium, ΔG = 0, so we can rearrange the above equation to find the ratio of [ATP] to [ADP]: ΔG = ΔG° + 1.42 log([ADP][P_i]/[ATP]) 0 = −7.3 + 1.42 log([ADP][P_i]/[ATP]) 1.42 log([ATP]/[ADP]) = −7.3 log([ATP]/[ADP]) = −5.14 [ATP]/[ADP] = 7.2 × 10−6 (using the fact that log10 (x) = y is equivalent to 10y = x) Therefore, the ratio of [ATP] to [ADP] at equilibrium is 7.2 × 10−6.

The Relationship of Free-Energy Change (ΔG) to the Concentrations of Reactants