Question

For the mitochondrial membrane described in Problem 31, how many protons must be transported to provide enough free energy for the synthesis of 1 mol of ATP (assuming standard biochemical conditions)?

Short answer

A minimum of two to three protons must be transported to provide free energy in order to synthesize one mole of ATP.

Step-by-step solution

Finding free energy for the transport of 1 mole of proton

On transporting 1 mol of protons across the mitochondrial membrane under the conditions specified in problem 31 is calculated as:

$$\begin{gathered} ∆\mathrm{G}=2.3\mathrm{RT}\left[\mathrm{pH}\left(\mathrm{side}1\right)+\mathrm{pH}\left(\mathrm{side}2\right)\right]+\mathrm{ZF}∆\mathrm{\psi } \\ ∆\mathrm{G}=\left(2.3\times 8.314\mathrm{J}/\mathrm{Kmol}\times 298\mathrm{K}\right)\times \left(-1.4\right)+1\times \left(96.485\mathrm{C}/\mathrm{mol}\times \left(-0.06\mathrm{V}\right)\right) \\ ∆\mathrm{G}=-13766.1\mathrm{J}/\mathrm{mol}=-13.8\mathrm{kJ}/\mathrm{mol} \end{gathered}$$

Therefore, the free energy change is found to be_{$-13.8\mathrm{kJ}/\mathrm{mol}$}.

Finding protons transported for production of 1 mol of ATP

Proton transport across the membrane has a free energy change of -13.8 kJmol^-1 The approximate free energy $∆{\mathrm{G}}^{\mathrm{o}1}$required for the production of ATP is -30.5 kJmol^-1 .

For one mole of ATP production, the number of protons required to provide free energy is$\frac{30.5{\mathrm{kJmol}}^{-1}}{13.8{\mathrm{kJmol}}^{-1}}=2.2$protons.

The number of protons transported to provide enough free energy for the synthesis of 1 mole of ATP assuming standard biochemical conditions is 2 to 3.