Chapter 20, Problem 1P

Interpretation Introduction

To propose:

From the given equation, the electron acceptor and electron donor with the standard conditions among the redox couples are determined. Also, to calculate the $\Delta E_0^{\text{'}}$ value and the energy change of the reaction, that is, in the favored direction thermodynamically.

Introduction:

Redox couple is defined where one element is oxidized and the other is reduced in the form of the substance that undergoes reduction half-reaction and oxidation. The pair of acid-base is conjugated by the redox couples.

Explanation of Solution

Two half-reactions for the given equation are given as:

  $\begin{array}{l}\text{FAD}+2{\text{H}}^{+}+2e^{-}\to {\text{FADH}}_2(E_0^{\text{'}}=0.02V)\\ \text{cytochrome }c,{\text{Fe}}^{3+}+e^{-}\to \text{cytochrome c},{\text{Fe}}^{2+}(E_0^{\text{'}}=0.254V)\end{array}$

According to the potentials of standard reduction, the electrons will flow to the cytochrome c in a higher range. First, it flows to ${\text{Fe}}^{3+}$ and then it flows to ${\text{FADH}}_{\text{2}}$ . So hence, here, electron acceptor is ${\text{Fe}}^{3+}$ and the electron donor is ${\text{FADH}}_{\text{2}}$ .

Calculation of $E_0^{\text{'}}$

  $\Delta E_0^{\text{'}}=\text{acceptor}\Delta E_0^{\text{'}}-\text{donor}\Delta E_0^{\text{'}}$

  $=\text{acceptor}\Delta E_0^{\text{'}}(cytC)-\text{donor}\Delta E_0^{\text{'}}(\text{FAD})$

  $\begin{array}{l}=0.254-(-0.219)\\ =0.473V\end{array}$

The free change of energy for the reaction is calculated with the transfer of two electrons in the above reaction,

  $\begin{array}{l}\Delta G^{0\text{'}}=-nF\Delta E_0^{\text{'}}\\ n=2\\ F=96.48\text{5 kJ/Vmol}\end{array}$

Calculation of $\Delta G^{0\text{'}}$

  $\Delta G^{0\text{'}}=-2(96.48\text{5 kJ/Vmol})(0.473\text{ V})$

  $=-91.3\text{ kJ/mol}$