Cytochrome, represented here as $CyF{e}^{2+},$ reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate $($ATP$).$

At $pH7\mathrm{.}0$ the following reduction potentials pertain to the oxidation of $CyF{e}^{2+}$ :

$O_2(g)+4H^{+}(aq)+4e^{-}2H_{2}O(l),E_{\text{r}\text{e}\text{d}}^o=+0\mathrm{.}82V$

$CyF{e}^{3+}(aq)+e^{-}CyF{e}^{2+}(aq),E_{\text{r}\text{e}\text{d}}=+0\mathrm{.}22V$

What is the $G$ for the oxidation of $CyF{e}^{2+}$ by air? If the synthesis of $1\mathrm{.}00$mol of ATP from adenosine diphosphate $($ADP$)$ requires $G$ of $37\mathrm{.}7kJ,$ how many moles of ATP are synthesized per $mol{O}_2?$

$($Adapted from Brown, LeMay, & Bersten, Chemistry The Central Science ${10}^{th}$ ed$.$ Chapter $20$ problem $20\mathrm{.}115$ p$.898)$

Faraday's constant $=96\mathrm{.}5k\frac{J}{1}V.mol{e}^{-}$