Calculate $G($in $k\frac{J}{m}ol)$ for the reaction ADP$++H^{+}ATP+H_{2}O$ using the proton motive

force and $)$ generated during oxidative phosphorylation. $(10$ points$)$ Consider that:

ADP and $$ concentration $=10M$

ATP concentration $=5mM$

$pH$ gradient difference between mitochondrial matrix and

intermembrane space$)$

Membrane potential $()=-180mV($inside negative with respect to outside$)$

$G^{\text{'}}$ for ATP synthesis at $pH7$ and $25C,$ which is $-30\mathrm{.}5k\frac{J}{m}ol$

Gas constant $(8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}*K})$

$F$ is the Faraday constant $(96\mathrm{.}485k\frac{C}{m}ol).$

T in Kelvin $(298$ K$)$

$1$ proton is translocated during the synthesis of one ATP molecule.