Consider the cell Pt ( s ) | H _ 2 ( s ) ( latm )| H ^ + (aq, [ H ^...

Cell reaction which occurs:
$\dfrac{1}{2}{H}_{2} ( g ) + {Fe}^{3 +}\text{(aq.)} ⟶ {H}^{+} ( aq ) + {Fe}^{2 +}\text{(aq.)}$
Using Nernst' equation:

$E = {E}^{o} - \dfrac{0 . 059}{1}log\dfrac{\left[{Fe}^{2 +}\right]}{\left[{Fe}^{3 +}\right]}$

$⇒ 0 . 712 = ( 0 . 771 - 0 ) - \dfrac{0 . 059}{1}log\dfrac{\left[{Fe}^{2 +}\right]}{\left[{Fe}^{3 +}\right]}$

$⇒ log\dfrac{\left[{Fe}^{2 +}\right]}{\left[{Fe}^{3 +}\right]} = \dfrac{( 0 . 771 - 0712 )}{0 . 059} = 1$

$⇒ \dfrac{\left[{Fe}^{2 +}\right]}{\left[{Fe}^{3 +}\right]} = 10$