The amount of manganese in steel is determined by changing it to permanganate ion. The steel is first dissolved in nitric acid, producing \(\mathrm{Mn}^{2+}\) ions. These ions are then oxidized to the deeply colored \(\mathrm{MnO}_{4}{ }^{-}\)ions by periodate ion \(\left(\mathrm{IO}_{4}^{-}ight)\)in acid solution.

a. Complete and balance an equation describing each of the above reactions.

b. Calculate \(\mathscr{C}^{\circ}, \Delta G^{\circ}\), and \(K\) at \(25^{\circ} \mathrm{C}\) for each reaction.