Question #44679

Consider the following three unbalanced redox reactions involving mixed-valence oxides in an acidic medium:

I. $\ce{Fe3O4(s) + MnO4^{-}(aq) + H+(aq) -> Fe^{3+}(aq) + Mn^{2+}(aq) + H2O(l)}$ II. $\ce{Pb3O4(s) + H2O2(aq) + H+(aq) -> Pb^{2+}(aq) + O2(g) + H2O(l)}$ III. $\ce{Mn3O4(s) + C2O4^{2-}(aq) + H+(aq) -> Mn^{2+}(aq) + CO2(g) + H2O(l)}$

Let $n_1, n_2,$ and $n_3$ be the $n$-factors (valency factors) of $\ce{Fe3O4}$, $\ce{Pb3O4}$, and $\ce{Mn3O4}$ respectively in the above reactions. Let $f_1, f_2,$ and $f_3$ be the exact fraction of metal atoms in each respective oxide formula unit that undergo a change in their oxidation state during the reactions.

Calculate the value of the expression: $\Omega = \frac{n_1}{f_1} + \frac{n_2}{f_2} + \frac{n_3}{f_3}$