The balanced reaction is:
\[ 2 \text{MnO}_4^- + 5 \text{C}_2\text{O}_4^{2-} + 16 \text{H}^+ \rightarrow 2 \text{Mn}^{2+} + 10 \text{CO}_2 + 8 \text{H}_2\text{O} \]From the stoichiometry, we see that 16 moles of \(\text{H}^+\) are required for 2 moles of \(\text{MnO}_4^-\). Therefore, 8 moles of \(\text{H}^+\) are needed for each mole of \(\text{MnO}_4^-\).