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For the redox reaction $MnO_4^- + C_2O_4^{2-} + H^+ \rightarrow Mn^{2+} + CO_2 + H_2O$, the correct coefficients of the reactants for the balanced equation are
Explanation
Electron balance gives 2 $MnO_4^-$ : 5 $C_2O_4^{2-}$, then balance O and H.
Detailed Solution
Mn: +7 → +2 (reduction); C: +3 → +4 (oxidation)
n-factor of $MnO_4^- = 5$
n-factor of $C_2O_4^{2-} = 2$
Ratio of n-factors of $MnO_4^-$ and $C_2O_4^{2-}$ is 5 : 2, so the molar ratio in the balanced reaction is 2 : 5.
The balanced equation is $2MnO_4^- + 5C_2O_4^{2-} + 16H^+ \rightarrow 2Mn^{2+} + 10CO_2 + 8H_2O$
So the coefficients are $MnO_4^-$ = 2, $C_2O_4^{2-}$ = 5, $H^+$ = 16.