$2MnO_4^- +bC_2O_4 ^{2-} + CH^+ $$\downarrow $$ xMn^{2+} + y CO_2 + z H_2 O $

$2MnO_4^- +bC_2O_4 ^{2-} + CH^+ \rightarrow xMn^{2+} + y CO_2 + z H_2 O $

If the above equation is balanced with integer coefficients, the value of c is _ _ _ _ . (Round off to the nearest integer)

Solution

$ Mn^{7+} + 5e \rightarrow Mn^{2+} $ .......... (*)

$ C_2 ^{3+} \rightarrow 2C^{4+} + 2e $ ...........(#)

2 $\times$ (*) + 5 $\times$ (#)

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$2Mn^{7+} + 5C_2 ^{3+} \rightarrow 2Mn^{2+} + 10 C ^{4+} $

So, $2MnO_4 ^- + 5C_2O_4 ^{2-} + 16 H^ + \rightarrow 2Mn^{2+} + 10 CO_2 + 8 H_2 O $

$\therefore c = 16 $