Complete the following equations: (a) 2 MnO_4^-+5 NO_2^-+6 H^+ → (b) Cr_2 O_7^2-+14 H^++6 e^- →

(a) \(\displaystyle \mathbf{2 ~ M n}_{\mathbf{4}}^{-}+\mathbf{5} \mathbf{N O}_{\mathbf{2}}^{-}+\mathbf{6 ~ H}^{+} \longrightarrow \mathbf{2} \mathbf{M n}^{\mathbf{2}+}+\mathbf{5} \mathbf{N O}_{\mathbf{3}}^{-}+\mathbf{3 ~ H}_{\mathbf{2}} \mathbf{O}\)

(b) \(\displaystyle \mathbf{C r}_{\mathbf{2}} \mathrm{O}_{7}^{2-}+\mathbf{1 4}^{+}+\mathbf{6 ~ e}^{-} \longrightarrow \mathbf{2 C r}^{\mathbf{3}+}+\mathbf{7 H}_{\mathbf{2}} \mathbf{O}\)