For the reaction, 2 MnO ₄⁻+b C ₂ O ₄²⁻+c H ⁺ x Mn ²⁺+y CO ₂+z H ₂ O Find b, c, x, y and z

Step-by-step solution

The given redox reaction is 2 MnO ₄⁻ + b C ₂ O ₄²⁻ + c H ⁺ x Mn ²⁺ + y CO ₂ + z H ₂ O . The oxidation half-reaction is C ₂ O ₄²⁻ 2 CO ₂ + 2e⁻ . The reduction half-reaction is MnO ₄⁻ + 8 H ⁺ + 5e⁻ Mn ²⁺ + 4 H ₂ O . To balance the electrons, multiply the oxidation half-reaction by 5 and the reduction half-reaction by 2: 5 C ₂ O ₄²⁻ 10 CO ₂ + 10e⁻ 2 MnO ₄⁻ + 16 H ⁺ + 10e⁻ 2 Mn ²⁺ + 8 H ₂ O Adding the two half-reactions gives: 2 MnO ₄⁻ + 5 C ₂ O ₄²⁻ + 16 H ⁺ 2 Mn ²⁺ + 10 CO ₂ + 8 H ₂ O Comparing this with the given equ