How do you balance these redox reactions by the half-reaction method?

Question

How do you balance these redox reactions by the half-reaction method?

1. Al2O3 + C → Al + CO2

2. Na + Hg2Cl2 → NaCl + Hg

Answer 1

Al₂O₃ + C ==> Al + CO₂

Al₂O₃ ==> Al ... reduction half reaction

Al₂O₃ ==> 2Al ... balanced for Al

Al₂O₃ ==> 2Al + 3H₂O ... balanced for O

Al₂O₃ + 6H⁺ ==> 2Al + 3H₂O ... balanced for H using acid (H⁺)

Al₂O₃ + 6H⁺ + 6e- ==> 2Al + 3H₂O ... balanced for charge and this is the final balanced reduction 1/2 rx

C ==> CO₂ ... oxidation half reaction

C + 2H₂O ==> CO₂ ... balanced for C and O

C + 2H₂O ==> CO₂ + 4H⁺ ... balanced for H using acid (H⁺)

C + 2H₂O ==> CO₂ + 4H⁺ + 4e- ... balanced for charge and this is the final balanced oxidation 1/2 reaction

Multiply the reduction half reaction by 2 and the oxidation half reaction by 3 in order to equalize the electrons.

2Al₂O₃ + 12H⁺ + 12e- ==> 4Al + 6H₂O

3C + 6H₂O ==> 3CO₂ + 12H⁺ + 12e-

----------------------------------------------------- add them and combine or cancel like terms....

2Al₂O₃ + 3C ==> 4Al + 3CO₂ ... balanced redox equation