J.R. S. answered 04/24/23
Ph.D. University Professor with 10+ years Tutoring Experience
So to balance any equation, the amount of each element must be the same on both sides of the equation. Not only that, but the charge (plus/minus) must also be the same. In this problem, we are given the two half-reactions. We can balance them separately, and then add them together.
NO2- ==> NO3- .. unbalanced oxidation reaction
NO2- + H2O ==> NO3- .. balanced for N and O
NO2- + H2O + 2OH- ==> NO3- + 2H2O .. balanced for N, O and H (by adding base, OH-)
NO2- + H2O + 2OH- ==> NO3- + 2H2O + 2e- .. balanced for N, O, H and charge
Ag+ + e- ==> Ag .. balanced for Ag and charge = balanced reduction reaction
Since 2 electrons were transferred in the oxidation reaction, and only 1 electron was transferred in the reduction reaction, we need to multiply the reduction reaction by 2 and then add the two together:
2Ag+ + 2e- ==> 2Ag
NO2- + H2O + 2OH- ==> NO3- + 2H2O + 2e-
-------------------------------------------------------------- add together and combine/cancel like terms......
2Ag+ + NO2- + 2OH- ==> 2Ag + NO3- + H2O .. balanced redox equation