Balancing redox equations in acidic solutions can be quite challenging but with the method of half-reactions, it can become more manageable. Let's go through each equation step-by-step:
a. Cu(s) + NO3-(aq) --> Cu2+(aq) + NO2(aq)
Step 1: Identify which elements are getting oxidized and reduced. In this case, copper (Cu) is getting oxidized from 0 to +2 oxidation state, and nitrogen (N) is getting reduced from +5 to +4.
Step 2: Split the reaction into two half-reactions, one for the oxidation and one for the reduction.
Oxidation half-reaction: Cu(s) --> Cu2+(aq)
Reduction half-reaction: NO3-(aq) --> NO2(aq)
Step 3: Balance the atoms in each half-reaction.
Oxidation half-reaction: Cu(s) --> Cu2+(aq) + 2e-
Reduction half-reaction: 3NO3-(aq) + 2H+(aq) + 2e- --> 3NO2(aq) + H2O(l)
Step 4: Balance the charges by multiplying the half-reactions as required. In this case, multiply the oxidation half-reaction by 3 and the reduction half-reaction by 2:
3Cu(s) --> 3Cu2+(aq) + 6e-
6NO3-(aq) + 4H+(aq) + 4e- --> 6NO2(aq) + 2H2O(l)
Step 5: Add the balanced half-reactions together and cancel out any common species:
3Cu(s) + 6NO3-(aq) + 4H+(aq) --> 3Cu2+(aq) + 6NO2(aq) + 2H2O(l)
b. Mn2+(aq) + NaBiO3(s) --> Bi3+(aq) + MnO4-(aq)
Step 1: Identify the elements that are getting oxidized and reduced. In this case, manganese (Mn) is getting oxidized from +2 to +7 oxidation state, and bismuth (Bi) is getting reduced from +5 to +3.
Step 2: Split the reaction into two half-reactions.
Oxidation half-reaction: Mn2+(aq) --> MnO4-(aq)
Reduction half-reaction: NaBiO3(s) --> Bi3+(aq)
Step 3: Balance the atoms in each half-reaction.
Oxidation half-reaction: Mn2+(aq) --> MnO4-(aq) + 5e-
Reduction half-reaction: 2NaBiO3(s) + 6H+(aq) + 5e- --> 2Bi3+(aq) + 2Na+(aq) + 3H2O(l)
Step 4: Balance the charges by multiplying the half-reactions as required. Multiply the oxidation half-reaction by 2, and the reduction half-reaction by 5:
2Mn2+(aq) --> 2MnO4-(aq) + 10e-
10NaBiO3(s) + 30H+(aq) + 25e- --> 10Bi3+(aq) + 10Na+(aq) + 15H2O(l)
Step 5: Add the balanced half-reactions together and cancel out any common species:
2Mn2+(aq) + 10NaBiO3(s) + 30H+(aq) --> 2MnO4-(aq) + 10Bi3+(aq) + 10Na+(aq) + 15H2O(l)
Remember, balancing redox equations requires practice and patience. Following the steps provided will help you accurately balance the equations using the method of half-reactions in acidic solutions.