Have a look at the
balanced half equations for the reduction of dichromate(VI) and
managate(VII) ions:
–Cr2O72- + 14H+ + 6e- ® 2Cr3+ + 7H2O
–MnO42- + 8H+ + 5e- ®
Mn2+ + 4H2O
When the reducing
agent is one without any oxygen (as in the example considered,
Cl-) notice that the number of
hydrogen ions and water molecules in the balanced half-equations
are dictated by the number of oxygen in the oxidizing
agent.
And therefore, the
number of hydrogen ions and water in the final balanced equation
is a multiple of that.
•Cr2O72- (aq) + 14H+ (aq) + 6Cl- (aq) ® 3Cl2 (g) + 2Cr3+ (aq) + 7H2O (l)
–1´ that in the reduction half-equation.
•2MnO42- (aq) + 10Cl- (aq) + 16H+ (aq) ® 2Mn2+ (aq) + 5Cl2 (aq) + 8H2O (l)
–2´ that in the balanced reduction
half-equation.
Not only that, the
balanced half equations appear on page 19 of the Data Booklet.