Chapter 4
Q. 4.8
Balance the following half-equations:
(1) NO_{3}^{-}(aq) → NO(g) (basic solution)
(2) Cl_{2}(g) → ClO_{3} ^{-}(aq) (acidic solution)
STRATEGY
Follow the steps outlined above in the order given.
Step-by-Step
Verified Solution
| N: +5 → +2; O: -2 → -2; N is reduced. | (1) (a) Oxidation numbers |
| 1 N on each side; no adjustment is required. | (b) Atom balance |
| N: 5(1) → N: 2(1) | (c) “total oxidation” number |
| The oxidation number for N goes from +5 to +2. It is reduced by 3.
Add 3 electrons to the reactant side. NO_{3}^{-}(aq) + 3e^{-} → NO(g) |
(d) Add electrons |
| reactants: -1 + 3(-1) = -4 products: 0
basic medium: add OH^{-}. To balance, add 4 OH^{-} on the right. NO_{3}^{-}(aq) + 3e^{-} → NO(g) + 4OH^{-}(aq) reactants: -1 + 3(-1) = -4 products: 4(-1) = -4 |
(e) Balance charge |
| reactants: 0 H products: 4 H To balance, add 2H_{2}O on the left. NO_{3}^{-}(aq) + 3e^{-} + 2H_{2}O → NO(g) + 4OH^{-}(aq) reactants: 4 H products: 4 H |
(f) Balance H |
| reactants: 3 + 2 = 5 products: 4 + 1 = 5
NO_{3}^{-}(aq) + 3e^{-} → NO(g) + 4OH^{-}(aq) |
(g) Check O:
The half-equation is balanced: |
| Cl: 0 → +5; O: -2 → -2; Cl is oxidized. | (2) (a) Oxidation numbers |
| reactant: 2 Cl product: 1 Cl Multiply ClO_{3}^{-} by 2. Cl_{2}(g) → 2ClO_{3} ^{-}(aq) |
(b) Atom balance |
| Cl: 0(2) = 0 → Cl: 5(2) = 10 | (c) “total oxidation” number |
| The oxidation number for Cl goes from 0 to 10. The oxidation number increases by 10. Add 10 electrons to the product side Cl_{2}(g) → 2ClO_{3} ^{-}(aq) + 10e^{-} |
(d) Add electrons |
| reactants: 0 products: 2(–1) + 10(–1) = –12
acidic medium: add H^{+}. To balance, add 12 H^{+} on the right. Cl_{2}(g) → 2ClO_{3} ^{-}(aq) + 10e^{-} + 12H^{+}(aq) reactants: 0 products: 2(-1) + 10(-1) + 12(+1) = 0 |
(e) Balance charge |
| reactants: 0 H products: 12 H
To balance, add 6H_{2}O on the left. Cl_{2}(g) + 6H_{2}O → 2ClO_{3} ^{-}(aq) + 10e^{-} + 12H^{+}(aq) reactants: 12 H products: 12 H |
(f) Balance H |
| reactants: 6 products: 2(3) = 6
Cl_{2}(g) + 6H_{2}O → 2ClO_{3} ^{-}(aq) + 10e^{-} + 12H^{+}(aq) |
(g) Check O:
The half-equation is balanced: |