Question

Balance each of the following oxidation-reduction reactions by using the oxidation states method. a. \(\mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{Mg}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cl}^{-}(a q)+\mathrm{H}_{2}(g)\) c. \(\mathrm{Co}^{3+}(a q)+\mathrm{Ni}(s) \rightarrow \mathrm{Co}^{2+}(a q)+\mathrm{Ni}^{2+}(a q)\) d. \(\mathrm{Zn}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q)+\mathrm{H}_{2}(g)\)

Short answer

a. \(C_2H_6(g) + O_2(g) \rightarrow 2 CO_2(g) + 7 H_2O(g)\) b. \(Mg(s) + 2 HCl(aq) \rightarrow Mg^{2+}(aq) + 2 Cl^-(aq) + H_2(g)\) c. \(Co^{3+}(aq) + Ni(s) \rightarrow Co^{2+}(aq) + Ni^{2+}(aq)\) d. \(Zn(s) + H_2SO_4(aq) \rightarrow ZnSO_4(aq) + H_2(g)\)

Step-by-step solution

Identify the oxidation states

Identify the oxidation states of each element in the reactants and products. C2H6: C = -3, H = +1, O = 0 CO2: C = +4, O = -2 H2O: H = +1, O = -2

Find the changes in oxidation states

Determine the changes in oxidation states for each element that undergoes a change. C : -3 -> +4 (change of +7) O : 0 -> -2 (change of -2)

Balance the changes in oxidation states

Balance the changes in oxidation states by multiplying the number of atoms by the oxidation states changes. C : 2 atoms * (+7) = +14 O : 2 atoms * (-2) = -4 Since C has 14 units increment and O has 4 units decrement, we must multiply the whole H2O by 7 to balance the oxidation states. C2H6(g) + O2(g) -> 2 CO2(g) + 7 H2O(g) b. Mg(s) + HCl(aq) -> Mg2+(aq) + Cl^-(aq) + H2(g)

Identify the oxidation states

Identify the oxidation states of each element in the reactants and products. Mg: 0 HCl: H = +1, Cl = -1 Mg2+: +2 Cl^-: -1 H2: 0

Find the changes in oxidation states

Determine the changes in oxidation states for each element that undergoes a change. Mg: 0 -> +2 (change of +2) H: +1 -> 0 (change of -1)

Balance the changes in oxidation states

Balance the changes in oxidation states by balancing the number of atoms that change oxidation states. In this case, we see that 1 Mg atom changes from Mg to Mg2+ and 2 H atoms from HCl change to H2. So, we just need to multiply HCl by 2 to balance the equation. Mg(s) + 2 HCl(aq) -> Mg2+(aq) + 2 Cl^-(aq) + H2(g) c. Co3+(aq) + Ni(s) -> Co2+(aq) + Ni2+(aq)

Identify the oxidation states

Identify the oxidation states of each element in the reactants and products. Co3+: +3 Ni: 0 Co2+: +2 Ni2+: +2

Find the changes in oxidation states

Determine the changes in oxidation states for each element that undergoes a change. Co: +3 -> +2 (change of -1) Ni: 0 -> +2 (change of +2)

Balance the changes in oxidation states

Balance the changes in oxidation states by balancing the number of atoms that change oxidation states. In this case, since the changes in oxidation states are already balanced, the equation is already balanced: Co3+(aq) + Ni(s) -> Co2+(aq) + Ni2+(aq) d. Zn(s) + H2SO4(aq) -> ZnSO4(aq) + H2(g)

Identify the oxidation states

Identify the oxidation states of each element in the reactants and products. Zn: 0 H2SO4: H = +1, S = +6, O = -2 ZnSO4: Zn = +2, S = +6, O = -2 H2: 0

Find the changes in oxidation states

Determine the changes in oxidation states for each element that undergoes a change. Zn: 0 -> +2 (change of +2) H: +1 -> 0 (change of -1)

Balance the changes in oxidation states

Balance the changes in oxidation states by balancing the number of atoms that change oxidation states. In this case, we see that 1 Zn atom changes from Zn to Zn2+ and 2 H atoms change from H2SO4 to H2. So, the equation is already balanced: Zn(s) + H2SO4(aq) -> ZnSO4(aq) + H2(g)