Indicate whether the following balanced equations involve oxidation-reduction. If they do, identify the elements that undergo changes in oxidation number. (a) $2 \mathrm{AgNO}_{3}(a q)+\mathrm{CoCl}_{2}(a q) \longrightarrow 2 \mathrm{AgCl}(s)+ \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}(a q)$ (b) $2 \mathrm{PbO}_{2}(s) \longrightarrow 2 \mathrm{PbO}(s)+\mathrm{O}_{2}(g)$ (c) $2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NaBr}(s) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{SO}_{2}(g)+ \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$

We must assign oxidation numbers to all elements involved in each balanced equation. We will use the following rules: 1. The oxidation number of an element in its free state is 0. 2. The oxidation number of a monoatomic ion is equal to its charge. 3. The oxidation number of hydrogen is +1 if it is bonded to a non-metal and -1 if bonded to a metal. 4. The oxidation number of oxygen is -2, except in peroxides (-1) and when bonded to fluorine (+2). 5. The oxidation number of fluorine is -1; all other halogens have an oxidation number of -1 in their compounds, except when they are bonded to a more electronegative element. 6. The sum of the oxidation numbers of all atoms in a compound must be zero; the sum of the oxidation numbers in a polyatomic ion must be equal to its charge.

We will compare the oxidation numbers before and after the reaction for each element in each balanced equation to determine if any changes occurred. (a) \(2\mathrm{AgNO}_{3}(a q)+\mathrm{CoCl}_{2}(a q) \longrightarrow 2\mathrm{AgCl}(s)+ \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) Ag: +1 -> +1 (no change) N: +5 -> +5 (no change) O: -2 -> -2 (no change) Co: +2 -> +2 (no change) Cl: -1 -> -1 (no change) (b) \(2\mathrm{PbO}_{2}(s) \longrightarrow 2\mathrm{PbO}(s)+\mathrm{O}_{2}(g)\) Pb: +4 -> +2 (change) O: -2 -> 0 (change) (c) \(2\mathrm{H}_{2}\mathrm{SO}_{4}(a q)+2\mathrm{NaBr}(s) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{SO}_{2}(g)+ \mathrm{Na}_{2}\mathrm{SO}_{4}(a q)+2\mathrm{H}_{2}\mathrm{O}(l)\) H: +1 -> +1 (no change) S: +6 -> +4 (change) O: -2 -> -2 (no change) Na: +1 -> +1 (no change) Br: -1 -> 0 (change)

We can now identify the elements that have undergone changes in oxidation numbers in the given balanced equations: (a) No elements underwent any changes in oxidation numbers, so the reaction does not involve oxidation-reduction. (b) In equation (b), Pb and O have changes in oxidation numbers. Pb changes from +4 to +2 and O changes from -2 to 0. Therefore, this is an oxidation-reduction reaction. (c) In equation (c), S and Br have changes in oxidation numbers. S changes from +6 to +4, and Br changes from -1 to 0. Therefore, this is an oxidation-reduction reaction.