Consider only the species (at standard conditions) $$ \mathrm{Br}^{-}, \quad \mathrm{Br}_{2}, \quad \mathrm{H}^{+}, \quad \mathrm{H}_{2}, \quad \mathrm{La}^{3+}, \quad \mathrm{Ca}, \quad \mathrm{Cd} $$ in answering the following questions. Give reasons for your answers. a. Which is the strongest oxidizing agent? b. Which is the strongest reducing agent? c. Which species can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acid? d. Which species can be reduced by \(\mathrm{Zn}(s) ?\)

Find the standard reduction potentials for each species in the table. The values are given below: \[ \begin{aligned} \mathrm{Br}^{-} / \mathrm{Br}_{2} &: +1.087 \, V \\ \mathrm{H}^{+} / \mathrm{H}_{2} &: 0 \, V \\ \mathrm{La}^{3+} / \mathrm{La} &: -2.52 \, V \\ \mathrm{Ca}^{2+} / \mathrm{Ca} &: -2.87 \, V \\ \mathrm{Cd}^{2+} / \mathrm{Cd} &: -0.402 \, V \end{aligned} \] (Note that we only search for half-reactions concerning the species mentioned in the exercise)

An oxidizing agent is a species that gains electrons and is reduced during the reaction. The stronger the oxidizing agent, the greater its tendency to gain electrons. Species with higher (more positive) reduction potentials have a greater tendency to be reduced. The highest reduction potential in the list above is for the reaction \(\mathrm{Br}^{-} / \mathrm{Br}_{2}\), with a value of +1.087 V. Therefore, the strongest oxidizing agent is \(\mathrm{Br}_{2}\). Answer (a): The strongest oxidizing agent is \(\mathrm{Br}_{2}\).

A reducing agent is a species that loses electrons and is oxidized during the reaction. The stronger the reducing agent, the greater its tendency to give up electrons. Species with lower (more negative) reduction potentials have a greater tendency to be oxidized. The lowest reduction potential in the list above is for the reaction \(\mathrm{Ca}^{2+} / \mathrm{Ca}\), with a value of -2.87 V. Therefore, the strongest reducing agent is \(\mathrm{Ca}\). Answer (b): The strongest reducing agent is \(\mathrm{Ca}\).

To determine which species can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acid, we must first find the standard reduction potential for the reaction involving \(\mathrm{MnO}_{4}^{-}\) as the oxidizing agent: \(\mathrm{MnO}_{4}^{-} + 8 \mathrm{H}^{+} + 5 e^{-} \rightarrow \mathrm{Mn}^{2+} + 4 \mathrm{H}_{2}\mathrm{O}\) : \(+1.51 \, V\) Now we are looking for any species (in our list) that can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acidic solution. In other words, we need to find species with a reduction potential lower than +1.51 V (because the oxidizing agent must have a higher reduction potential than the species being oxidized). Comparing the reduction potentials from Step 1 with +1.51 V, we can see that \(\mathrm{H}^{+}\) (0 V) and \(\mathrm{Cd}^{2+}\) (-0.402 V) can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acid. Answer (c): \(\mathrm{H}^{+}\) and \(\mathrm{Cd}^{2+}\) can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acid.

To determine which species can be reduced by \(\mathrm{Zn}(s)\), we first find the standard reduction potential for the reaction involving \(\mathrm{Zn}^{2+}\) as the reducing agent: \(\mathrm{Zn}^{2+} + 2 e^{-} \rightarrow \mathrm{Zn}\) : \(-0.76 \, V\) Now we are looking for any species (in our list) that can be reduced by \(\mathrm{Zn}(s)\). In other words, we need to find species with a reduction potential higher than -0.76 V (because the reducing agent must have a lower reduction potential than the species being reduced). Comparing the reduction potentials from Step 1 with -0.76 V, we can see that no species can be reduced by \(\mathrm{Zn}(s)\). Answer (d): No species given can be reduced by \(\mathrm{Zn}(s)\).