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 \(\mathrm{Zn}(s) ?\)

Reduction potentials measure the tendency of a chemical species to be reduced or gain electrons. Positive reduction potentials indicate a greater tendency for a species to be reduced, while negative values signify a lower tendency for reduction. In general, species with higher reduction potentials prefer to be reduced, while those with lower reduction potentials prefer to be oxidized.

The following standard reduction potentials are taken from a standard reduction potential table: \(\mathrm{Br}_2/ \mathrm{Br}^-\): +1.087 V \(\mathrm{H_2/ H}^+\): 0 V \(\mathrm{La^{3+}/La}\): -2.52 V \(\mathrm{Ca/Ca}^{2+}\): -2.87 V \(\mathrm{Cd/Cd}^{2+}\): -0.40 V \(\mathrm{MnO}_4^-/\mathrm{Mn}^{2+}\): +1.51 V (in acidic conditions) \(\mathrm{Zn/Zn}^{2+}\): -0.76 V

The strongest oxidizing agent has the highest reduction potential since these species gain electrons most readily. Comparing the reduction potentials listed above, \(\mathrm{Br}_2\) has the highest value of +1.087 V. Therefore, \(\mathrm{Br}_2\) is the strongest oxidizing agent.

The strongest reducing agent has the lowest reduction potential since these species lose electrons most readily. Comparing the reduction potentials listed above, \(\mathrm{Ca}\) has the lowest value of -2.87 V. Therefore, \(\mathrm{Ca}\) is the strongest reducing agent.

For a reaction to occur, the reduction potential of the oxidizing agent has to be greater than that of the reducing agent. Given that the reduction potential for \(\mathrm{MnO}_4^-\) in acid is +1.51 V, any species with a smaller reduction potential can be oxidized. From the table, the species that can be oxidized are: \(\mathrm{H_2}, \mathrm{La}, \mathrm{Ca}, \mathrm{Cd}, \mathrm{Zn}\)

For a reaction to occur, the reduction potential of the oxidizing agent has to be greater than that of the reducing agent. Given that the reduction potential for \(\mathrm{Zn}\) is -0.76 V, any species with a larger reduction potential can be reduced. From the table, the species that can be reduced are: \(\mathrm{Br}_2, \mathrm{H_2}, \mathrm{Cd}\) To summarize, the answers to the questions are: a) Strongest oxidizing agent: \(\mathrm{Br}_{2}\) b) Strongest reducing agent: \(\mathrm{Ca}\) c) Species that can be oxidized by \(\mathrm{MnO}_{4}^{-}\) in acid: \(\mathrm{H_2}, \mathrm{La}, \mathrm{Ca}, \mathrm{Cd}, \mathrm{Zn}\) d) Species that can be reduced by \(\mathrm{Zn}(s) :\) \(\mathrm{Br}_2, \mathrm{H}_2, \mathrm{Cd}\)