Write equations for the half-reactions that occur at the anode and cathode for the electrolysis of each aqueous solution. a. NaBr(aq) b. PbI₂(aq) c. Na₂SO₄(aq)

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1. Identify the ions present in each aqueous solution. For NaBr(aq), the ions are Na^+ and Br^-. For PbI_2(aq), the ions are Pb^2+ and I^-. For Na_2SO_4(aq), the ions are Na^+, SO_4^2-, and H_2O.
2. Determine the possible half-reactions at the anode and cathode. At the anode, oxidation occurs, and at the cathode, reduction occurs. Consider the standard reduction potentials to identify which species will be oxidized and reduced.
3. For NaBr(aq), at the anode, Br^- ions are oxidized to Br_2 gas. The half-reaction is: 2Br^- \rightarrow Br_2 + 2e^-. At the cathode, water is reduced to hydrogen gas: 2H_2O + 2e^- \rightarrow H_2 + 2OH^-.
4. For PbI_2(aq), at the anode, I^- ions are oxidized to I_2. The half-reaction is: 2I^- \rightarrow I_2 + 2e^-. At the cathode, Pb^2+ ions are reduced to Pb metal: Pb^2+ + 2e^- \rightarrow Pb.
5. For Na_2SO_4(aq), at the anode, water is oxidized to oxygen gas: 2H_2O \rightarrow O_2 + 4H^+ + 4e^-. At the cathode, water is reduced to hydrogen gas: 2H_2O + 2e^- \rightarrow H_2 + 2OH^-.