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)

Verified step by step guidance

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^-.

Key Concepts

Electrolysis

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In this process, an electric current is passed through an electrolyte, causing the decomposition of the compound into its constituent elements or ions. The reactions occur at two electrodes: oxidation at the anode and reduction at the cathode.

Half-Reactions

Half-reactions are the individual oxidation or reduction reactions that occur at the electrodes during electrolysis. Each half-reaction shows the transfer of electrons and the change in oxidation states of the species involved. By writing half-reactions, one can clearly identify what is being oxidized and what is being reduced in the overall electrochemical process.

Electrolyte Composition

The composition of the electrolyte determines the ions available for the electrolysis process. Different electrolytes, such as NaBr, PbI2, and Na2SO4, will produce different ions in solution, which can lead to various products at the electrodes. Understanding the dissociation of these compounds in water is crucial for predicting the half-reactions that will occur during electrolysis.