Question

Predict the half-cell reactions that occur when aqueous solutions of the following salts are electrolyzed in a cell with inert electrodes. What is the overall cell reaction in each case? (a) \(\mathrm{LiCl}\) (b) \(\mathrm{CuSO}_{4}\) (c) \(\mathrm{K}_{2} \mathrm{SO}_{4}\)

Short answer

Electrolytic reactions: (a) \(\mathrm{Cl_2 + H_2}\), (b) \(\mathrm{Cu + O_2}\), (c) \(\mathrm{H_2 + O_2}\).

Step-by-step solution

Identify Ions Present in the Solution

For each salt, we need to identify the ions present in the aqueous solution. (a) \[\mathrm{LiCl \rightarrow Li^{+} (aq) + Cl^{-} (aq)} \](b) \[\mathrm{CuSO}_{4} \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{SO}_{4}^{2-}(aq)\](c) \[\mathrm{K}_{2} \mathrm{SO}_{4} \rightarrow 2\mathrm{K}^{+}(aq) + \mathrm{SO}_{4}^{2-}(aq)\]

Determine Potential Half-Cell Reactions

Identify the possible half-cell reactions for each cation and anion in the solution and water, since water can also participate in electrolysis.(a) - \( \mathrm{Li^+ + e^- \rightarrow Li} \)- \( \mathrm{Cl^- \rightarrow \frac{1}{2}Cl_{2} + e^-} \)(b)- \( \mathrm{Cu^{2+} + 2e^- \rightarrow Cu} \)- \( \mathrm{2H_{2}O + 2e^- \rightarrow H_{2} + 2OH^-} \)- \( \mathrm{SO_{4}^{2-}} \) usually does not discharge; instead, \( \mathrm{H_{2}O \rightarrow \frac{1}{2}O_{2} + 2H^+ + 2e^-} \) may occur.(c)- \( \mathrm{K^+} \) usually not reduced; water reduction preferred.- \( \mathrm{SO_{4}^{2-}} \) same as for (b), typically involves water oxidation.

Select Feasible Half-Reactions

Based on reduction potentials, determine which reactions are most feasible during electrolysis according to standard electrode potentials.(a)- Does not involve \(\mathrm{Li^+}\), so consider \(\mathrm{H_{2}O}\):- Anode: \( \mathrm{2Cl^- \rightarrow Cl_{2} + 2e^-} \)- Cathode: \( \mathrm{2H_{2}O + 2e^- \rightarrow H_{2} + 2OH^-} \)(b)- Anode: \( \mathrm{H_{2}O \rightarrow \frac{1}{2}O_{2} + 2H^+ + 2e^-} \)- Cathode: \( \mathrm{Cu^{2+} + 2e^- \rightarrow Cu} \)(c)- Anode: \( \mathrm{H_{2}O \rightarrow \frac{1}{2}O_{2} + 2H^+ + 2e^-} \)- Cathode: \( \mathrm{2H_{2}O + 2e^- \rightarrow H_{2} + 2OH^-} \)

Write Overall Cell Reactions

Combine the selected half-reactions to write the overall cell reaction for each part.(a) Overall Reaction:\[ \mathrm{2Cl^- + 2H_2O \rightarrow Cl_2 + H_2 + 2OH^-} \](b) Overall Reaction:\[ \mathrm{Cu^{2+} + H_2O \rightarrow Cu + \frac{1}{2}O_2 + 2H^+} \](c) Overall Reaction:\[ \mathrm{2H_2O \rightarrow 2H_2 + O_2} \]

Key concepts

Half-cell reactions

Half-cell reactions are fundamental to understanding the electrolysis process. In electrolytic cells, these reactions take place at the two electrodes: one half-reaction at the anode (oxidation) and another at the cathode (reduction). For each substance in question, potential half-cell reactions must be identified for both cations and anions present in the aqueous solution.

For example, in the electrolysis of \(\mathrm{LiCl}\), ions present are \(\mathrm{Li^+}\) and \(\mathrm{Cl^-}\). The potential half-cell reactions that could occur include the reduction of \(\mathrm{Li^+}\) to \(\mathrm{Li}\) and the oxidation of \(\mathrm{Cl^-}\) to chlorine gas, \(\mathrm{Cl_2}\). However, due to relative reduction potentials, certain reactions may be more favorable.

The selection of the feasible half-cell reactions during electrolysis depends on the energy requirement, which is determined by the reduction potential of each possible reaction. It is not always the ions in the solution that will prefer to react, but sometimes water molecules if they have a higher or more favorable reduction potential.

Aqueous solution

An aqueous solution is one where the solute is dissolved in water, resulting in the ions that are crucial for electrolysis. Water is a polar solvent, effectively dissolving many salts into their constituent ions.

For example, an aqueous solution of \(\mathrm{CuSO}_{4}\) breaks down into \(\mathrm{Cu^{2+}}\) and \(\mathrm{SO}_{4}^{2-}\) ions. In the electrolysis of this solution, not only do these ions participate, but water itself can undergo electrolysis to produce oxygen and hydrogen gases.

This significance of water's role in aqueous solutions necessitates considering its potential reactions in electrolysis, especially when the ions in the solution are not likely to discharge, or if they require more energy to do so than water.

The interactions in aqueous solutions showcase the diversity of potential reactions and their dependency on ion type, concentration, and reduction potentials available.

Inert electrodes

Inert electrodes are used in electrolysis to provide a surface for the reaction without participating in it. These electrodes, typically made of materials like platinum or graphite, do not react with the solutions or influence the chemical reactivity directly.

For instance, during the electrolysis of \(\mathrm{K}_{2}\mathrm{SO}_{4}\), inert electrodes allow for the oxidation of water to produce oxygen without the electrodes themselves undergoing any chemical change.

The choice of inert electrodes is crucial because they ensure that the electrodes do not dissolve into the solution or contribute additional ions, which could affect the purity of the reaction products. By providing a stable environment, inert electrodes allow the focus to be solely on the ions in solution and their interactions, simplifying system complexity and ensuring predictable electrochemical behavior.

Reduction potentials

Reduction potentials are critical in identifying feasible reactions during electrolysis. They measure the tendency of a chemical species to acquire electrons and thereby be reduced.

Reduction potentials are quantified in volts and are used to determine which half-cell reactions will occur preferentially during electrolysis.

In an aqueous solution of \(\mathrm{LiCl}\), for instance, while it may appear plausible to reduce \(\mathrm{Li^+}\) directly to lithium, water reduction is typically more favorable due to its reduction potential.

This potential is also instrumental in deciding which reactions occur at the anode and cathode during electrolysis.

• Lower reduction potential: Substance more likely to give up electrons (undergo oxidation).
• Higher reduction potential: Substance more likely to gain electrons (undergo reduction).

Understanding this concept helps predict and control which elements will form or break bonds at each electrode during electrolysis, significantly influencing the efficiency and outcome of electrochemical processes.