Question

List the anode and cathode half-reactions that might occur when an aqueous solution of \(\mathrm{MgCl}_{2}\) is electrolyzed in a cell having inert electrodes. Predict which half-reactions will occur, and justify your answer.

Short answer

Anode: \(2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2(g) + 2e^-\), cathode: \(2\mathrm{H}_2\mathrm{O(l)} + 2e^- \rightarrow \mathrm{H}_2(g) + 2\mathrm{OH}^-\). Chlorine and hydrogen gases form.

Step-by-step solution

Identify Possible Anode Reactions

When electrolyzing an aqueous solution of \(\mathrm{MgCl}_{2}\), we consider two potential anode reactions. The oxidation of \(\mathrm{Cl}^-\):\[ 2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2(g) + 2e^- \]and water oxidation: \[ 2\mathrm{H}_2\mathrm{O(l)} \rightarrow \mathrm{O}_2(g) + 4\mathrm{H}^+(aq) + 4e^- \]. We need to consider the standard reduction potentials or reactivity to predict which will occur in practice.

Determine Which Anode Reaction Occurs

Compare the standard potential for \(\mathrm{Cl}^-/\mathrm{Cl}_2\) oxidation (\(E^\circ = -1.36\, \mathrm{V}\)) and water oxidation (\(E^\circ = -1.23\, \mathrm{V}\)). Water oxidation is often less favorable because \([\mathrm{H}^+]\) would need to be increased, making chlorine oxidation more likely at the anode.

Identify Possible Cathode Reactions

For the cathode, consider the reduction of \(\mathrm{Mg}^{2+}\): \[ \mathrm{Mg}^{2+}(aq) + 2e^- \rightarrow \mathrm{Mg(s)} \]and the reduction of water: \[ 2\mathrm{H}_2\mathrm{O(l)} + 2e^- \rightarrow \mathrm{H}_2(g) + 2\mathrm{OH}^-(aq) \]. These are the plausible cathode half-reactions.

Determine Which Cathode Reaction Occurs

Compare the standard potentials for \(\mathrm{Mg}^{2+}/\mathrm{Mg}\) reduction (\(E^\circ = -2.37\, \mathrm{V}\)) and water reduction (\(E^\circ = -0.83\, \mathrm{V}\)). Water reduction is more favorable due to its less negative \(E^\circ\) value, meaning hydrogen gas is more likely to form at the cathode.

Summarize the Electrolysis Reactions

The likely anode reaction is \(2\mathrm{Cl}^- \rightarrow \mathrm{Cl}_2(g) + 2e^-\), and the likely cathode reaction is \(2\mathrm{H}_2\mathrm{O(l)} + 2e^- \rightarrow \mathrm{H}_2(g) + 2\mathrm{OH}^-\). This is because chlorine oxidation and water reduction have more favorable potentials compared to alternative reactions.

Key concepts

Anode Reactions

In the process of electrolysis, an anode reaction is where oxidation occurs. During electrolysis of an aqueous solution of \( \text{MgCl}_2 \), there are typically two possible reactions at the anode. These are the oxidation of chloride ions \( (\text{Cl}^-) \) and the oxidation of water. Both reactions can lead to the loss of electrons (oxidation).

• The chloride ion oxidation can be expressed as \( 2\text{Cl}^- \rightarrow \text{Cl}_2(g) + 2e^- \).
• For water, the oxidation can be represented as \( 2\text{H}_2\text{O(l)} \rightarrow \text{O}_2(g) + 4\text{H}^+(\text{aq}) + 4e^- \).

To decide which reaction will occur at the anode, one must assess their standard reduction potentials and their reactivity. This will help us determine which reaction is thermodynamically more favorable.

Cathode Reactions

Cathode reactions involve reduction, where electrons are gained by a substance. In the context of electrolysis of \( \text{MgCl}_2 \), there are possible cathode reactions to evaluate. These include the reduction of \( \text{Mg}^{2+} \) ions and the reduction of water.

• The reduction of magnesium ions is represented as \( \text{Mg}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Mg(s)} \).
• Water reduction can be shown by the equation \( 2\text{H}_2\text{O(l)} + 2e^- \rightarrow \text{H}_2(g) + 2\text{OH}^-(\text{aq}) \).

The choice of which reaction predominantly occurs at the cathode is guided by comparing the standard reduction potentials of the possible reactions. The one with the more positive or less negative potential is generally more likely to take place.

Standard Reduction Potential

Standard reduction potential refers to the propensity of a chemical species to be reduced, i.e., to gain electrons. This potential is measured in volts (\ \ text{V} ) and is crucial in predicting the direction of electrochemical reactions.

• A more positive standard reduction potential suggests a higher tendency to gain electrons (be reduced).
• A more negative potential suggests the species is less likely to accept electrons.

During the electrolysis of \( \text{MgCl}_2 \), the standard reduction potential for chloride oxidation and water oxidation must be compared:

• Chloride oxidation: \( E^{\circ} = -1.36 \ \ text{V} \)
• Water oxidation: \( E^{\circ} = -1.23 \ \ text{V} \).

Since chloride has a more negative potential, it favors oxidation at the anode. Similarly, at the cathode, water reduction with a potential of \( E^{\circ} = -0.83 \ \ text{V} \) overpowers magnesium ion reduction with \( E^{\circ} = -2.37 \ \ text{V} \).

Aqueous Solutions

An aqueous solution means that a chemical species is dissolved in water as the solvent. In electrolysis, this means that the solute reacts within a water-based medium, influencing the reactions that occur.

• Water can either undergo oxidation at the anode or be reduced at the cathode because it's part of the solution.
• The presence of water allows for additional reactions to occur that may not be possible in non-aqueous solutions.

This is important in electrolyzing \( \text{MgCl}_2 \), as the water present is capable of participating in both anode and cathode reactions, affecting which overall reactions are energetically favorable and thus more likely to occur. This highlights how solute and solvent interactions are key in determining electrolysis outcomes.