Question

In the electrolysis of an aqueous solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4},\) what reactions occur at the anode and the cathode (assuming standard conditions)? $$\begin{array}{lr} \mathrm{S}_{2} \mathrm{O}_{8}^{2-}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{SO}_{4}^{2-} & 80^{\circ} \\ \mathrm{O}_{2}+4 \mathrm{H}^{+}+4 \mathrm{e}^{-} \longrightarrow_{2 \mathrm{H}_{2} \mathrm{O}} & 2.01 \mathrm{V} \\ 2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}+2 \mathrm{OH}^{-} & -0.83 \mathrm{V} \\ \mathrm{Na}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Na} & -2.71 \mathrm{V} \end{array}$$

Short answer

In the electrolysis of an aqueous solution of Na2SO4, the following reactions occur under standard conditions: At the anode (oxidation): \(2SO_4^{2-} \longrightarrow S_2O_8^{2-} + 2e^-\) At the cathode (reduction): \(2H_2O + 2e^- \longrightarrow H_2 + 2OH^-\)

Step-by-step solution

1. Identify the possible reactions at the anode and cathode

: First, we need to identify the possible reactions at the anode and the cathode. When Na2SO4 dissociates in water, it forms Na+ and SO4(2-) ions. At the anode, oxidation reactions occur, which involves the loss of electrons. At the cathode, reduction reactions take place, where electrons are gained. The possible anode reactions are the processes that involve the production of electrons. These reactions are: a) \(S_2O_8^{2-} + 2e^- \longrightarrow 2SO_4^{2-}\) b) \(O_2 + 4H^+ + 4e^- \longrightarrow 2H_2O\) The possible cathode reactions are: c) \(2H_2O + 2e^- \longrightarrow H_2 + 2OH^-\) d) \(Na^+ + e^- \longrightarrow Na\)

2. Determine which reactions will occur based on their reduction potentials

: We will use the reduction potential values given to determine which reactions are most likely to occur at the anode and the cathode. For the anode reaction, we should look for the process with lower reduction potential, since it will be reversed (oxidation). Comparing the values from reactions (a) and (b): a) 0 V (assuming standard conditions) b) 2.01 V Reaction (a) has a lower reduction potential, so it is more likely to occur at the anode after reversing: \(2SO_4^{2-} \longrightarrow S_2O_8^{2-} + 2e^-\) For the cathode reaction, we should look for the process with the higher reduction potential, as it will be more likely to occur. Comparing the values from reactions (c) and (d): c) -0.83 V d) -2.71 V Reaction (c) has a higher reduction potential, so it is more likely to occur at the cathode: \(2H_2O + 2e^- \longrightarrow H_2 + 2OH^-\)

3. Write the final answer

: After analyzing the reduction potentials, we can determine the reactions that are most likely to occur at the anode and the cathode for the electrolysis of the aqueous Na2SO4 solution. At the anode (oxidation): \(2SO_4^{2-} \longrightarrow S_2O_8^{2-} + 2e^-\) At the cathode (reduction): \(2H_2O + 2e^- \longrightarrow H_2 + 2OH^-\)

Key concepts

Anode and Cathode Reactions

Understanding anode and cathode reactions is vital when studying electrolysis reactions. These are the sites where oxidation and reduction occur, respectively.

During electrolysis of an aqueous solution, such as Na_2SO_4, at the anode, which is positively charged, we would typically see the loss of electrons – an oxidation process. This can be seen in the likely production of S_2O_8^{2-} from SO_4^{2-} ions by giving off two electrons.

At the cathode, the negatively charged component, reduction takes place, involving the gain of electrons. In our example, water molecules gain electrons to form hydrogen gas (H_2) and hydroxide ions (OH^-).

Significance in Electrolysis

The correct identification of these reactions is essential in predicting the products of electrolysis and understanding the overall chemical changes in the system.

Standard Reduction Potentials

Standard reduction potentials are utilized to predict the outcome of reactions in electrolytic processes. These values, measured under standard conditions (298 K, 1 atm pressure, and 1 M concentrations), provide insight into the likelihood of a substance to gain electrons – the more positive the number, the greater this tendency.

By considering the reduction potentials given, as in our exercise with Na_2SO_4 electrolysis, chemists can forecast which reactions are feasible. The higher reduction potential for the conversion of water to hydrogen gas and hydroxide ions (-0.83 V) over the reduction of sodium ions (-2.71 V) suggests the former is the preferred reaction at the cathode under standard conditions.

Oxidation and Reduction Processes

Oxidation and reduction processes are two halves of the redox reaction puzzle that characterizes electrolysis. Oxidation involves losing electrons, while reduction refers to gaining electrons.

The distinction is crucial as it determines the direction in which the reactions proceed at the anode and cathode. In our electrolysis example, the SO_4^{2-} ions undergo oxidation at the anode, releasing electrons, and water molecules receive electrons during reduction at the cathode, completing the redox cycle.

Redox in Daily Life

Recognizing these processes aids students in understanding not only laboratory electrolysis but also in appreciating the redox reactions that occur in batteries and biological systems.

Aqueous Solution Electrolysis

Electrolysis in aqueous solutions involves the movement of ions in a water-based environment under the influence of an electrical current. The ions originate from solutes, like in the given exercise where Na_2SO_4 dissociates into Na^+ and SO_4^{2-}.

Water itself can also split into H^+ and OH^- ions, and this is crucial because electrolysis in aqueous solutions often involves water as a key reactant or product. The preference for certain reactions in aqueous electrolysis is influenced not just by the potential of the solute ions but also the ions of water itself, as demonstrated by the favored production of H_2 and OH^- at the cathode in our example.