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)?

Short answer

During the electrolysis of an aqueous solution of \(\mathrm{Na_2SO_4}\) (assuming standard conditions), the following reactions occur: Anode (Oxidation): \(\mathrm{OH^- (aq) \rightarrow \frac{1}{2}O_2(g) + H_2O(l) + e^-}\) Cathode (Reduction): \(\mathrm{2H^+ (aq) + 2e^- \rightarrow H_2(g)}\) The oxidation of hydroxide ions (\(\mathrm{OH^-}\)) takes place at the anode, and the reduction of hydrogen ions (\(\mathrm{H^+}\)) occurs at the cathode.

Step-by-step solution

Identify the possible reactions at the anode and the cathode

In the case of an aqueous solution of \(\mathrm{Na_2SO_4}\), there can be several ions present in solution. The principal ions will be: 1. Cations: \(\mathrm{Na^+}\) and \(\mathrm{H^+}\) (from water) 2. Anions: \(\mathrm{SO_4^{2-}}\) and \(\mathrm{OH^-}\) (from water) From these, we can list the possible oxidation reactions at the anode and reduction reactions at the cathode. For Anode (Oxidation): a) \(\mathrm{OH^- (aq) \rightarrow \frac{1}{2}O_2(g) + H_2O(l) + e^-}\); Standard electrode potential = +0.40 V b) \(\mathrm{SO_4^{2-} (aq) \rightarrow SO_2(g) + O_2(g) + 2e^-}\); Unable to give its standard electrode potential due to some limitations For Cathode (Reduction): c) \(\mathrm{2H^+ (aq) + 2e^- \rightarrow H_2(g)}\); Standard electrode potential = 0.00 V d) \(\mathrm{Na^+ (aq) + e^- \rightarrow Na(s)}\); Standard electrode potential = -2.71 V

Determine the favorable reactions at the anode and the cathode

To determine which reaction is favorable at each electrode, we need to compare their standard electrode potentials. For Anode (Oxidation): The \(\mathrm{OH^-}\) has a higher standard electrode potential (+0.40 V) than the reaction involving \(\mathrm{SO_4^{2-}}\), which suggests that the \(\mathrm{OH^-}\) reaction is more likely to occur at the anode. For Cathode (Reduction): The \(\mathrm{H^+}\) reaction has a higher standard electrode potential (0.00 V) than the reaction involving \(\mathrm{Na^+}\) (-2.71 V), which means that the \(\mathrm{H^+}\) reaction is more favorable.

Present the final reactions at the electrodes

Based on our analysis, we can determine the most likely reactions at each electrode during the electrolysis of aqueous \(\mathrm{Na_2SO_4}\): Anode (Oxidation): \(\mathrm{OH^- (aq) \rightarrow \frac{1}{2}O_2(g) + H_2O(l) + e^-}\) Cathode (Reduction): \(\mathrm{2H^+ (aq) + 2e^- \rightarrow H_2(g)}\) So the reactions that occur during the electrolysis of an aqueous solution of \(\mathrm{Na_2SO_4}\) (assuming standard conditions) are the oxidation of hydroxide ions (\(\mathrm{OH^-}\)) at the anode and the reduction of hydrogen ions (\(\mathrm{H^+}\)) at the cathode.

Key concepts

Aqueous Solution

In chemistry, an aqueous solution is a solution where water is the solvent. This term is important because water's polarity allows it to dissolve many substances, enabling various chemical reactions. In the electrolysis of an aqueous solution of \(\mathrm{Na_2SO_4}\), water not only dissolves \(\mathrm{Na_2SO_4}\) into \(\mathrm{Na^+}\) and \(\mathrm{SO_4^{2-}}\) ions, but also contributes \(\mathrm{H^+}\) and \(\mathrm{OH^-}\) ions from water's autoionization.

This results in a mix of different ions in solution, creating the potential for multiple reactions at both the anode and the cathode. Understanding this concept helps us determine which ions are available and can participate in the electrolysis reactions.

Anode and Cathode Reactions

In an electrolysis process, the anode and cathode are the sites where reactions occur. The anode is the positive electrode where oxidation occurs, and the cathode is the negative electrode where reduction takes place.

During the electrolysis of \(\mathrm{Na_2SO_4}\), the anode reaction involves \(\mathrm{OH^-}\) ions losing electrons to form \(\mathrm{O_2}\) gas and water. Simultaneously, at the cathode, \(\mathrm{H^+}\) ions gain electrons to form \(\mathrm{H_2}\) gas. These reactions transform the energy supplied into chemical energy as gas is produced.

• Anode: Oxidation Reaction – \(\mathrm{OH^-}\) → \(\mathrm{\frac{1}{2}O_2(g) + H_2O(l) + e^-}\)
• Cathode: Reduction Reaction – \(\mathrm{2H^+ + 2e^- \rightarrow H_2(g)}\)

Standard Electrode Potential

The standard electrode potential (SEP) is a measure of the tendency of a chemical species to gain or lose electrons, measured in volts. It's essential in predicting the direction of redox reactions. In electrolysis, we use SEP to determine which reactions are more favorable.

In our example, the reaction with \(\mathrm{OH^-}\) at the anode has an SEP of +0.40 V, and the \(\mathrm{H^+}\) at the cathode has 0.00 V. These are more favorable compared to other possibilities, such as \(\mathrm{Na^+}\) reduction, which has a more negative SEP at -2.71 V. Therefore, calculations of electrode potentials help us understand and predict electrolysis behaviors more accurately.

Oxidation and Reduction

Oxidation and reduction are fundamental concepts in chemistry, often remembered by the acronym OIL RIG—Oxidation Is Loss (of electrons), and Reduction Is Gain (of electrons).

In electrolysis, the anode is where oxidation occurs. Here, \(\mathrm{OH^-}\) ions lose electrons. Conversely, at the cathode, reduction takes place as \(\mathrm{H^+}\) ions gain electrons to form hydrogen gas. Recognizing these processes allows us to write balanced equations and understand the energy transformations happening within an electrolytic cell.

Ions in Solution

Ions in solution play a critical role in electrolysis. When salts like \(\mathrm{Na_2SO_4}\) dissolve in water, they dissociate into ions, making the solution conductive. This conductivity is essential because it allows the electrical current to pass through the solution, leading to electrochemical reactions at the electrodes.

Notably, the presence of \(\mathrm{H^+}\), \(\mathrm{OH^-}\), \(\mathrm{Na^+}\), and \(\mathrm{SO_4^{2-}}\) ions from both the salt and the water are crucial in identifying which reactions will occur during electrolysis. Understanding the composition and behavior of ions gives a clearer picture of the electrolysis process, allowing accurate predictions of products formed.