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)?

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

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.

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.