A solution of sodium sulphate in water is electrolyzed using inert electrodes. The products at the cathode and anode are respectively: (a) \(\mathrm{O}_{2}, \mathrm{H}_{2}\) (b) \(\mathrm{O}_{2}, \mathrm{Na}\) (c) \(\mathrm{O}_{2}, \mathrm{SO}_{2}\) (d) \(\mathrm{H}_{2}, \mathrm{O}_{2}\)

Understanding the cathode and anode reactions is crucial when studying electrolysis. At the cathode, reduction occurs—meaning electrons are gained. For aqueous solutions containing sodium sulphate, the reduction of water takes place over the reduction of sodium ions. This is because water has a higher tendency to gain electrons compared to sodium ions in an electrolytic cell. The reaction can be represented as follows:
At the cathode:
\[\begin{equation}2H_{2}O(l) + 2e^{-} \rightarrow H_{2}(g) + 2OH^{-}(aq)\tag{1}\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\end{equation}\]\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br At the anode, oxidation takes place—meaning electrons are lost. Given that sulphate ions are stable and resistant to oxidation, water molecules are more likely to be oxidized, leading to the production of oxygen gas. The reaction at the anode is: At the anode: \[\begin{equation}\tag{2}2H_{2}O(l) - 4e^{-} \rightarrow O_{2}(g) + 4H^+{aq}\end{equation}\] Through these reactions, we see the electrolysis process in sodium sulphate solution preferring hydrogen and oxygen gas formation, respectively at the cathode and anode.

Electrode potentials play a pivotal role in determining the direction and extent of the chemical reactions occurring during electrolysis. These potentials are a measure of the ability of a substance to gain or lose electrons—hence to undergo reduction or oxidation. In the context of sodium sulphate electrolysis, we must look at the standard electrode potentials of water and sodium to predict the reactions at the electrodes.
Water has a standard reduction potential of approximately \(-0.83\) V for the reaction where it forms hydrogen gas, whereas sodium's potential is more negative at about \(-2.71\) V. This implies that, under standard conditions, water is more likely to be reduced than sodium. Similarly, the oxidation potential for water to turn into oxygen gas is \(+1.23\) V, while sulphate ions do not oxidize under standard conditions or require a significantly higher potential than water. Thus, electrode potential information confirms that during electrolysis of an aqueous sodium sulphate solution, hydrogen and oxygen gases are preferentially produced over sodium metal or sulphur dioxide.

Electrolysis in an aqueous solution like sodium sulphate involves the movement of ions towards electrodes, where they undergo chemical reactions. Understanding which species, cations or anions, will be involved in electrolysis reactions is determined by factors such as their oxidation states, concentration, and the electrode potentials.
To reinforce learning and ensure comprehension, it is important to grasp that though sodium ions and sulphate ions are present in the solution, the preferential reactions involve the reduction of water at the cathode and the oxidation of water at the anode. This preference is due to the intrinsic stability of water's oxidised and reduced forms compared to those of the dissolved salt.
The overall reaction for the electrolysis of sodium sulphate can be summarized as:\[\begin{equation} \tag{3} 2H_{2}O(l) \rightarrow 2H_{2}(g) + O_{2}(g) \br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\br\end{equation}\] This reaction demonstrates the fundamental understanding of electrolysis in an aqueous sodium sulphate solution and highlights the resulting products being hydrogen and oxygen gases.