Aqueous copper sulphate solution is electrolyzed using platinum electrodes. The electrode reaction occurring at cathode is: (a) \(\mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(\mathrm{s})\) (b) \(\mathrm{Cu}(\mathrm{s}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-}\) (c) \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}(\mathrm{aq})+4 \mathrm{e}^{-}\) (d) \(\mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}(\mathrm{aq})+4 \mathrm{e} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)\)

Understanding the cathode reduction reaction is crucial when studying electrolysis in chemistry. During electrolysis of a copper sulphate solution, the cathode serves as the site where copper ions (\text{Cu}^{2+}) in the solution are reduced.

Reduction refers to the gain of electrons in a chemical reaction. At the cathode, the reduction half-reaction is essentially a process where the positively charged copper ions accept two electrons each to become neutral copper atoms. This can be represented by the chemical equation: \[ \text{Cu}^{2+}(\text{aq}) + 2 \text{e}^{-} \rightarrow \text{Cu}(\text{s}) \].

This process is also an example of a redox reaction, where reduction and oxidation occur simultaneously. A common sign that reduction has occurred at the cathode is the formation of solid metal debris or plating on the cathode, which in this case, is solid copper metal.

Electrolytic cell reactions are the reactions that occur in an electrolytic cell, which is used to bring about a chemical change through the application of electrical energy. An electrolytic cell set-up includes two electrodes: the cathode (negative electrode) and the anode (positive electrode), and an electrolyte such as copper sulphate solution (\text{CuSO}_4).

During electrolysis, two key reactions occur: the reduction at the cathode, as already described, and the oxidation at the anode. In the example of the copper sulphate solution, water molecules (\text{H}_2\text{O}) are usually oxidized at the anode, leading to the release of oxygen gas (\text{O}_2) and protons (\text{H}^+), which can be represented by: \[ 2 \text{H}_2\text{O}(\text{l}) \rightarrow \text{O}_2(\text{g}) + 4 \text{H}^+(\text{aq}) + 4 \text{e}^- \].

It's important to note that the specific reactions at the electrodes depend on the electrolyte used and the type of electrodes. Also, the electrode material plays a crucial role; for instance, inert electrodes like platinum do not participate in the reaction themselves but provide a surface for the reactions to occur.

Reduction and oxidation processes, commonly known as redox reactions, are fundamental concepts in chemistry where one substance gains electrons (reduction) and another loses electrons (oxidation).

In the context of electrolysis in copper sulphate solution, the copper ion's reduction at the cathode is matched by water's oxidation at the anode. Oxidation at the anode usually competes with the oxidation of the metal cations if present, but in the case of a high concentration of copper sulphate, copper ions are preferentially reduced. Furthermore, the electrons lost in the anode reaction are the same electrons gained by the copper cations at the cathode.

This simultaneous transfer of electrons keeps the electrical circuit complete and allows the electrolytic process to continue. The overall electrolytic reaction in the copper sulphate solution demonstrates the interdependent nature of reduction and oxidation reactions, which must always occur together, maintaining the principle of conservation of charge.