Question

\(\mathrm{K}^{+}\)and \(\mathrm{H}^{+}\)ions are present in an electrolyte. Which would get discharged at cathode? Why?

Short answer

Answer: The ion that will be discharged at the cathode is the potassium ion, \(\mathrm{K}^{+}\), as it has a lower reduction potential compared to the hydrogen ion, \(\mathrm{H}^{+}\). The lower reduction potential means that \(\mathrm{K}^{+}\) has a higher tendency to be reduced (gain electrons) than \(\mathrm{H}^{+}\) at the cathode.

Step-by-step solution

Understand the basic principles of electrolysis

During the process of electrolysis, a direct current flows through an ionic compound in a molten or aqueous state. The positively charged ions (cations) are attracted to the negatively charged electrode (cathode), leading to their discharge at the cathode through reduction reactions.

Identify the electrode potentials of \(\mathrm{K}^{+}\) and \(\mathrm{H}^{+}\) ions

To determine which ion is more likely to undergo reduction and be discharged at the cathode, we need to compare the standard electrode potentials of these ions. Standard electrode potentials are the potentials of their half-cell reactions under standard conditions. The standard reduction potentials (E°) of the two ions are: - \(\mathrm{K}^{+}\): \(\mathrm{K}^{+} + \mathrm{e}^{-} \rightarrow \mathrm{K}\) (E° = -2.93 V) - \(\mathrm{H}^{+}\): \(2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{H}_{2}\) (E° = 0.00 V)

Compare the electrode potentials and determine the ion to be discharged at the cathode

During the process of electrolysis, the ion with a lower reduction potential will be discharged at the cathode, as it is more likely to undergo reduction. Comparing the reduction potentials of \(\mathrm{K}^{+}\) (-2.93 V) and \(\mathrm{H}^{+}\) (0.00 V), we find that the reduction potential of \(\mathrm{K}^{+}\) is lower.

Explain the reason for the ion being discharged at the cathode

Since \(\mathrm{K}^{+}\) has a lower reduction potential, it is more likely to undergo reduction and be discharged at the cathode compared to \(\mathrm{H}^{+}\). The reason for this is that the reduction potential of an ion describes its tendency to get reduced (gain electrons). The lower the reduction potential, the higher the tendency of the ion to be reduced. In this case, \(\mathrm{K}^{+}\) has a higher tendency to be reduced than \(\mathrm{H}^{+}\), so it would get discharged at the cathode. Thus, the ion that will be discharged at the cathode is the potassium ion, \(\mathrm{K}^{+}\).