Mixture containing aqueous `Li^+,Na^+ , K^+` ions are electrolysed . Cations are discharged at cathode in the order : (easiest at the end)
`M^(+) (aq) +e^(-) rarrM`

Options

A. `Li^(+),Na^(+),K^(+)`
B. `K^(+),Na^(+),Li^(+)`
C. `Li^(+),K^(+),Na^(+)`
D. `Na^(+),K^(+),Li^(+)`

Answer

To determine the order of discharge of the cations \( \text{Li}^+, \text{Na}^+, \text{K}^+ \) at the cathode during electrolysis, we need to consider their standard reduction potentials (SRP). The cation with the least negative (or most positive) standard reduction potential will be discharged first, while the one with the most negative standard reduction potential will be discharged last.

### Step-by-Step Solution:

1. **Identify the Cations and Their Standard Reduction Potentials:**
- The standard reduction potentials for the cations are as follows:
- \( \text{Li}^+ + e^- \rightarrow \text{Li} \) has a standard reduction potential of approximately \( -3.05 \, \text{V} \).
- \( \text{Na}^+ + e^- \rightarrow \text{Na} \) has a standard reduction potential of approximately \( -2.71 \, \text{V} \).
- \( \text{K}^+ + e^- \rightarrow \text{K} \) has a standard reduction potential of approximately \( -2.93 \, \text{V} \).

2. **Rank the Cations Based on Their Reduction Potentials:**
- The more negative the standard reduction potential, the less likely the ion is to be reduced (discharged) at the cathode. Therefore, we rank them as follows:
- \( \text{Li}^+ \) (most negative, discharged last)
- \( \text{K}^+ \) (intermediate)
- \( \text{Na}^+ \) (least negative, discharged first)

3. **Conclusion on the Order of Discharge:**
- Based on the standard reduction potentials, the order of discharge at the cathode is:
- \( \text{Na}^+ \) (discharged first)
- \( \text{K}^+ \) (discharged second)
- \( \text{Li}^+ \) (discharged last)

### Final Answer:
The cations are discharged at the cathode in the order:
\[ \text{Na}^+ < \text{K}^+ < \text{Li}^+ \]