Which has maximum vlaue of `A_(eq)` at constant temperature assuming 100% ionisation of each electrolyte?

Options

A. 0.1M HCl
B. 0.1M NaCl
C. 0.1 M KCl
D. Equal

Answer

To determine which electrolyte has the maximum value of equivalent conductivity (\(A_{eq}\)) at constant temperature, assuming 100% ionization of each electrolyte, we can follow these steps:

### Step 1: Understand the Formula for Equivalent Conductivity
The equivalent conductivity (\(A_{eq}\)) is given by the formula:
\[ A_{eq} = \frac{\kappa}{N} \times 1000 \]
where \(\kappa\) is the conductivity and \(N\) is the normality of the solution.

### Step 2: Identify Factors Affecting Equivalent Conductivity
The equivalent conductivity depends on:
1. Concentration of the electrolyte
2. Temperature (constant in this case)
3. Nature of the electrolyte (strong vs. weak)
4. Mobility of the ions

### Step 3: Analyze the Given Electrolytes
We are given three electrolytes:
- 0.1 M HCl
- 0.1 M NaCl
- 0.1 M KCl

Since the concentration and temperature are constant, we need to focus on the nature of the electrolytes and the mobility of the ions.

### Step 4: Determine Ion Mobilities
The ions in the solutions are:
- HCl: H\(^+\) and Cl\(^-\)
- NaCl: Na\(^+\) and Cl\(^-\)
- KCl: K\(^+\) and Cl\(^-\)

Among these ions, the mobility of H\(^+\) is significantly higher than that of Na\(^+\) and K\(^+\). The order of mobility is:
\[ \text{H}^+ > \text{Na}^+ > \text{K}^+ \]
The anion Cl\(^-\) has the same mobility in all three solutions.

### Step 5: Conclusion on Equivalent Conductivity
Since HCl has the highest mobility due to the presence of H\(^+\), it will have the highest equivalent conductivity among the three electrolytes. Therefore, the electrolyte with the maximum value of \(A_{eq}\) is:
\[ \text{0.1 M HCl} \]

### Final Answer
The electrolyte with the maximum value of equivalent conductivity at constant temperature, assuming 100% ionization, is **0.1 M HCl**.

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