$\lambda_{m}^{\circ}$ for NaCl, HCl and NaAc are 126.4, 425.9 and $91.0 S cm^{2}mol^{-1}$ respectively, then $\lambda^{\circ}$ for HAC is :

Question

Accepted Answer

To determine the molar conductivity at infinite dilution, $\lambda^{\circ}$, for acetic acid (HAc), we can use the principle of Kohlrausch's Law of Independent Migration of Ions. According to this law, the molar conductivity at infinite dilution for an electrolyte can be expressed as the sum of the molar conductivities of its constituent ions.

Given:
- $\lambda_{m}^{\circ}$ for NaCl = 126.4 S cm² mol⁻¹
- $\lambda_{m}^{\circ}$ for HCl = 425.9 S cm² mol⁻¹
- $\lambda_{m}^{\circ}$ for NaAc = 91.0 S cm² mol⁻¹

We need to find $\lambda^{\circ}$ for HAc. The equation to find this is:

$$
\lambda^{\circ}(\text{HAc}) = \lambda^{\circ}(\text{HCl}) + \lambda^{\circ}(\text{NaAc}) - \lambda^{\circ}(\text{NaCl})
$$

Substituting the given values:

$$
\lambda^{\circ}(\text{HAc}) = 425.9 + 91.0 - 126.4
$$

Calculating the above expression:

$$
\lambda^{\circ}(\text{HAc}) = 425.9 + 91.0 - 126.4 = 390.5 \, \text{S cm}^2 \text{mol}^{-1}
$$

Thus, the correct answer is Option 3: $390.5 \, \text{S cm}^2 \text{mol}^{-1}$.

**Explanation for Incorrect Options:**

1. **Option 1: $652.3 \, \text{S cm}^2 \text{mol}^{-1}$**
   - This value is significantly higher than the calculated value. It does not align with the principle of independent migration of ions and the given data.

2. **Option 2: $299.5 \, \text{S cm}^2 \text{mol}^{-1}$**
   - This value is lower than the calculated value. It does not match the result obtained from the correct application of Kohlrausch's Law.

3. **Option 4: $217.4 \, \text{S cm}^2 \text{mol}^{-1}$**
   - This value is much lower than the calculated value. It is inconsistent with the calculation based on the given data and the principle of independent migration of ions.

Therefore, based on the calculation and the application of Kohlrausch's Law, Option 3 is the correct answer.