For the strong electrolytes NaCl, HCI and NaAc the molar conductivities at infinite dilution are 126.4, 425.9 and $91.0~S~cm^{2} mol^{-1}$ respectively. $\lambda_{m}^{\circ}$ for HAc in $S~cm^{2}mol^{-1}$:

Question

Accepted Answer

To determine the molar conductivity at infinite dilution 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 a weak electrolyte can be calculated by summing the molar conductivities of its constituent ions, which are derived from strong electrolytes.

Given:
- Molar conductivity of NaCl at infinite dilution, $\lambda_{m}^{\circ}(\text{NaCl}) = 126.4~S~cm^{2}mol^{-1}$
- Molar conductivity of HCl at infinite dilution, $\lambda_{m}^{\circ}(\text{HCl}) = 425.9~S~cm^{2}mol^{-1}$
- Molar conductivity of NaAc at infinite dilution, $\lambda_{m}^{\circ}(\text{NaAc}) = 91.0~S~cm^{2}mol^{-1}$

We need to find $\lambda_{m}^{\circ}(\text{HAc})$.

Using Kohlrausch's Law, we can express the molar conductivity of HAc as:
$$
\lambda_{m}^{\circ}(\text{HAc}) = \lambda_{m}^{\circ}(\text{HCl}) + \lambda_{m}^{\circ}(\text{NaAc}) - \lambda_{m}^{\circ}(\text{NaCl})
$$

Substituting the given values:
$$
\lambda_{m}^{\circ}(\text{HAc}) = 425.9 + 91.0 - 126.4
$$

Calculating the above expression:
$$
\lambda_{m}^{\circ}(\text{HAc}) = 425.9 + 91.0 - 126.4 = 390.5~S~cm^{2}mol^{-1}
$$

Thus, the molar conductivity at infinite dilution for acetic acid (HAc) is $390.5~S~cm^{2}mol^{-1}$, which corresponds to Option 3.

**Explanation for Incorrect Options:**

1. **Option 1 (643.3):** This value is significantly higher than the calculated value. It does not align with the principle of adding and subtracting the molar conductivities of the given strong electrolytes.

2. **Option 2 (461.3):** This value is also incorrect as it exceeds the calculated value of 390.5. It suggests an overestimation of the molar conductivity of HAc.

3. **Option 4 (208.5):** This value is much lower than the calculated value. It underestimates the molar conductivity of HAc and does not fit the logical calculation based on the given data.

Therefore, based on the calculations and logical reasoning using Kohlrausch's Law, Option 3 is the correct answer.