For a salt XY, which is a strong electrolyte, the plot of $\Lambda_{\mathrm{m}}$ versus $\sqrt{\mathrm{c}}$ has a slope of $-90.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-3 / 2} \mathrm{L}^{1 / 2}$ at 298 K . At 0.01 M concentration of $\mathbf{X Y}$, the value of $\Lambda_{\mathrm{m}}$ is $145.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The limiting molar conductivity of $\mathbf{Y}^{-}$ion $\left(\lambda_{\mathbf{Y}^{-}}^0\right.$, in $\left.\mathrm{S} \mathrm{cm}^2 \mathrm{~mol}^{-1}\right)$ at 298 K will be (Given : $\lambda_{\mathrm{X}^{+}}^0=74.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ )

Question

Accepted Answer

B. 1. **Concept**: For a strong electrolyte, the Debye-Hückel-Onsager equation describes how molar conductivity varies with concentration:
$$
\Lambda_{\mathrm{m}} = \Lambda_{\mathrm{m}}^{\circ} - A\sqrt{c}
$$
where $\Lambda_{\mathrm{m}}^{\circ}$ is the limiting molar conductivity and $A$ is the given slope (with a negative sign already built into the equation).

2. **Finding** $\sqrt{c}$: since $c = 0.01\ \mathrm{M}$,
$$
\sqrt{c} = \sqrt{0.01} = 0.1
$$

3. **Substituting the known values** $\Lambda_{\mathrm{m}} = 145.0$ and slope $= -90.0$:
$$
145.0 = \Lambda_{\mathrm{m}}^{\circ} - 90.0 	imes 0.1
$$
$$
\Lambda_{\mathrm{m}}^{\circ} = 145.0 + 9.0 = 154.0\ \mathrm{S\ cm^2\ mol^{-1}}
$$

4. **Using Kohlrausch's law of independent migration of ions**: the limiting molar conductivity of a salt is the sum of the limiting ionic conductivities of its ions.
$$
\lambda_{\mathrm{m(XY)}}^{\circ} = \lambda_{\mathrm{X}^{+}}^{\circ} + \lambda_{\mathrm{Y}^{-}}^{\circ}
$$
$$
154.0 = 74.0 + \lambda_{\mathrm{Y}^{-}}^{\circ}
$$
$$
\lambda_{\mathrm{Y}^{-}}^{\circ} = 80.0\ \mathrm{S\ cm^2\ mol^{-1}}
$$

**Hence, the answer is Option B: 80.0.**