For a salt XY , which is a strong electrolyte, the plot of _m...

According to the Debye-Huckel-Onsager equation for strong electrolytes:

$\Lambda_m = \Lambda_m^0 - A\sqrt{c}$

The slope of the plot of $\Lambda_m$ versus $\sqrt{c}$ is $-A$.

Given slope $= -90.0$, we have $A = 90.0$.

At $c = 0.01$ M, $\sqrt{c} = 0.1$ M$^{1/2}$.

Substituting the given values into the equation:

$145.0 = \Lambda_m^0 - 90.0 \times 0.1$

$145.0 = \Lambda_m^0 - 9.0$

$\Lambda_m^0 = 154.0$ S cm$^2$ mol$^{-1}$

According to Kohlrausch's law of independent migration of ions:

$\Lambda_m^0(\text{XY}) = \lambda^0_{\text{X}^+} + \lambda^0_{\text{Y}^-}$

$154.0 = 74.0 + \lambda^0_{\text{Y}^-}$

$\lambda^0_{\text{Y}^-} = 154.0 - 74.0 = 80.0$ S cm$^2$ mol$^{-1}$

Answer: $80.0$