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For a salt XY, which is a strong electrolyte, the plot of $\Lambda_m$ versus $\sqrt{c}$ has a slope of -90.0 S cm$^2$ mol$^{-3/2}$ L$^{1/2}$ at 298 K. At 0.01 M concentration of XY, the value of $\Lambda_m$ is 145.0 S cm$^2$ mol$^{-1}$. The limiting molar conductivity of $Y^-$ ion ($\lambda^0_{Y^-}$, in S cm$^2$ mol$^{-1}$) at 298 K will be (Given: $\lambda^0_{X^+}=74.0$ S cm$^2$ mol$^{-1}$)
Detailed Solution
Debye-Huckel-Onsager equation: $\Lambda_m=\Lambda_m^0-A\sqrt{c}$. The slope of $\Lambda_m$ vs $\sqrt{c}$ is $-A=-90$, so A = 90. At c = 0.01 M: $145=\Lambda_m^0-90\times\sqrt{10^{-2}}=\Lambda_m^0-9 \Rightarrow \Lambda_m^0=154$ S cm$^2$ mol$^{-1}$. $\Lambda_m^0(XY)=\lambda^0(X^+)+\lambda^0(Y^-) \Rightarrow \lambda^0(Y^-)=154-74=80$ S cm$^2$ mol$^{-1}$.