For a strong electrolyte, the molar conductivity $\Lambda_{m}$ is related to the concentration $c$ by the equation: $$ \Lambda_{m} = \Lambda_{m}^{0} - A\sqrt{c} $$ where $\Lambda_{m}^{0}$ is the limiting molar conductivity and $A$ is the slope of the plot.
Given: $\Lambda_{m} = 145.0$, $A = 90.0$ (magnitude of slope), and $c = 0.01$ M. $$ 145.0 = \Lambda_{m}^{0} - 90.0 \times \sqrt{0.01} $$ $$ 145.0 = \Lambda_{m}^{0} - 90.0 \times 0.1 $$ $$ 145.0 = \Lambda_{m}^{0} - 9.0 $$ $$ \Lambda_{m}^{0} = 145.0 + 9.0 = 154.0 \, S \, cm^{2} mol^{-1} $$
According to Kohlrausch Law of independent migration of ions: $$ \Lambda_{m}^{0} = \lambda_{X^{+}}^{0} + \lambda_{Y^{-}}^{0} $$ Given $\lambda_{X^{+}}^{0} = 74.0$, we solve for $\lambda_{Y^{-}}^{0}$: $$ 154.0 = 74.0 + \lambda_{Y^{-}}^{0} $$ $$ \lambda_{Y^{-}}^{0} = 154.0 - 74.0 = 80.0 \, S \, cm^{2} mol^{-1} $$
Final Answer: 80
AI generated content. Review strictly for academic accuracy.