Which of the following expressions correctly represents the equivalent conductance at infinite dilution of…

Which of the following expressions correctly represents the equivalent conductance at infinite dilution of $\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$. Given that $\Lambda_{\mathrm{Al}^{3+}}^{\circ}$ and $\Lambda_{\mathrm{SO}_4^{2-}}^{\circ}$ are the equivalent conductances at infinite dilution of the respective ions?
  1. $2 \Lambda_{\mathrm{Al}^{3+}}^{\circ}+3 \mathrm{\Lambda}_{\mathrm{SO}_4^{2-}}^{\circ}$
  2. $\Lambda_{\mathrm{Al}^{3+}}^{\circ}+\Lambda_{\mathrm{SO}_4^{2-}}^{\circ}$
  3. $\left(\Lambda_{\mathrm{Al}^{\circ+}}^{\circ}+3 \Lambda_{\mathrm{SO}_4^{2-}}^{\circ}\right) \times 6$
  4. $\frac{1}{3} \Lambda_{\mathrm{Al}^{3+}}^{\circ}+\frac{1}{2} \Lambda_{\mathrm{SO}_4^{2-}}^{\circ}$

Solution

$\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3 \rightleftharpoons 2 \mathrm{Al}^{3+}+3 \mathrm{SO}_4^{2-}$ Since equivalent conductances are given only for ions, the equivalent conductance at infinite dilution, $\Lambda_{\mathrm{eq}}^{\infty}=\Lambda_{\mathrm{Al}^{3+}}^{\circ}+\Lambda_{\mathrm{SO}_4^{2-}}^{\circ}$

Asked in: NEET 2010 (Mains)

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