Given the ionic conductance of \(\begin{aligned} & \mathrm{COO}^- \\ & | \\ & \mathrm{COO}^{-}…

Given the ionic conductance of \(\begin{aligned} & \mathrm{COO}^- \\ & | \\ & \mathrm{COO}^{-} \end{aligned}\) \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) are 74,50 , and \(73 \mathrm{~cm}^{2} \mathrm{ohm}^{-1} \mathrm{eq}^{-1}\), respectively. The equivalent conductance at infinite dilution of the salt \(\begin{aligned} & \text {COONa } \\ & | \\ & \text {COOK } \end{aligned}\) is
  1. $197 \mathrm{~cm}^{2} \mathrm{ohm}^{-1} \mathrm{eq}^{-1}$
  2. $172 \mathrm{~cm}^{2} \mathrm{ohm}^{-1} \mathrm{eq}^{-1}$
  3. $135.5 \mathrm{~cm}^{2} \mathrm{ohm}^{-1} \mathrm{eq}^{-1}$
  4. $160.5 \mathrm{~cm}^{2} \mathrm{ohm}^{-1} \mathrm{eq}^{-1}$

Solution

Total charge $=2$ Number of equivalent of ion
$=\frac{\text { Charge on the ion }}{\text { Total charge }}$
$\therefore$ Eq of $\left(\begin{array}{l}\mathrm{COO}^{-} \\ \mathrm{COO}^{-}\end{array}ight)=\frac{2}{2}=1$
Eq of $\mathrm{Na}^{+}=\frac{1}{2}$, Eq of $\mathrm{K}^{+}=\frac{1}{2}$
$\therefore \lambda_{\mathrm{eq}}^{\circ}\left(\begin{array}{l}\mathrm{COONa} \\ \mathrm{COOK}\end{array}ight)$
$=\lambda_{\mathrm{eq}}^{\circ}\left(\begin{array}{l}\mathrm{COO}^{-} \\ \mathrm{COO}^{-}\end{array}ight)+\frac{1}{2} \lambda^{\circ} \mathrm{Na}^{+}+\frac{1}{2} \lambda^{\circ} \mathrm{K}^{+}$
$=74+\frac{50}{2}+\frac{73}{2}=135.5 \mathrm{ohm}^{-1} \mathrm{~cm}^{2} \mathrm{eq}^{-1}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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