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JEE MAIN 2025
04-04-2025 S2
Question
The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and $70 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is $85.5 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$, its degree of dissociation is given by $x \times 10^{-1}$. The value of $x$ is $\_\_\_\_$ (Nearest integer)
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Solution
$\begin{aligned} & \lambda_{\mathrm{m}}^{\circ} \text { of } \mathrm{NH}_4 \mathrm{Cl}=185 \\ & \left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4^{+}}+\left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{Cl}^{-}}=185 \\ & \left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4^{+}}=185-70=115 \mathrm{Scm}^2 \mathrm{~mol}^{-1} \\ & \left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4 \mathrm{OH}}=\left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4^{+}}+\left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{OH}^{-}}=115+170 \\ & \left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4 \mathrm{OH}}=285 \mathrm{Scm}^2 \mathrm{~mol}^{-1} \\ & \text { degree of dissociation }=\frac{\left(\lambda_{\mathrm{m}}\right)_{\mathrm{NH}_4 \mathrm{OH}}}{\left(\lambda_{\mathrm{m}}^{\circ}\right)_{\mathrm{NH}_4 \mathrm{OH}}} \\ & =\frac{85.5}{285} \\ & =0.3 \\ & =3 \times 10^{-1}\end{aligned}$
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