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At $25^{\circ} \mathrm{C}$ molar conductance of 0.1 molar aqueous solution of ammonium hydroxide is $9.54 \mathrm{ohm}^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and at infinite dilution its molar conductance is $238 \mathrm{ohm}^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The degree of ionisation of ammonium hydroxide at the same concentration and temperature is
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$4.008 \%$
Given, molar conductance at $0.1 \mathrm{M}$ concentration,
$\lambda_c=9.54 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$
Molar conductance at infinite dilution,
$\lambda_c^{\infty}=238 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$
We know that, degree of ionisation,
$\begin{aligned} \alpha & =\frac{\lambda_c}{\lambda_c^{\infty}} \times 100 \\ & =\frac{9.54}{238} \times 100=4.008 \%\end{aligned}$
$\lambda_c=9.54 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$
Molar conductance at infinite dilution,
$\lambda_c^{\infty}=238 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$
We know that, degree of ionisation,
$\begin{aligned} \alpha & =\frac{\lambda_c}{\lambda_c^{\infty}} \times 100 \\ & =\frac{9.54}{238} \times 100=4.008 \%\end{aligned}$
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