At $25^\circ ext{C}$, molar conductance of $0.1 ext{ molar}$ aqueous solution of ammonium hydroxide is $9.5

Question

At $25^\circ	ext{C}$, molar conductance of $0.1 	ext{ molar}$ aqueous solution of ammonium hydroxide is $9.54 	ext{ ohm}^{-1}	ext{cm}^2	ext{mol}^{-1}$ and at infinite dilution, its molar conductance is $238 	ext{ ohm}^{-1}	ext{cm}^2 	ext{mol}^{-1}$. The degree of ionization of ammonium hydroxide at the same concentration and temperature is:

Accepted Answer

The degree of ionization ($\alpha$) of a weak electrolyte is the ratio of its molar conductance at a given concentration ($\Lambda_m^c$) to its molar conductance at infinite dilution ($\Lambda_m^\circ$).
$\alpha = \frac{\Lambda_m^c}{\Lambda_m^\circ}$
Given:
Molar conductance at given concentration, $\Lambda_m^c = 9.54 	ext{ ohm}^{-1}	ext{cm}^2	ext{mol}^{-1}$
Molar conductance at infinite dilution, $\Lambda_m^\circ = 238 	ext{ ohm}^{-1}	ext{cm}^2	ext{mol}^{-1}$
$\alpha = \frac{9.54}{238} = 0.04008$
Percentage degree of ionization = $\alpha 	imes 100 = 0.04008 	imes 100 = 4.008\%$.

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