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At 25C25^{\circ} \text{C} molar conductance of 0.1 molar0.1 \text{ molar} aqueous solution of ammonium hydroxide is 9.54 ohm1cm2mol19.54 \text{ ohm}^{-1} \text{cm}^2 \text{mol}^{-1} and at infinite dilution its molar conductance is 238 ohm1cm2mol1238 \text{ ohm}^{-1} \text{cm}^2 \text{mol}^{-1}. The degree of ionisation of ammonium hydroxide at the same concentration and temperature is

A

2.080%2.080\%

B

20.800%20.800\%

C

4.008%4.008\%

D

40.800%40.800\%

Step-by-Step Solution

The degree of dissociation (α\alpha) of a weak electrolyte is the ratio of its molar conductivity at a given concentration (Λmc\Lambda_m^c) to its limiting molar conductivity at infinite dilution (Λm\Lambda_m^\infty).

Given: Molar conductance at concentration cc, Λmc=9.54 ohm1 cm2 mol1\Lambda_m^c = 9.54 \text{ ohm}^{-1} \text{ cm}^2 \text{ mol}^{-1} Molar conductance at infinite dilution, Λm=238 ohm1 cm2 mol1\Lambda_m^\infty = 238 \text{ ohm}^{-1} \text{ cm}^2 \text{ mol}^{-1}

Degree of dissociation (α\alpha) =ΛmcΛm= \frac{\Lambda_m^c}{\Lambda_m^\infty} α=9.54238=0.04008\alpha = \frac{9.54}{238} = 0.04008

To find the percentage degree of ionisation: α%=0.04008×100%=4.008%\alpha \% = 0.04008 \times 100\% = 4.008\%

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