JEE Advance - Chemistry (1994 - No. 9)
A 4 : 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out initially?
4 : 1
1 : 4
8 : 1
1 : 8
2 : 1
Explanation
Partial pressure of a gas in a mixture = Mole fraction of gas $$\times$$ Total pressure
$$\therefore$$ $${P_{He}} = {X_{He}} \times P = {4 \over 5} \times 20 = 16$$ bar
$${P_{C{H_4}}} = {X_{C{H_4}}} \times P = {1 \over 5} \times 20 = 4$$ bar
$${r_{He}} = {{k\,.\,{P_{He}}} \over {\sqrt {{M_{He}}} }} = {{k\,.\,16} \over {\sqrt 4 }} = 8k$$
$${r_{C{H_4}}} = {{k\,.\,{P_{C{H_4}}}} \over {\sqrt {{M_{C{H_4}}}} }} = {{k \times 4} \over {\sqrt {16} }} = k$$
$$\therefore$$ Composition of the mixture (He : CH4) effusion out = 8k : k = 8 : 1.
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