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Question

At 1200C, the following equilibrium is established between chlorine atoms and molecule:

Cl2(g)2Cl(g)
The composition of the equilibrium mixture may be determined by measuring the rate of effusion of the mixture through a pin hole. It is found that at 1200C and 1 atm pressure the mixture effuses 1.16 times as fast as krypton effuses under the same condition. The equilibrium constant Kc is:

A
6.71×104
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B
6.92×104
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C
7.71×104
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D
7.34×104
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Solution

The correct option is B 6.71×104
The rate of effusion is inversely proportional to the molecular weight.
The molecular weight of krypton is 83.8.
1.161=83.8M
M=62.27
Thus, the average molecular weight of the mixture of Cl2 and Cl is 62.27.
Let x be the mole fraction of Cl2. The mole fraction of Cl will be 1x.
Hence, 71x+35.5(1x)=62.27
x=0.754
The mole fractions of Cl2 and Cl are 0.754 and 0.246 respectively. They are also equal to the partial pressures as total pressure is 1 atm.
Kp=PCl2PCl2=0.24620.754=0.08
As Δn=1, KP=Kc(RT)
Thus, 0.08=Kc(0.082×1473)
Kc=6.71×104

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