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Question

The equilibrium constants Kp1 and Kp2 for the reactions A2B and PQ+R, respectively, are in the ratio of 2 : 3. If the degree of dissociation of A and P are equal, the ratio of the total pressure at equilibrium is:

A
1:36
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B
1:9
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C
1:6
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D
1:4
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Solution

The correct option is B 1:6
A11α2B02α
Total moles =1α+2α=1+α
PA= (mole fraction of A)× Initial pressure =(1α1+α)P1
Similarly PB=(2α1+α)P
Kp1=(PB)2(PA)=2α1+αP121α1+αP1=4α2P1(1α2)
P11αQ0α+R0α
Total moles =1α+α+α=1+α
PP=(1α1+α)P2;PQ=(α1+α)P2;PR=(α1+α)P2
KP2=PR×PQPP=(α1+α)P2×(α1+α)P2(1α1+α)P2=α2P2(1α2)
KP1KP2=23(given)=4α2P1(1α2)×(1a2α2P2)=4P1P2
P1P2=16

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