The equilibrium constants Kp1 and Kp2 for the reactions X⇌2Y and Z⇌P+Q, respectively are in the ratio of 1:9. If degree of dissociation of X and Z be equal then the ratio if total pressures at these equlibria is
A
1:9
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B
1:36
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C
1:1
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D
1:3
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Solution
The correct option is B1:36 X⇌2Y,Z⇌P+Q Initial moles10100 at equilibrium1−α2α1−ααα Kp1=P2YPX=(2α1+αP1)2(1−α1+αP1) Kp2=PPPQPZ=(α1+αP2)(α1+αP2)1−α1+αP2)...(i) ⇒KP1=4α2P11−α2...(ii)
Given, KP1KP2=19...(iii)
Substituting values from equation (i) and (ii) into (iii), we get 4α2P11−α2α2P21−α2=19 ⇒4P1P2=19 ⇒P1P2=136