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Explanation:
Let P be the initial pressure of AB2
The equilibrium pressures of AB2, AB and B2 are P(1−x), xP and 0.5xP respectively.
The equilibrium constant expression is
Kp=PAB22PAB2 PB2
Kp=[P(1−x)]2[xP]2×0.5xP
Kp=P[(1−x)]20.5x3
Since the degree of dissociation is small compared to 1,1−x can be approximated to 1.
Kp=P×0.5x3 .... (1)
The total pressure is
P(1−x)+Px+0.5Px=P(1+0.5x)=p
P=1+0.5xp.....(2)
Substitute (2) in (1),
Kp=1+0.5xp×0.5x3
Since the degree of dissociation is small compared to 1,1+0.5x can be approximated to 1.
Kp=p×0.5x3
x=(2Kp/p)1/3
Hence, the expression relating the degree of dissociation (x) with equilibrium constant Kp and total pressure p is x=(2Kp/p)1/3
HOPE IT HELPS YOU...........
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