Equilibrium Question 856

Question: In the dissociation of $ PCl_5 $ as $ PCl_5(g)\rightarrow PCl_3(g)+Cl_2(g) $ if the degree of dissociation is a at equilibrium pressure P, then the equilibrium constant for the reaction is

Options:

A) $ K_{P}=\frac{{{\alpha }^{2}}}{1+{{\alpha }^{2}}P} $

B) $ K_{P}=\frac{{{\alpha }^{2}}P^{2}}{1-{{\alpha }^{2}}} $

C) $ K_{P}=\frac{P^{2}}{1-{{\alpha }^{2}}} $

D) $ K_{P}=\frac{{{\alpha }^{2}}P}{1-{{\alpha }^{2}}} $

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Answer:

Correct Answer: D

Solution:

Total mole $ =1-\alpha +\alpha +\alpha =1+\alpha $

$ K_{p}=\frac{\frac{\alpha }{1+\alpha }P.\frac{\alpha }{1+\alpha }.P}{\frac{1-\alpha }{1+\alpha }P}=\frac{{{\alpha }^{2}}P}{1-{{\alpha }^{2}}} $



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