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NCERT Class XI Chemistry Equilibrium Solutions

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Question : 30 of 73
Marks: +1, -0
At 473 K, equilibrium constant KcK_c for decomposition of phosphorus pentachloride, PCl5\mathrm{PCl}_5 is 8.3 × 10−310^{-3}. If decomposition is depicted as :
PCl5(g)\mathrm{PCl}_{5(\mathrm{g})} ⇌ PCl3(g)+Cl2(g)\mathrm{PCl}_{3(\mathrm{g})} + \mathrm{Cl}_{2(\mathrm{g})} ; ΔrH∘\Delta_r H^\circ = 124.0 kJ mol−1\mathrm{kJ}\,\mathrm{mol}^{-1}
(a) Write an expression for Kc for the reaction.
(b) What is the value of Kc for the reverse reaction at the same temperature?
(c) What would be the effect on KcK_c if
(i) more PCl5\mathrm{PCl}_5 is added
(ii) pressure is increased
(iii) the temperature is increased?
Solution:  
(a) KcK_c = [PCl3(g)][Cl2(g)][PCl5(g)]\frac{[\mathrm{PCl}_{3(\mathrm{g})}][\mathrm{Cl}_{2(\mathrm{g})}]}{[\mathrm{PCl}_{5(\mathrm{g})}]}
(b) PCl3(g)+Cl2(g)\mathrm{PCl}_{3(\mathrm{g})} + \mathrm{Cl}_{2(\mathrm{g})} ⇌ PCl5(g)\mathrm{PCl}_{5(\mathrm{g})}
∴ Kc′K_c' = [PCl5(g)][PCl3(g)][Cl2(g)]\frac{[\mathrm{PCl}_{5(\mathrm{g})}]}{[\mathrm{PCl}_{3(\mathrm{g})}][\mathrm{Cl}_{2(\mathrm{g})}]}
(c) PCl5(g)\mathrm{PCl}_{5(\mathrm{g})} ⇌ PCl3(g)+Cl2(g)\mathrm{PCl}_{3(\mathrm{g})} + \mathrm{Cl}_{2(\mathrm{g})}
(i) If more PCl5\mathrm{PCl}_5 is added, then QcQ_c becomes less than Kc, the reaction will shift in the forward direction.
(ii) If the pressure is increased, the reaction will shift towards backward direction as it contains less number of gaseous species.
(iii) As the reaction is endothermic, the increase in temperature will favour the forward reaction. More PCl5\mathrm{PCl}_5 will dissociate to form PCl3\mathrm{PCl}_3 and Cl2\mathrm{Cl}_2.
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