Question 30 of 69intermediate🔧 ApplyShort Answer3 marks

At 473 K, equilibrium constant KcK_c for decomposition of phosphorus pentachloride, PCl5PCl_5 is 8.3×10−38.3 \times 10^{-3}. If decomposition is depicted as,

PCl5(g)⇌PCl3(g)+Cl2(g)ΔrH∘=124.0 kJ mol−1PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) \quad \Delta_r H^\circ = 124.0 \text{ kJ 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_5 is added (ii) pressure is increased (iii) the temperature is increased?

(a)
Answer

The expression for KcK_c for the reaction is Kc=[PCl3][Cl2][PCl5]K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}.

(b)
Answer

The value of KcK_c for the reverse reaction is the reciprocal of the forward reaction's KcK_c. Thus, Kc′=18.3×10−3=120.48K'_c = \frac{1}{8.3 \times 10^{-3}} = 120.48.

(c)
Answer

(i) Adding more PCl5_5 has no effect on KcK_c as it is constant at a given temperature. (ii) Increasing pressure also has no effect on KcK_c. (iii) Since the reaction is endothermic (ΔrH∘=124.0 kJ mol−1\Delta_r H^\circ = 124.0 \text{ kJ mol}^{-1}), increasing the temperature will increase the value of KcK_c.

Explanation

The expression for KcK_c is derived from the molar concentrations of products over reactants. The reverse reaction's equilibrium constant is the inverse of the forward reaction's constant. According to Le Chatelier's principle and the thermodynamics of equilibrium, KcK_c is only affected by changes in temperature. Since the decomposition of PCl5 is endothermic, increasing the temperature shifts the equilibrium towards the products, thereby increasing KcK_c.

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