Question

At 473 K, equilibrium constant ${K_c}$ for decomposition of phosphorus pentachloride$PC{l_5}$ is 8.3$ \times {10^{ - 3}}$. if decomposition is depicted as,
$PC{l_5}(g) \rightleftharpoons PC{l_3}(g) + C{l_2}(g){\Delta _r}{H^ \circ } = 124.0KJmo{l^{ - 1}}$
(i)Write an expression for ${K_c}$ for the reaction.
(ii)What is the value of ${K_c}$ for the reverse reaction at the same temperature?
(iii)What would be the effect on ${K_c}$ if-
a)more $PC{l_5}$ is added
b) pressure is increased
c) the temperature is increased?

Answer 1

Hint: According to the law of mass action we know that rate of a reaction at a given temperature is directly proportional to the product of active masses of reactants raised to the power equal to the stoichiometric coefficient of the balanced chemical equation at a particular instant of reaction

Complete Step by step answer: The above law can be mathematically depicted as for the above written balanced equation of decomposition of phosphorus pentachloride,
Rate of reaction= k[$PC{l_5}$]
Since the reaction has attained equilibrium then
Rate of forward reaction= ${k_f}[PC{l_5}]$
Rate of backward reaction= ${k_b}[PC{l_3}][C{l_2}]$
i)At equilibrium two rates are equal

${k_f}[PC{l_5}]$=${k_b}[PC{l_3}][C{l_2}]$
this ratio gives the equilibrium constant K
$\dfrac{{{k_f}}}{{{k_b}}} = {K_c} = K = \dfrac{{[PC{l_3}][C{l_2}]}}{{[PC{l_5}]}}$
ii) therefore equilibrium constant for the reverse reaction would be given by
rate of reaction=$\dfrac{1}{{{K_C}}} = \dfrac{1}{{8.3 \times {{10}^{ - 3}}}} = 120.48$
iii)a) on adding $PC{l_5}$that is increasing the concentration of the reactant only the direction of equilibrium gets shifted but the equilibrium constant remains unchanged until the temperature changes.
b) similarly increasing the pressure does not affect the equilibrium constant.
c) since it is a decomposition reaction therefore it is endothermic in nature. Increasing the temperature increases the rate of forward reaction to be carried out leading to increase in the value of equilibrium constant.

Note: We must know that a very large value of equilibrium constant signifies that the forward reaction goes to completion or very nearly so and the forward reaction does not occur to a significant extent if its value is small, only its mediocre value signifies the state of equilibrium.