At 473 K, equilibrium constant Kc for decomposition of phosphorus pentachloride,

Question:

At $473 \mathrm{~K}$, equilibrium constant $K_{c}$ for decomposition of phosphorus pentachloride, $\mathrm{PCl}_{5}$ is $8.3 \times 10^{-3} .$ If decomposition is depicted as,

$\mathrm{PCl}_{5}(\mathrm{~g}) \longleftrightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \Delta_{r} H^{\circ}=124.0 \mathrm{kJmol}^{-1}$

a) Write an expression for $K_{c}$ for the reaction.

b) What is the value of $K_{c}$ for the reverse reaction at the same temperature?

c) What would be the effect on $K_{c}$ if (i) more $\mathrm{PCl}_{5}$ is added (ii) pressure is increased? (iii) The temperature is increased?

Solution:

(a) $K_{c} \frac{\left[\mathrm{PCl}_{3(\mathrm{~g})}\right]\left[\mathrm{Cl}_{2(\mathrm{~g})}\right]}{\left[\mathrm{PCl}_{\mathrm{S}(\mathrm{g})}\right]}$

(b) Value of $K_{c}$ for the reverse reaction at the same temperature is:

$K_{c}^{\prime}=\frac{1}{K_{c}}$

$=\frac{1}{8.3 \times 10^{-3}}=1.2048 \times 10^{2}$

$=120-48$

(c) (i) $K_{c}$ would remain the same because in this case, the temperature remains the same.

(ii) $K_{c}$ is constant at constant temperature. Thus, in this case, $K_{c}$ would not change.

(iii) In an endothermic reaction, the value of $K_{c}$ increases with an increase in temperature. Since the given reaction in an endothermic reaction, the value of $K_{c}$ will increase if the temperature is increased.