Question

Phosphorus pentachloride decompose according to the reaction ${PCl}_3\left(g\right)\rightleftharpoons {PCl}_3\left(g\right)+{Cl}_2\left(g\right)$, 1 mol of ${PCl}_5$ is placed in a 500 mL closed reaction vessel and allowed to reach equilibrium with decomposition products, phosphorus trichloride and chlorine at 523 K. Equilibrium constant, $K_c=1.80$. What is the composition of the mixture at equilibrium?

Answer 1

Initial concentration of $PC{l}_5=\frac{1}{0.5}=2M.$

$PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$

At $t=0:-200$

At equilibrium :- $(2-x)xx$

Now, $K_C=\frac{x\times x}{2-x}1.80=\frac{x^2}{2-x}3.6-1.8x-x^2=0x=1.2$

$\therefore$ The equilibrium concentration of both the components of product is $1.2M$.

Therefore, the composition of mixture at equilibrium is,

$PC{l}_5=\frac{0.8}{3.2}=0.25=25\%$

$PC{l}_3=\frac{1.2}{3.2}=0.375=37.5\%$

$C{l}_2=\frac{1.2}{3.2}=0.375=37.5\%$