Question

2 Moles Of PCl₅ were heated in a closed vessel of 2 Litre capacity. At equilibrium, 40% Of PCl₅ Is dissociated Into PCl₃ And Cl₂. What is the value of the equilibrium constant?

Answer 1

Step 1: Given data

As given in the question, the chemical equation is

${\mathrm{PCl}}_5\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

With The degree of dissociation,

$$\begin{gathered} \alpha =40\% \\ =0.4. \end{gathered}$$

Step 2: Formula used :

Molarity = $\frac{numberofmoles}{volume}$

Step 3: Calculating molar concentration

At equilibrium, the molar concentration of the component of the mixture is:

For Phosphorus pentachloride

$$\begin{gathered} {\mathrm{PCl}}_5=\frac{2(1-\alpha )}{V} \\ =\frac{2(1-0.4)}{2} \\ =0.6mol/L \end{gathered}$$

For Phosphorus trichloride

$$\begin{gathered} {\mathrm{PCl}}_3=\frac{2\alpha }{V} \\ =\frac{2\times 0.4}{2} \\ =0.4mol/L \end{gathered}$$

For chlorine gas :

$$\begin{gathered} C{l}_2=\frac{2\times 0.4}{2} \\ =0.4mol/L \end{gathered}$$

Step 4: Calculating Equilibrium constant

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

$$\begin{gathered} =\frac{0.4\times 0.4}{0.6} \\ =0.27mol/L \end{gathered}$$