Question

The equilibrium constant Kp for the reaction: ${\mathbf{CCl}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{C}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{Cl}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}$

at 700⁰C is 0.76. Determine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at 700⁰C.

Given: Kp = 0.76 P_{0 =} initial pressure of CCl₄

Short answer

Initial pressure(P₀) of Carbon tetrachloride is 0.88 atm.

Step-by-step solution

First, form an equation by seeing a change in the mass of the gaseous molecule from compounds goes from initial to equilibrium position as follows:

${\mathbf{CCl}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{C}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{Cl}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}$

initial P₀→-0

change -x→-+2x

at equilibrium (P_{0 –}x)→- +2x

P_total = P₀- x + 2x = P₀+x = 1.20 atm

Now find the value of x  by using the equilibrium constant formula:

${\mathbf{K}}_{\mathbf{P}}\mathbf{=}\frac{{\mathbf{\left(}\mathbf{2}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}}{{\mathbf{P}}_{\mathbf{0}}\mathbf{-}\mathbf{x}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{76}$

4x² = (0.76) P₀- (0.76) x

${\mathrm{P}}_0=\frac{4{\mathrm{x}}^2+(0.76)\mathrm{x}}{0.76}$

Now, substitute the value into P₀+x = 1.20 atm

We get $\frac{4{\mathrm{x}}^2}{0.76}+\mathrm{x}+\mathrm{x}=1.20\mathrm{atm}$

On solving the above eq., we get: $(5.3){\mathrm{x}}^2+2\mathrm{x}-1.20=0$

Now solving the quadratic eq. formula:

$\begin{array}{l}\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{b}\mathbf{\pm }\sqrt{{\mathbf{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathbf{ac}}}{\mathbf{2}\mathbf{a}}\\ \mathbf{onputting}\mathbf{}\mathbf{the}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{:}\\ \mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{2}\mathbf{\pm }\sqrt{\mathbf{4}\mathbf{-}\mathbf{25}\mathbf{.}\mathbf{4}}}{\mathbf{2}\mathbf{(}\mathbf{5}\mathbf{.}\mathbf{3}\mathbf{)}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{32}\mathbf{atm}\end{array}$

On putting the value of x in eq. P₀+x = 1.20 atm

The initial pressure of carbon tetrachloride is:

P₀+ = 1.20 atm,

Hence, P₀= 0.88atm.