# Problem: At 700 K, CCl4 decomposes to carbon and chlorine. The Kp for the decomposition is 0.76. Find the starting pressure of CCl4 at this temperature that produces a total pressure of 1.6 atm at equilibrium.

###### FREE Expert Solution

Reaction:         CCl4(g) ⇌ C(s) + 2 Cl2(g)             Kp = 0.76

Step 1: Construct an ICE chart for the equilibrium reaction.

Let y = initial pressure of CCl4 Step 2: Calculate the change (x) in the reaction using the equilibrium constant.

(y – x) + 2x = total pressure

– x + 2x = 1.6

y + x = 1.6

y = 1.6 x

$\overline{){{\mathbf{K}}}_{{\mathbf{p}}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\frac{{\left({P}_{{\mathrm{Cl}}_{2}}\right)}^{\mathbf{2}}}{{\mathbf{P}}_{{\mathbf{CCl}}_{\mathbf{4}}}}\phantom{\rule{0ex}{0ex}}\mathbf{0}\mathbf{.}\mathbf{76}\mathbf{=}\frac{{\left(2x\right)}^{\mathbf{2}}}{\mathbf{y}\mathbf{-}\mathbf{x}}\phantom{\rule{0ex}{0ex}}\mathbf{0}\mathbf{.}\mathbf{76}\mathbf{=}\frac{{\left(2x\right)}^{2}}{\left(1.6-x\right)\mathbf{-}\mathbf{x}}\phantom{\rule{0ex}{0ex}}\mathbf{0}\mathbf{.}\mathbf{76}\left(1.6-2x\right)\mathbf{=}\frac{4{x}^{2}}{\overline{)1.6-2x}}\left(\overline{)1.6-2x}\right)\phantom{\rule{0ex}{0ex}}\mathbf{1}\mathbf{.}\mathbf{216}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{x}\mathbf{=}\mathbf{4}{\mathbf{x}}^{\mathbf{2}}\phantom{\rule{0ex}{0ex}}\overline{)\mathbf{0}\mathbf{=}\mathbf{4}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{x}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{216}}$

Now, we will use the quadratic formula to solve for x. The quadratic formula is:

$\overline{){\mathrm{x}}{=}\frac{-\mathrm{b}±\sqrt{{\mathrm{b}}^{2}-4\mathrm{ac}}}{2\mathrm{a}}}$

Solving for x:

$\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{\left(}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{\right)}\mathbf{±}\sqrt{\mathbf{\left(}\mathbf{1}\mathbf{.}\mathbf{52}{\mathbf{\right)}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathbf{\left(}\mathbf{4}\mathbf{\right)}\mathbf{\left(}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{216}\mathbf{\right)}}}{\mathbf{2}\mathbf{\left(}\mathbf{4}\mathbf{\right)}}\phantom{\rule{0ex}{0ex}}\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{±}\sqrt{\mathbf{2}\mathbf{.}\mathbf{3104}\mathbf{+}\mathbf{19}\mathbf{.}\mathbf{456}}}{\mathbf{8}}\phantom{\rule{0ex}{0ex}}\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{±}\sqrt{\mathbf{21}\mathbf{.}\mathbf{7664}}}{\mathbf{8}}\phantom{\rule{0ex}{0ex}}\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{52}\mathbf{±}\mathbf{4}\mathbf{.}\mathbf{66}}{\mathbf{8}}$

The calculation then splits into two ways:

80% (292 ratings) ###### Problem Details

At 700 K, CCl4 decomposes to carbon and chlorine. The Kp for the decomposition is 0.76. Find the starting pressure of CCl4 at this temperature that produces a total pressure of 1.6 atm at equilibrium.

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