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Write the equilibrium constant expression for the reaction C(s) + CO2(g) + 2Cl2(g) <=> 2COCl2(g). Calculate Kc for this reaction using the given values.
Chemistry
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3 partsStep-by-step solution
8 stepsHere are the solutions to the problems.
Part 1· 3 steps
-
Equilibrium constant expression: For the reaction , the equilibrium constant expression is:
(Note: Solids like are not included in the equilibrium constant expression.)
-
Calculation of the equilibrium constant: Given reactions:
- with
- with
Target reaction:
Manipulate the given reactions to obtain the target reaction.
Multiply reaction (2) by 2: $2CO(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g)$ The new equilibrium constant for this reaction is $(K_{c2})^2$.Add reaction (1) and the modified reaction (2).
$(C(s) + CO_2(g) \rightleftharpoons 2CO(g))$ $+$ $(2CO(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g))$ Summing these gives: $C(s) + CO_2(g) + 2CO(g) + 2Cl_2(g) \rightleftharpoons 2CO(g) + 2COCl_2(g)$ Canceling $2CO(g)$ from both sides yields the target reaction: $C(s) + CO_2(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g)$Calculate the overall equilibrium constant.
When reactions are added, their equilibrium constants are multiplied. $$ K_c = K_{c1} \times (K_{c2})^2 $$ $$ K_c = (1.4 \times 10^{12}) \times (5.5 \times 10^1)^2 $$ $$ K_c = (1.4 \times 10^{12}) \times (30.25 \times 10^2) $$ $$ K_c = (1.4 \times 10^{12}) \times (3.025 \times 10^3) $$ $$ K_c = (1.4 \times 3.025) \times 10^{12+3} $$ $$ K_c = 4.235 \times 10^{15} $$ The equilibrium constant for the reaction is $\boxed{\mathbf{4.235 \times 10^{15}}}$.
Part 2
Given reaction: with at 700 K.
Part a
For the reaction
Identify the relationship between the given reaction and the target reaction.
This reaction is the reverse of the original reaction.Calculate the new .
When a reaction is reversed, the new equilibrium constant is the reciprocal of the original. $$ K_p' = \frac{1}{K_p} $$ $$ K_p' = \frac{1}{7.1 \times 10^4} $$ $$ K_p' \approx 1.408 \times 10^{-5} $$ The value of $K_p$ is $\boxed{\mathbf{1.408 \times 10^{-5}}}$.
Part b
For the reaction
Identify the relationship between the given reaction and the target reaction.
This reaction is the original reaction multiplied by a factor of $\frac{1}{2}$.Calculate the new .
When a reaction is multiplied by a factor 'n', the new equilibrium constant is the original constant raised to the power 'n'. Here, $n = \frac{1}{2}$. $$ K_p'' = (K_p)^{1/2} = \sqrt{K_p} $$ $$ K_p'' = \sqrt{7.1 \times 10^4} $$ $$ K_p'' = \sqrt{71000} $$ $$ K_p'' \approx 266.458 $$ The value of $K_p$ is $\boxed{\mathbf{266.458}}$.
Part 3· 1 step
Calculate a value for the equilibrium constant for the reaction:
Given information:
- with
- with
Target reaction:
Manipulate the given reactions
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