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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 parts
1

4.235×1015\mathbf{4.235 \times 10^{15}}

a

1.408×10−5\mathbf{1.408 \times 10^{-5}}

b

266.458\mathbf{266.458}

Step-by-step solution

8 steps

Here are the solutions to the problems.

Part 1· 3 steps

  • Equilibrium constant expression: For the reaction C(s)+CO2(g)+2Cl2(g)⇌2COCl2(g)C(s) + CO_2(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g), the equilibrium constant expression KcK_c is:

    Kc=[COCl2(g)]2[CO2(g)][Cl2(g)]2K_c = \frac{[COCl_2(g)]^2}{[CO_2(g)][Cl_2(g)]^2}

    (Note: Solids like C(s)C(s) are not included in the equilibrium constant expression.)

  • Calculation of the equilibrium constant: Given reactions:

    1. C(s)+CO2(g)⇌2CO(g)C(s) + CO_2(g) \rightleftharpoons 2CO(g) with Kc1=1.4×1012K_{c1} = 1.4 \times 10^{12}
    2. CO(g)+Cl2(g)⇌COCl2(g)CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g) with Kc2=5.5×101K_{c2} = 5.5 \times 10^1

    Target reaction: C(s)+CO2(g)+2Cl2(g)⇌2COCl2(g)C(s) + CO_2(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g)

  1. 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 $(K_{c2})^2$.
    
  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:  
    $C(s) + CO_2(g) + 2Cl_2(g) \rightleftharpoons 2COCl_2(g)$
    
  3. 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: H2(g)+Br2(g)⇌2HBr(g)H_2(g) + Br_2(g) \rightleftharpoons 2HBr(g) with Kp=7.1×104K_p = 7.1 \times 10^4 at 700 K.

Part a

1.408×10−5\mathbf{1.408 \times 10^{-5}}

For the reaction 2HBr(g)⇌H2(g)+Br2(g)2HBr(g) \rightleftharpoons H_2(g) + Br_2(g)

  1. Identify the relationship between the given reaction and the target reaction.

    This reaction is the reverse of the original reaction.
    
  2. Calculate the new KpK_p.

    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

266.458\mathbf{266.458}

For the reaction 12H2(g)+12Br2(g)⇌HBr(g)\frac{1}{2}H_2(g) + \frac{1}{2}Br_2(g) \rightleftharpoons HBr(g)

  1. Identify the relationship between the given reaction and the target reaction.

    This reaction is the original reaction multiplied by a factor of $\frac{1}{2}$.
    
  2. Calculate the new KpK_p.

    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: O2(g)+O(g)⇌O3(g)O_2(g) + O(g) \rightleftharpoons O_3(g)

Given information:

  1. NO2(g)⇌NO(g)+O(g)NO_2(g) \rightleftharpoons NO(g) + O(g) with Kc1=6.8×10−49K_{c1} = 6.8 \times 10^{-49}
  2. O3(g)+NO(g)⇌NO2(g)+O2(g)O_3(g) + NO(g) \rightleftharpoons NO_2(g) + O_2(g) with Kc2=5.8×10−34K_{c2} = 5.8 \times 10^{-34}

Target reaction: O2(g)+O(g)⇌O3(g)O_2(g) + O(g) \rightleftharpoons O_3(g)

  1. Manipulate the given reactions

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