To determine the correct expression for the equilibrium constant ([tex]\(K\)[/tex]) for the given chemical reaction:
[tex]\[
COCl_2(g) \Leftrightarrow CO(g) + Cl_2(g)
\][/tex]
we need to consider the general form for the equilibrium constant expression, which is given by:
[tex]\[
K = \frac{[ \text{products} ]}{[ \text{reactants} ]}
\][/tex]
Each concentration term is raised to the power of its stoichiometric coefficient in the balanced chemical equation. The balanced chemical equation given is:
[tex]\[
COCl_2(g) \Leftrightarrow CO(g) + Cl_2(g)
\][/tex]
Here, the stoichiometric coefficients are:
- 1 for [tex]\(COCl_2(g)\)[/tex]
- 1 for [tex]\(CO(g)\)[/tex]
- 1 for [tex]\(Cl_2(g)\)[/tex]
Based on these coefficients, the equilibrium expression becomes:
[tex]\[
K = \frac{[CO][Cl_2]}{[COCl_2]}
\][/tex]
Now, let's match this result with the given options:
1. [tex]\(K = \frac{\left[ COCl_2\right]^2}{[ CO ]\left[ Cl_2\right]}\)[/tex]
2. [tex]\(K = \frac{\left[ COCl_2\right]}{[ CO ]\left[ Cl_2\right]}\)[/tex]
3. [tex]\(K = \frac{\left[ CO\right][\left[Cl_2\right]}{\left[COCl_2 \right]} \)[/tex]
4. [tex]\(K = \frac{[ CO ]\left[ Cl_2\right]}{\left[ COCl_2\right]^2}\)[/tex]
The correct option is:
[tex]\[
K = \frac{[CO][Cl_2]}{[COCl_2]}
\][/tex]
Thus, the correct answer is:
[tex]\(K=\frac{\left[ CO \right]\left[ Cl_2 \right]}{\left[ COCl_2 \right]}\)[/tex]
Which corresponds to option 3.
