To write the equilibrium expression for the reaction:
[tex]\[
2 \text{O}_{3(g)} \longleftrightarrow 3 \text{O}_{2(g)}
\][/tex]
you need to use the stoichiometry of the balanced chemical equation. The equilibrium constant expression for a given reaction is based on the concentrations of the products and reactants raised to the power of their respective coefficients in the balanced equation.
In this reaction:
- The coefficient of [tex]\(\text{O}_3(g)\)[/tex] (ozone) is 2.
- The coefficient of [tex]\(\text{O}_2(g)\)[/tex] (oxygen) is 3.
The general form of the equilibrium constant [tex]\(K\)[/tex] is given by the ratio of the concentrations of the products to the reactants, each raised to the power of their coefficients.
Thus, for the reaction [tex]\(2 \text{O}_{3(g)} \longleftrightarrow 3 \text{O}_{2(g)}\)[/tex], the equilibrium expression [tex]\(K\)[/tex] would be:
[tex]\[
K = \frac{[\text{O}_2]^3}{[\text{O}_3]^2}
\][/tex]
This equation indicates that the concentration of [tex]\(\text{O}_2\)[/tex] is cubed (since its coefficient is 3) and the concentration of [tex]\(\text{O}_3\)[/tex] is squared (since its coefficient is 2).
Therefore, the correct equilibrium expression for this reaction is:
[tex]\[
K = \frac{[\text{O}_2]^3}{[\text{O}_3]^2}
\][/tex]
From the given options, the correct answer is:
[tex]\[
K = \frac{\left[ \text{O}_2 \right]^3}{\left[ \text{O}_3 \right]^2}
\][/tex]
