Chlorine monoxide and dichlorine dioxide are involved in the catalytic destruction of stratospheric ozone. They are related by the equation 2 ClO(g) ⇌ Cl2O2(g) for which Kc is 4.96 * 10^11 at 253 K. For an equilibrium mixture in which [Cl2O2] is 6.00 * 10^-6 M, what is [ClO]?

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Identify the equilibrium expression for the reaction: 2 \text{ClO}(g) \rightleftharpoons \text{Cl}_2\text{O}_2(g). The equilibrium constant expression K_c is given by K_c = \frac{[\text{Cl}_2\text{O}_2]}{[\text{ClO}]^2}.

Substitute the given values into the equilibrium expression. You know K_c = 4.96 \times 10^{11} and [\text{Cl}_2\text{O}_2] = 6.00 \times 10^{-6} \text{ M}.

Rearrange the equilibrium expression to solve for [\text{ClO}]. This involves isolating [\text{ClO}]^2 on one side of the equation.

Take the square root of both sides of the equation to solve for [\text{ClO}].

Ensure that the units are consistent and check your work to confirm that the calculated concentration of [\text{ClO}] is reasonable given the context of the problem.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. In this case, Kc = [Cl2O2] / [ClO]^2. A large Kc value, such as 4.96 * 10^11, indicates that at equilibrium, the concentration of products (Cl2O2) is much greater than that of the reactants (ClO), suggesting a reaction that favors product formation.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. This principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium, which is essential for understanding how the concentrations of ClO and Cl2O2 will relate in the given reaction.

Concentration Calculations

Concentration calculations involve determining the molarity of a substance in a solution, which is crucial for solving equilibrium problems. In this scenario, knowing the concentration of Cl2O2 allows us to use the equilibrium expression to find the unknown concentration of ClO. The relationship between the concentrations at equilibrium is key to applying the Kc value effectively.

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