The value of Kc for the reaction 3 O21g2 ∆ 2 O31g2 is 1.7 * 10-56 at 25°C. Do you expect pure air at 25 °C to contain much O3 (ozone) when O2 and O3 are in equilib- rium? If the equilibrium concentration of O2 in air at 25 °C is 8 * 10-3 M, what is the equilibrium concentration of O3?

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Identify the given reaction: \(3 \text{O}_2(g) \rightleftharpoons 2 \text{O}_3(g)\).

Write the expression for the equilibrium constant \(K_c\): \(K_c = \frac{[\text{O}_3]^2}{[\text{O}_2]^3}\).

Substitute the given values into the \(K_c\) expression: \(1.7 \times 10^{-56} = \frac{[\text{O}_3]^2}{(8 \times 10^{-3})^3}\).

Solve for \([\text{O}_3]\) by rearranging the equation: \([\text{O}_3]^2 = 1.7 \times 10^{-56} \times (8 \times 10^{-3})^3\).

Take the square root of both sides to find \([\text{O}_3]\).

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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. A very small Kc value, such as 1.7 * 10^-56, indicates that the reaction favors the reactants significantly over the products, suggesting that at equilibrium, the concentration of products (in this case, O3) will be very low compared to the reactants (O2).

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. In the context of the reaction involving O2 and O3, if the concentration of O2 is increased, the equilibrium will shift to produce more O3, but given the very low Kc, the amount of O3 produced will still be minimal.

Calculating Equilibrium Concentrations

To find the equilibrium concentration of a species in a reaction, one can use the expression for Kc, which relates the concentrations of the products and reactants. For the reaction 3 O2(g) ⇌ 2 O3(g), the Kc expression is Kc = [O3]^2 / [O2]^3. By substituting the known concentration of O2 into this equation, one can solve for the equilibrium concentration of O3, which will be very small due to the low value of Kc.