The value of Kc for the reaction 3O2 (g) = 2O3 (g) is 2.0 ×10–50 at 25°C. If the equilibrium concentration of O2 in air at 25°C is 1.6 ×10–2, what is the concentration of O3

To find the concentration of O3 at equilibrium for the reaction 3O2 (g) ⇌ 2O3 (g) with a given equilibrium constant (Kc) of 2.0 × 10–50, we can use the expression for Kc and the provided concentration of O2. Let's break this down step by step.

Understanding the Equilibrium Constant Expression

The equilibrium constant expression for the reaction can be written as:

• Kc = [O3]^2 / [O2]^3

Here, [O3] and [O2] represent the molar concentrations of ozone and oxygen, respectively. Given that Kc is extremely small (2.0 × 10–50), this indicates that at equilibrium, the concentration of products (O3) is very low compared to the reactants (O2).

Substituting Known Values

We know the equilibrium concentration of O2:

• [O2] = 1.6 × 10–2 M

We can substitute this value into the Kc expression:

• 2.0 × 10–50 = [O3]^2 / (1.6 × 10–2)^3

Calculating [O3]

First, we need to calculate (1.6 × 10–2)^3:

• (1.6 × 10–2)^3 = 4.096 × 10–6 M^3

Now, substituting this back into the Kc expression gives us:

• 2.0 × 10–50 = [O3]^2 / 4.096 × 10–6

Next, we can rearrange this equation to solve for [O3]^2:

• [O3]^2 = 2.0 × 10–50 × 4.096 × 10–6

Calculating this gives:

• [O3]^2 = 8.192 × 10–56

To find [O3], we take the square root:

• [O3] = √(8.192 × 10–56)

Calculating the square root results in:

• [O3] ≈ 9.05 × 10–28 M

Final Concentration of Ozone

Thus, the equilibrium concentration of O3 at 25°C is approximately:

• [O3] ≈ 9.05 × 10–28 M

This extremely low concentration of ozone reflects the fact that, under normal atmospheric conditions, ozone is much less prevalent than oxygen, which aligns with the very small value of Kc we started with.