# Chemical Reaction Kinetics: Half-Life Calculation

## What is the half-life for the decomposition of O₃ with given concentration and rate constant?

Calculate the half-life for the decomposition of O₃ when the concentration is 2.38 x 10⁻⁶ M and the rate constant for this second-order reaction is 50.4 L/mol/h.

## Half-Life Calculation

The half-life of the decomposition of O₃ (ozone) with a concentration of 2.38 x 10⁻⁶ M and a rate constant of 50.4 L/mol/h is approximately 3.5352 x 10⁹ hours.

To determine the half-life (t1/2) of the decomposition of O₃ (ozone) with a concentration of 2.38 x 10⁻⁶ M and a rate constant of 50.4 L/mol/h, we can use the second-order reaction equation:

Rate = k [O₃]²

We can rearrange this equation to solve for the half-life:

t1/2 = 1 / (k [O₃]²)

Substituting the given values:

t1/2 = 1 / (50.4 L/mol/h * (2.38 x 10⁻⁶ M)²

Calculating the result:

t1/2 = 1 / (50.4 * (2.38 x 10⁻⁶)²) h

t1/2 = 1 / (50.4 * 5.6644 x 10⁻¹²) h

t1/2 ≈ 3.5352 x 10⁹ h

Therefore, the half-life of the decomposition of O₃ under the given conditions is approximately 3.5352 x 10⁹ hours.