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.