99 % of a 1st order reaction completed in 2.303 minutes. What is the rate constant and half-life of the reaction

Explanation:

In a first-order reaction, the time required for 99% completion is given as 2.303 minutes. To determine the rate constant (k) and half-life (t_1/2), we can use the following relationships:

1. Rate Constant (k):

The integrated rate law for a first-order reaction is:

t = (2.303 / k) * log([A₀] / [A])

Where:

• t is the time taken for the reaction to reach a certain completion percentage.
• [A₀] is the initial concentration of the reactant.
• [A] is the concentration of the reactant at time t.

For 99% completion, 1% of the reactant remains. Assuming an initial concentration of 100 units:

t = 2.303 minutes
[A₀] = 100
[A] = 1

Substituting these values into the rate law:

2.303 = (2.303 / k) * log(100 / 1)

Simplifying:

2.303 = (2.303 / k) * 2 k = (2.303 * 2) / 2.303 = 2 min⁻¹

2. Half-Life (t_1/2):

The half-life for a first-order reaction is related to the rate constant by:

t₁/₂ = 0.693 / k

Substituting the value of k:

t₁/₂ = 0.693 / 2 = 0.3465 minutes

Final Answer

The rate constant (k) is 2 min⁻¹, and the half-life (t_1/2) is 0.3465 minutes. Therefore, the correct option is: b) 2 and 0.3465