For a particular first-order reaction,it takes 24 minutes for the concentration of the reactant to decrease to 25% of its initial value.What is the value for rate constant (in s^-1)for the reaction?

Question

Quizplus · Accepted Answer

The first-order rate law is given by:

Rate = k[A]

where [A] is the concentration of the reactant and k is the rate constant.

From the problem, we know that:

[A]t = 0.25[A]0

where [A]t is the concentration of the reactant at time t and [A]0 is the initial concentration of the reactant.

We can use the integrated rate law for a first-order reaction to solve for the rate constant:

ln([A]t/[A]0) = -kt

Taking natural logarithms of both sides:

ln(0.25) = -k(24 min)

Solving for k:

k = ln(0.25) / (-24 min) = 9.6 × 10^-4 min^-1

Since the answer choices are given in units of s^-1, we need to convert the rate constant:

k = 9.6 × 10^-4 min^-1 x 60 s/min = 5.8 × 10^-5 s^-1

Therefore, the best choice is B.

For a Particular First-Order Reaction,it Takes 24 Minutes for the Concentration