The first-order reaction A$\rightarrow$B, has k = 5.67 s^-¹. If [A]₀ = 0.500 M, how long will it take to reach [A] = 0.124 M?

Question

Quizplus · Accepted Answer

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

ln([A]t/[A]0) = −kt

where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and ln is the natural logarithm.

We can rearrange this equation to solve for t:

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

Substituting the values given in the problem:

t = (ln(0.500) - ln(0.124))/5.67 = 0.2458 s

Rounding to the nearest hundredth, the answer is 0.246 s, which is choice D.

The First-Order Reaction A →\rightarrow→ B, Has K = 5