The rate constant for a certain reaction is k=8.90×10^−3 s^-1. If the initial reactant concentration was 0.400M, what will the concentration be after 13.0 minutes?
With unit for rate constant in s^-1, you know it is first order. Therefore, use the equation ln(No/N) = kt
You know No = 0.400M, solve for N, you know k and t.
0.000395
To determine the final concentration of the reactant after a certain time, we can use the first-order reaction kinetics equation:
ln([A]t/[A]0) = -kt
Where:
[A]t = final concentration of reactant
[A]0 = initial concentration of reactant
k = rate constant
t = time
In this case, we are given:
k = 8.90 × 10^−3 s^-1 (rate constant)
[A]0 = 0.400 M (initial concentration of reactant)
t = 13.0 minutes = 13.0 × 60 seconds = 780 seconds
We need to solve for [A]t.
Rearranging the equation, we have:
[A]t = [A]0 * e^(-kt)
Substituting the given values into the equation:
[A]t = 0.400 M * e^(-8.90 × 10^−3 s^-1 * 780 s)
Now we can calculate [A]t using a scientific calculator or software:
[A]t = 0.400 M * e^(-6.942) ≈ 0.400 M * 0.0010126 ≈ 0.000405 M
Therefore, the concentration of reactant after 13.0 minutes is approximately 0.000405 M.