A first order reaction has a half-life of 30 min.If the initial concentration of the reactant is 0.50 M,what will the concentration of the reactant be after 2.00 hr?

Question

Quizplus · Accepted Answer

We can use the first-order kinetics equation:

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

where [A] is the concentration at a given time, [A]0 is the initial concentration, k is the rate constant, and t is time.

We know that the half-life (t1/2) is 30 min. This means that when t = t1/2, [A]/[A]0 = 1/2:

ln(1/2) = -k(30)

Solving for k:

k = ln(2)/30 = 0.0231 min^-1

Now we can use the equation to find [A] after 2 hours (120 min):

ln([A]/0.50) = -0.0231(120)

ln([A]/0.50) = -2.772

[A]/0.50 = e^-2.772

[A] = (e^-2.772)(0.50) = 0.031 M

Therefore, the concentration of the reactant after 2.00 hr is 0.031 M.

A First Order Reaction Has a Half-Life of 30 Min