Answer to Question #83276 in General Chemistry for natasha

Question

The reaction A (aq) ---> B (aq) is a first order reaction with respect to A (aq). The concentration of A (aq) is reduced to 30.2% of its initial value 1.50 minutes. What is the value of the half-life (in s) of the reaction?

Answer 1

Answer on Question #83276, Chemistry/ General Chemistry

The reaction A (aq) ---> B (aq) is a first order reaction with respect to A (aq). The concentration of A (aq) is reduced to 30.2% of its initial value 1.50 minutes. What is the value of the half-life (in s) of the reaction?

Solution

For the first order reaction

[A]=[A]*e^-kt

[A]/[A] = e^-kt

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

Find k:

[A]/[A] = 0.302, t = 1.50 min = 110 s

ln(0.302) = -k*110

k= 0.0109

For the first order reaction the value of the half-life is:

t_1/2 = ln2/k = ln2/0.0109 = 63.6 (s)

Answer: 63.6 s