what is the half-life in seconds?

Question

A → B is a first order reaction. Using the data below, what is the half-life in seconds? 0 sec, [A] = 1.22 M 3 sec, [A] = 0.86 M 6 sec, [A] = 0.61 M 9 sec, [A] = 0.43 M 12 sec, [A] = 0.31 M 15 sec, [A] = 0.22 M 18 sec, [A] = 0.15 M

The correct answer is 6

Answer 1

For a 1st order reaction, the integrated rate law is [A] = [A_o]e^-kt

We can solve for k and then for 1st order reaction, t_1/2 = 0.693/k so we can find t_1/2

[A] = 0.15 M

[Ao] = 1.22 M

t = 18 sec

Solve for k

0.15 = 1.22e^-18k

ln 0.15 = -18k ln 1.22

-1.897 - 0.1989 = -18k

-2.0959 = -18k

k = 0.1164

Now solve for t_1/2

t_1/2 = -.693/k = 0.693/0.1164

t_1/2= 5.95 = 6 sec