Question

If it takes 87.0 min for the concentration of a reactant to drop to 20.0% of its initial value in a first-order reaction, what is the rate constant for the reaction in the units min-1?

Answer 1

Answer:

0.0185 min⁻¹

Explanation:

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

Given:

20.0 % of the initial values is left which means that 0.20 of $[A_0]$ is left. So,

$\frac {[A_t]}{[A_0]}$ = 0.20

t = 87.0 min

$\frac {[A_t]}{[A_0]}=e^{-k\times t}$

$0.20=e^{-k\times 87.0}$

k = 0.0185 min⁻¹