Question

The rate constant for the decomposition of reactant a is 0. 0092 s-1. How long will it take for 80% of the reactant to decompose? please answer in seconds and round your answer to one decimal place.

Answer 1

To calculate the time it will take for 80% of the reactant to decompose, we can use the first-order rate equation:

ln([a]t/[a]0) = -kt

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

Rearranging this equation, we get:

t = (ln([a]0/[a]t))/k

We know that k = 0.0092 s-1, and we want to find the time it takes for 80% of the reactant to decompose, which means [a]t = [a]0 x 0.20. Therefore, we can plug in these values and solve for t:

t = (ln(1/0.20))/0.0092 s-1

t = 3,784.5 seconds

Therefore, it will take approximately 3,784.5 seconds, or 63 minutes and 4.5 seconds, for 80% of the reactant to decompose.