The rate constant for this first‑order reaction is 0.770 s−1 at 400 ∘C.

Question

The rate constant for this first‑order reaction is 0.770 s−1 at 400 ∘C.

A⟶products

How long, in seconds, would it take for the concentration of A

to decrease from 0.600 M to 0.250 M?

Answer 1

There are several ways to approach this. I find the following to be the easiest.

For a 1st order reaction, t_1/2 = 0.693/k

t_1/2 = 0.693 / 0.770 s^-1 = 0.900 s

For a 1st order reaction

Fraction remaining (FR) = 0.5ⁿ where n = number of half lives that have elapsed.

FR = 0.250/0.600 = 0.417

0.417 = 0.5ⁿ

n = 1.26 half lives

1.26 half lives x 0.900 s / half life = 1.13 seconds