First order reaction

Question

If a reaction is first order with a rate constant of 0.0450 s⁻¹, how much time is required for 55% of the initial quantity of reactant to be consumed?

Answer 1

For a first order reaction, the half life (t_1/2) is given at 0.693/k

t_1/2 = 0.693 / 0.0450 = 15.40 seconds

Also, for a first order reaction, the fraction that remains = 0.5ⁿ where n = number of half lives elapsed.

In this case, the fraction remaining = 45% since 55% has been consumed. We can then write our equation as:

0.45 = 0.5ⁿ

log 0.45 = n log 0.5

n = 1.15 half lives have elapsed

Since each half life is 15.4 s, total time required = 15.4 s x 1.15 = 17.7 seconds