How long, in seconds, would it take for the concentration of A to decrease from 0.950 M to 0.350 M?

Question

The rate constant for this first-order reaction is 0.170 s^-1 at 400 degrees Celsius. A-->products

t=

Answer 1

[A]/[A]₀ = e^–kt means that

ln([A]/[A]₀) = –kt which can be solved for t

t = (ln([A]/[A]₀))/(–k)

We're given [A]/[A]₀ = 0.350/0.950 = 7/19, and k = 0.170 s^–1

So t = (ln(7/19))/(–0.170) = (–0.9985)/(–0.170) = 5.874 s

Answer (rounded to 3 significant figures)

t = 5.87 s