The rate constant for this first‑order reaction is 0.0130 s−1 at 400 ∘C. A⟶products After how many seconds will 18.5% of the reactant remain? t=s?

Answer 1

Method 1:

For a first order reaction,

t_1/2 = 0.692 / k = 0.692 / 0.0130 = 53.2 s

Also, for a first order reaction,

FR = 0.5ⁿ

FR = fraction remaining = 0.185

n = number of half lives that have elapsed

0.185 = 0.5ⁿ

taking log of both sides: -0.733 = -0.301n

n = 2.44 half lives have elapsed

Each half life = 53.2 s, so ...

Total time = 2.44 half lives x 53.2 s / half life = 130. seconds

Method 2:

For a first order reaction, the integrated rate law is:

ln[A] = -kt + ln[A]_o

Let [A]_o = 100, and then [A] = 18.5

ln 18.5 = -0.0130 t + ln 100

2.92 = -0.0130 t + 4.61

1.69 = 0.0130 t

t = 130. seconds