How long will it take for the concentration of A to decrease from 0.910 M to 0.205 for the reaction A → Products? (k = 0.153 M/s)

Answer 1

If we assume the reaction of A => products is a first order reaction, then we can use

t_1/2 = 0.693 / k and

FR = 0.5ⁿ

t_/12 = half life = 0.693 / 0.153 M/s = 4.53 s

FR = fraction remaining = 0.5ⁿ where n = number of half lives that have elapsed

FR = 0.205 M / 0.910 M = 0.225

So now we can find out how many half lives have elapsed, and then multiply that by 4.53 sec / half life

0.225 = 0.5ⁿ

log 0.225 = n log 0.5

n = 2.15 half lives have elapsed

Time = 2.15 half lives x 4.53 sec / half life = 9.74 seconds

You could also use the integrated rate equation for a first order reaction

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

ln(0.205) = -0.153 t + ln(0.910)

t = -1.585 + 0.094 / -0.153

t = 9.75 seconds