An overall 1st order reaction has a rate constant of 1.8 x 10^-3 1/s. How long will it take for the reaction to be 30% complete?

Question

Answer choices:

240 s

198 s

1730 s

129 s

None of the above

Answer 1

Two ways to solve this

(i) FR = 0.5ⁿ

FR = fraction remaining = 70% = 0.70

n = number of half lives that have elapsed (see below)

For 1st order reaction t_1/2 = 0.693/k = 0.693/1.8x10^-3 = 385 s

Now we can solve for n in the above equation:

0.70 = 0.5ⁿ

log 0.70 = n log 0.5

-0.155 = -0301n

n = 0.51 half lives have elapsed

0.51 half lives x 385 s / half life = 198 s (ANSWER)

(ii) ln[A] = -kt + ln [A]_o

ln 70 = -1.8x10^-3k + ln 100

4.25 = -1.8x10^-3k + 4.61

-0.36 = -1.8x10^-3k

k = 200 s =~ 198 s (ANSWER)