Question

The reactant concentration in a first-order reaction was 7.40×10−2 M after 10.0 s and 9.70×10−3 M after 100 s . What is the rate constant for this reaction?The reactant concentration in a second-order reaction was 0.800 M after 180 s and 1.60×10−2 M after 890 s . What is the rate constant for this reaction?

Answer 1

1)

we have:

[A]1 = 0.074 M

[A]2 = 0.0097 M

t2-t1 = 100 s - 10 s = 90. s

use integrated rate law for 1st order reaction

ln[A]2 = ln[A]1 - k*(t2-t1)

ln(0.0097) = ln(0.074) - k*90

-4.635629 = -2.60369 - k*90

k*90 = 2.031939

k = 2.26*10^-2 s-1

Answer: 2.26*10^-2 s-1

2)

we have:

[A]1 = 0.8 M

[A]2 = 0.016 M

t2-t1 = 890 s - 180 s = 710 s

use integrated rate law for 2nd order reaction

1/[A]2 = 1/[A]1 + k*(t2-t1)

1/(0.016) = 1/(0.8) + k*710

62.5 = 1.25 +k*710

k*710 = 61.25

k = 8.63*10^-2 M-1.s-1

Answer: 8.63*10^-2 M-1.s-1