Question

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.42×10−4 s−1 at a certain temperature.

a. What is the half-life for this reaction?

b. How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration?

c. If the initial concentration of SO2Cl2 is 1.00 M, how long will it take for the concentration to decrease to 0.80 M ?

d. If the initial concentration of SO2Cl2 is 0.175 M , what is the concentration of SO2Cl2 after 200 s ?

e. If the initial concentration of SO2Cl2 is 0.175 M , what is the concentration of SO2Cl2 after 530 s ?

Answer 1

c.

ln ([A]t / [A]o) = -kt

here [A]t = the concentration of A at time t

[A]o = initial concentration.

according to the problem, [A]o = 1.00, [A]t = 0.80, k = 1.40 x 10^-4 s^-1

Therefore,
ln (0.80 / 1.00) = -(1.40 x 10^-4)(t)
-0.223 = -(1.40 x 10^-4)(t)
t = 1600 s

d.

initial concentration of SO2Cl2 = 0.175 M , time = 200 s

ln ([A]t / [A]o) = -kt
ln ([A]t / 0.175) = -(1.4 x 10^-4)(200)
ln [A]t - ln 0.175 = -0.028
ln [A]t =-1.74 -0.028

ln [A]t =- 1.768
[A]t = e^-1.768

= 0.171 M

e.

initial concentration of SO2Cl2 = 0.175 M , time = 530 s

ln ([A]t / [A]o) = -kt
ln ([A]t / 0.175) = -(1.4 x 10^-4)(530)
ln [A]t - ln 0.175 = -0.0742
ln [A]t =-1.74 -0.0742

ln [A]t = -1.8142
[A]t = e^-1.8142 = 0.163 M