Question

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10⁻⁴ s−1 at a certain temperature.

If the initial concentration of SO2Cl2 is 1.00 M, how long will it take for the concentration to decrease to 0.72 M ?

If the initial concentration of SO2Cl2 is 0.175 M , what is the concentration of SO2Cl2 after 460 s?

Answer 1

The concentration-time equation for a first order reaction is

ln ([A]_t / [A]_o) = -kt , here [A]t is the concentration of A at time t and [A]o = initial concentration.

1)

[A]_o = 1.00, [A]_t = 0.72,

and k = 1.44 x 10^-4

ln (0.72 / 1.00) = -(1.44 x 10^-4)(t)
-0.328 = -(1.44 x 10^-4)(t)
t = 2281 seconds ................. Answer

2)

[A]_o = 0.175, [A]_t = ?,

and k = 1.44 x 10^-4 , t = 460 s

ln (0.175/ [A]_t) = -(1.44 x 10^-4)(460)

[A]_t = 0.163 ..................... Answer