Chemistry Kinetics

Question

The reaction

H2 (g) + Br2 (g) -> 2HBr (g)

is first order in both H2 and Br2, with

k=7.61x10^-4 L/mol*s

at 291 °C. If 1.00 L of at a concentration of 0.0584 M is rapidly mixed with the same volume of also at a concentration of 0.0584 M, what is the time (in seconds) required for the concentration to decrease to a value of 0.0192 M?

t= ____ s

Answer 1

This is a special case of an overall 2nd order reaction of the form A + B ---> products where A and B have the same initial concentrations

If A and B do not have the same initial concentrations then you end up with a totally different equation.

ln [A][Bo] - ln [B][Ao] = ([Ao]-[Bo]) kt

According to an old 4th edition Physical Chemistry by Daniels and Alberty

Answer 2

Since the reaction is 1st order in both H₂ and Br₂, this makes the overall order 2nd order. The integrated rate law for a 2nd order reaction is 1/[A] = 1/[A]_o + kt.

[A]_o = 0.0584 M

[A] = 0.0192

k = 7.61x10^-4 M^-1s^-1

t = ?

Solving for t ...

1/0.0192 = 1/0.0584 + 7.61x10^-4 t

52.08 = 17.12 + 7.61x10^-4 t

t = 45940 s = 4.59x10⁴ seconds