Kinetics in gas phases

Question

The kinetics of a gas phase reaction of the form A → Products results in a rate constant of 1.308 M⁻¹ s⁻¹. For this reaction, the initial concentration of A is 0.947 M. At what time would the concentration of A reach 0.042 M?

Answer 1

From the units of the rate constant (M^-1s^-1), we can tell this is a SECOND ORDER reaction.

The integrate rate equation for 2nd order reaction is

1/[A] = 1/[A]_o + kt

Solving for t, we have...

1/0.042 = 1/0.947 + (1.308)(t)

23.81 = 1.056 + 1.308t

22.75 = 1.308t

t = 17 .4 sec = 17 sec (2 sig.figs.)