The kinetics of a gas phase reaction of the form A → Products results in a rate constant of 1.308 M⁻¹ s⁻¹.

Question

For this reaction, the initial concentration of A is 0.571 M. What is the half-life for this reaction?

. At what time would the concentration of A reach 0.042 M?

Answer 1

You can always tell the order of a reaction by looking at the units of the rate constant. In this case, the units are M^-1s^-1, which tells us this is a SECOND order reaction.

For a second order reaction the half life (t_1/2) = 1 / k[A]_o

t_1/2 = 1 / (1.308 M^-1s^-1)(0.571 M)

t_1/2 = 1.339 s

1/[A] = 1/[A]_o + kt .. integrated rate law for a 2nd order reaction

1/0.042 = 1/0.571 + 1.308t

23.81 = 1.751 + 1.308 t

t = 16.86 s