Up untill this point our rate expressions have dealt with concentration and change in concentration with respect to time. If the expression was integrated then we would have an expression that deals with concentration and time.

The rate law for this reaction is

Let's integrate from t = 0 to t

first you must separate the d[N2O5] from the dt

now integrate from t = 0 to t

and evaluate from time 0 to time t.

-(ln[N2O5]t - ln[N2O5]0 )= kt - k0

ln[N2O5]t - ln[N2O5]0 = -kt

 

ln[N2O5]t = -kt + ln[N2O5]0

 

[N2O5]t is the concentration of N2O5 after some time t.

[N2O5]0 is the initial concentration of N2O5 at time 0.

Any first order one reactant process will have an integral rate law that fits the following form.

ln[reactant]t = -kt + ln[reactant]0

 

A second order one reactant process would have the following integral rate law: