The connection between the differential rate equation and integrated rate equation for a first order reaction is shown below.
The integrated rate equation can be used to
| differential rate equation: | – | d[A] | = k[A] |  Integrated rate equation: | ln[A] = -kt + ln[A]0 | useful rearranged form: | ln | [A] | = -kt |
| dt | [A]0 |
The integrated rate equation can be used to
- determine if a reaction is first order as this shows that a plot ln[A] against time is a straight line.
- calculate the time taken for a the concentration to drop by a specified amount.
- calculate the change in concentration after a specific time has elapsed since the onset of reaction.