First-order rate constants have units of s−1.
A CLOSER LOOK
The most common example of a first-order reaction is the process of radioactive decay.The most common example of a first-order reaction is the process of radioactive decay. Each atom
of a radioactive species has a certain probability of undergoing decay within a window of time. The
more of these “reactants” there are, therefore, the more of these decay events we will see, which
means that the process occurs faster the more radioactive atoms are around. From the rate law
above, one can, with the use of calculus, derive the following relationship between the
concentration of radioactive substance A and the time t, as shown on the next page.
A graph of [A] versus time is an exponential function:
Plotting the natural logarithm of [A] versus time, however, would yield a straight line: