Determining the value of k

Finding k now involves only substituting in the data from any one row of the table. Let’s use row #1 of the problem we've been working on:

rearranging for k gives:

Solving that (pretty straight-forward) leaves us with:

To be sure that you understand, you should try some problems on your own.

All of this raises the question “why do I care?” There are really four answers to that question... the first is basic, the other three are important

1. Your teacher is going to ask you to do it on the test.
2. Knowing the rate law allows you to predict rates under other conditions.
3. First order reactions (those with only one exponent and where that exponent is 1) act in very useful and predictable ways
4. Rate laws are the basis of equilibrium