Consider a bathtub in which there is some bathing salt dissolved. We now fill in more water, keeping the bottom plug in. What happens?
Since there is no reaction,  and since there is no outflow . The mass balance becomes
or
Using a mass balance for total volume, however, it is evident that and that  Thus we get
Note that there is no reaction and hence no reaction rate or rate law involved, and yet . We can thus draw the conclusion that reaction rate can not be defined in a general manner using . One must first write down a mass balance before a link between  and the reaction rate can be found. Many textbooks, however, define reaction rate as
without mentioning that this definition implicitly assumes that the system is closed, has a constant volume and that there is only one reaction.