To understand how to use integrated rate laws to solve for concentration.
A car starts at mile marker 145 on a highway and drives at 55 mi/hr in the direction of decreasing marker numbers. What mile marker will the car reach after 2 hours?
This problem can easily be solved by calculating how far the car travels and subtracting that distance from the starting marker of 145.
55 mi/hrÃ2 hr=110 miles traveled
milemarker 145â110 miles=milemarker 35
If we were to write a formula for this calculation, we might express it as follows:
milemarker=milemarker0â(speedÃtime)
where milemarker is the current milemarker and milemarker0 is the initial milemarker.
Similarly, the integrated rate law for a zero-order reaction is expressed as follows:
[A]=[A]0ârateÃtime
or
[A]=[A]0âkt
since
rate=k[A]0=k
A zero-order reaction (Figure 1) proceeds uniformly over time. In other words, the rate does not change as the reactant concentration changes. In contrast, first-order reaction rates (Figure 2) do change over time as the reactant concentration changes.
Because the rate of a first-order reaction is nonuniform, its integrated rate law is slightly more complicated than that of a zero-order reaction.
The integrated rate law for a first-order reaction is expressed as follows:
[A]=[A]0eâkt
where k is the rate constant for this reaction.
The integrated rate law for a second-order reaction is expressed as follows:
1[A]=kt+1[A0]
where k is the rate constant for this reaction.
PART A
The rate constant for a certain reaction is k = 3.50Ã10â3 sâ1 . If the initial reactant concentration was 0.400 M, what will the concentration be after 5.00 minutes?
Express your answer with the appropriate units.
PART B
A zero-order reaction has a constant rate of 5.00Ã10â4M/s. If after 75.0 seconds the concentration has dropped to 2.50Ã10â2M, what was the initial concentration?
Express your answer with the appropriate units.
