A car starts at mile marker 145 on a highway and drives at 55 mi/hrmi/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/hr2 hr=110 miles traveled55 mi/hr2 hr=110 miles traveled

milemarker 145110 miles=milemarker 35milemarker 145110 miles=milemarker 35

If we were to write a formula for this calculation, we might express it as follows:

milemarker=milemarker0(speedtime)milemarker=milemarker0(speedtime)

where milemarkermilemarker is the current milemarker and milemarker0milemarker0 is the initial milemarker.

Similarly, the integrated rate law for a zero-order reaction is expressed as follows:

[A]=[A]0ratetime[A]=[A]0ratetime

or

[A]=[A]0kt[A]=[A]0kt

since

rate=k[A]0=krate=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]0ekt[A]=[A]0ekt

where kk is the rate constant for this reaction.

The integrated rate law for a second-order reaction is expressed as follows:

1[A]=kt+1[A]01[A]=kt+1[A]0

where kk is the rate constant for this reaction.

Part A: The rate constant for a certain reaction is kk = 8.2010³ s1s1 . If the initial reactant concentration was 0.100 MM, what will the concentration be after 14.0 minutes?

Part B: A zero-order reaction has a constant rate of 3.9010⁴ M/sM/s. If after 80.0 seconds the concentration has dropped to 5.5010² MM, what was the initial concentration?