A car starts at mile marker 145 on a highway and drives at 55 mi/hr in the direc

Question

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/hr×2 hr=110 miles traveled

milemarker 145110 miles=milemarker 35

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

milemarker=milemarker0(speed×time)

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]0rate×time

or

[A]=[A]0kt

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]0ekt

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.

1) The rate constant for a certain reaction is k = 5.40×103 s1 . If the initial reactant concentration was 0.500 M, what will the concentration be after 19.0 minutes?

2) A zero-order reaction has a constant rate of 3.30×104 M/s. If after 50.0 seconds the concentration has dropped to 2.00×102 M, what was the initial concentration?

Explanation / Answer

here ,

speed of car , v = 55 mi/hr

time taken , t = 2 hours

total distance travelled = speed * time taken

total distance travelled = 55 * 2

total distance travelled = 110 miles

Now, mile marker = 145 - total distance travelled

mile marker = 145 - 110

mile marker = 35 mile

the car will reach 35 mile marker after 2 hours

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