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

Part A

The rate constant for a certain reaction is k = 6.70×103 s1 . If the initial reactant concentration was 0.950 M, what will the concentration be after 14.0 minutes?

Part B

A zero-order reaction has a constant rate of 3.00×104 M/s. If after 75.0 seconds the concentration has dropped to 8.50×102 M, what was the initial concentration?

Explanation / Answer

A) given a first order reaction

we know that

for first order reactions

ln[A] = ln [Ao] - kt

given

[Ao] = 0.95

k = 6.7 x 10-3

time (t) = 14 min

t = 14 x 60 = 840 s

so

ln [A] = ln 0.95 - ( 6.7 x 10-3 x 840)

[A] = 3.416 x 10-3

so

the concentration will be 3.416 x 10-3 M

B)

given a zero order reaction

for zero order reactions

[A] = [Ao] - kt

given

[A] = 8.5 x 10-2

k = 3 x 10-4

t = 75

so

8.5 x 10-2 = [Ao] - ( 3 x 10-4 x 75)

[Ao] = 0.1075

so

the initial concentration is 0.1075 M

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