Applications of Kinetics

Edward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

04/18/23

Kinetics Applications

Reading assignment:• Zumdahl: Chapter 21.1-21.7

Comparison of• orders of reaction• rates of reaction

Half-life Percentage Completion Nuclear dating processes

Orders of Reaction

On a graph of concentration versus time,plot zero, first and second order data sets

that have the same initial concentration andthe same numeric value for the rate constant.

Will the lines ever cross?

Describe the shape of each lineand interpret the line shape.

Microsoft Excel Chart

Reaction Rate Constants

On a graph of concentration versus time,plot a system with the same reaction order, but

with three different numeric values for the rate constant.

The second rate constant should betwice the first rate constant,

and the third rate constant should beten times the first rate constant.

Will the lines ever cross?Describe the shape of each line

and interpret the line shape.

Microsoft Excel Chart

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Half-Life

The half-life of a reaction is the time required for a given amount of a reactant to be consumed.• Could be a concentration or a pressure.• Can be determined either graphically or

analytically.

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Graphical Determination of Half-Life2 NO2(g) 2 NO(g) + O2(g)

Determine if the half-life for the decompositionof nitrogen dioxide is constant.

0 200 400 600 800 1000Time (s)

100

200

300

400

500P

NO

2 (t

orr

)

474 torr

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Graphical Determination of Half-Life2 NO2(g) 2 NO(g) + O2(g)

Determine if the half-life for the decompositionof nitrogen dioxide is constant.

0 200 400 600 800 1000Time (s)

100

200

300

400

500P

NO

2 (t

orr

)

474 torr

237 torr

139 s118 torr

417-139 = 278 s

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Half-Life and Percentage Completion

The half-life equation is derived from the integrated solution of the rate equation.

Percentage completion calculations are similar, using appropriate initial and final amounts of reactant.

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NO2 Decomposition is Second-Order

(PNO2)t-1 = 1.52 x 10- 5 (t - to) + (PNO2)o

-1

47404742

time until thefirst half-life

t = 139 s

Determine the second half-life for NO2.

t = 278 s

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Percentage Completion

Use the integrated form of the rate equation to determine the amount of time required for the reaction to be 80% completed from the original reaction conditions.

Confirm your answer using the graph.

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If 80% of the nitrogen dioxide is decomposed,then 20% remains.

0 200 400 600 800 1000Time (s)

100

200

300

400

500P

NO

2 (t

orr

)

474 torr

95 torr

555 s

Graphical Determination of Percent Completion

2 NO2(g) 2 NO(g) + O2(g)

Alcohol Evaporation at Room Temperature

0123456789

0 100 200 300 400 500 600 700 800

Time (s)

Mas

s (

g)

Ethanoly = - 0.0099x + 7.941

R2 = 0.9991

Determine if the half-life for the evaporationof ethanol is constant.

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Radioactive Dating

First-order kinetic processes have constant half-lives.• Can you prove this?

Almost all radioactive processes are first-order.• This allows "dating" of objects if such a

first-order process is occurring.

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Radioactive Dating

131I (mg)

100.

50.0

25.0

12.5

6.25

PercentReacted

0

50

75

87½

93¾

Period

0

1

2

3

4

Time (d)

0

8.1

16.2

24.3

32.4

TimeChange (d)

8.1

8.1

8.1

8.1

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Radioactive Dating

The length of the dating "window" depends on the half-life of the process.• A practical limit is about 0.1 to 10 half-lives.

How much of a reactant remains after• 0.1 half-lives• 10 half-lives

Why does this dating "window" exist?

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Radioactive ProcessesRadioactive

SpeciesReaction Half-Life Applications

3H 3H3He + 12.3 y tracer studies

14C 5730 y dating of formerliving artifacts

234U 2.47 x 105 y

238U age of rocks

14C 14N +

234U 230Th + 4He

238U 234Th + 4He 4.51 x 109 y

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Carbon-14 Dating

14C is produced in the upper atmosphere by the bombardment of 14N with cosmic rays.

The carbon-14 produced reacts to form carbon dioxide, consumed by plants which are eaten by animals.

Every living thing has carbon-14 in it, but the ingestion process stops at death.

The ratio of the amount of carbon-14 when measured to the amount expected while alive can be used to estimate the age of the organism.

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Carbon-14 Dating

What assumptions are implicit in this dating process?

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Atomic Clocks

Radioactive dating has been used to estimate the age of rocks.

If the age of the earth is about 4.5 x 109 years, why does a typical uranium sample contain mostly 238U and a small amount of 235U, but virtually no 234U?

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