Applications of Kinetics Edward A. Mottel Department of Chemistry Rose-Hulman Institute of...
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Transcript of Applications of Kinetics Edward A. Mottel Department of Chemistry Rose-Hulman Institute of...
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.
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.
04/18/23
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.
04/18/23
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
04/18/23
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
04/18/23
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.
04/18/23
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
04/18/23
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.
04/18/23
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.
04/18/23
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.
04/18/23
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
04/18/23
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?
04/18/23
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
04/18/23
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.
04/18/23
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?