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Chemical Kinetics
The area of chemistry concernedwith the rates, or speeds, of
chemical reactions.
The Rate of a Chemical
Reaction
Reaction rate -
Units of M/s.
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What is happening to the concentration of A as timegoes by?
A+B C
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What is the sign of the change of
concentration of A: [A]?
Remember, is final initial.
1. Positive
2. Negative
A+ B C
As the reaction proceeds, the concentrationof A decreases
The rate of change can be defined in termsof A decreasing:
What is happening to the concentration of C as timegoes by?
A+B C
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If rate is defined by Cyou have:
A+B C
Which reaction has the faster
rate?1. A + B C
2. D + E F
A+B C
D+E F
Is the rate of the
reaction constant during
the course of the
reaction?
AB
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Therefore, calculations of rate using the change
in concentration formula will give differentresults depending on what time interval youchoose.
Making the interval of time smaller and smallerwe can calculate the rate of the reaction at aspecific instance in time.
Rates can be defined interms of changes of
pressure as well aschanges ofconcentration.
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Comparing Rate of Change
of Reactants and Products
Not all substances in a chemical reaction appearor disappear at the same rate.
Lets look at a simple demonstration tounderstand the relationships.
2
Paper Demo
Two pieces of paper make one booklet.
2A B
The process was recorded for 30 s.
Initial Final
Paper
Booklets
How does the rate of disappearance of
A (the paper) relate to
B (the booklets)?
Paper Demo. 2A B
t
B
t
A
2
1rate
1. B appears at twice the rate that A isdisappearing.
2. A disappears at twice the rate that B isappearing.
3. A disappears at the same rate that B appears.
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t
B
t
A
2
1rate
So, for the reaction:
aA + bB cC + dD
When a question asks you to write therate expression for a reaction in terms ofthe disappearance of the reactants and theappearance of the products, this (above)
is what they want you to do.
For the reaction
BrO3- + 5Br - + 6H+ 3Br2 + 3H2O
the value of [BrO3-]/t = 1.5 10-2 M/s at a particular
time. What is the value of the [Br -]/t at the sameinstant?
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For the reaction
BrO3+ 5Br + 6H+ 3Br2 + 3H2O
Brdisappears at a rate of 7.5 10-2 M/s at a particular
time. What is the value of the appearance of Br2 at the sameinstant?
The Rate Law
Rate Law -
For the reaction:
aA + bB cC + dD
The rate law is:
rate = .
We will learn how to determine
x and y later, for now, lets look at someexamples of reactions and rate laws.
3
A(aq) + B(aq) C(aq) + D(aq)
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k is called the rate constant.
khas units and is obtained by solving theequation for k.
Every time this reaction takes place, at a constanttemperature, the same value for kwill beobtained
Rate = k[A]
For the reaction:
2NO(g) + 2H2 N2(g) + 2H2O(g)
The rate law was determined to be:
rate = k[NO]2[H2]
The reaction is said to be
Orders can be zero (whenconcentration does not affect the rate.)
Orders can be fractions
Rate = k[NO]2[H2]
Lets look at what this rate law tells us about
the connection between concentrations and
rate. What happens to the rate if [H2] is
doubled (while [NO] remains constant?)
1. Rate stays the same2. Rate doubles
3. Rate is cut in half
4. Rate quadruples
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Rate = k[NO]2[H2]
Lets look at what this rate law tells us about
the connection between concentrations and
rate. What happens to the rate if [NO] is
doubled (while [H2]remains constant?)
1. Rate stays the same
2. Rate doubles
3. Rate is cut in half
4. Rate quadruples
Determination of a Rate Law
As stated earlier, the orders of the rate law mustbe determined experimentally.
The best way to learn how to take experimentaldata and obtain a rate law is throughdemonstration. Lets work through a couple ofexamples.
4
Nitric oxide gas, NO, reacts with chlorine gasaccording to the equation: NO + 1/2 Cl2NOCl.
The following initial rates of reaction have beenmeasured for the given reagent concentration.Rate (M/hr) NO (M) Cl2(M)
1.19 0.25 1.5
4.79 0.50 1.59.59 0.50 3.0
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Hydroxide ion is involved in but not consumed by thereaction:
OCl- + I- OI- + Cl-
(a) From the data in the table, determine the order of thereaction with respect to OCl-, I-, and OH-
OH-
[OCl-],M [I-], M [OH-], M Rate, M/s
0.0080 0.0040 2.00 4.8 10-4
0.0040 0.0080 2.00 5.0 10-4
0.0040 0.0040 2.00 2.4 10-4
0.0040 0.0040 1.00 4.6 10-4
0.0040 0.0040 0.50 9.4 10-4
(b) Write therate law, anddetermine avalue of therate constant, k
[OCl-],M [I-], M [OH-] , M Ra te , M/ s
0.0080 0.0040 2.00 4.8 10-4
0.0040 0.0080 2.00 5.0 10-4
0.0040 0.0040 2.00 2.4 10-4
0.0040 0.0040 1.00 4.6 10-4
0.0040 0.0040 0.50 9.4 10-4
Now that we know the order, what
is the rate law and the value of k?
1. Rate = k[OCl-][I-][OH-] k = 60 M/s
2. Rate = k[OCl-][I-]/[OH-] k= 30 1/Ms
3. Rate = k[OCl-][I-][OH-]-1 k= 30 1/s
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The Integrated Rate Law
Rate laws can be used to determine the
concentration of reactants at any time during thecourse of a reaction.
We will look at the most simple cases:
1st order overall
2nd order overall
0th order
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First-Order Kinetics
For the reaction:
Aproducts
because the coefficient is one
This can give us:
ln = kt[A]
[A]o
The previous equation forms this equation using calculus.
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1st Order Kinetics
2N2O5 4NO2 + O2
Because concentration is proportional topressure in a gas, partial pressures can be usedin place of the concentrations.
ln P = -kt + ln Po
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A(g) B(s) + C(s)
Half-life - (t1/2) -
at t1/2,
For a first order reaction we have:
ln = kt[A][A]o
Gives:
First-Order Kinetics and
the Half-Life6
t1/2 =0.693
k
This is the half-life equation for a first order
reaction.
Notice that it is independent of the [A].
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If a 1st order reaction started with 8 M of
substance A, and the half-life was 1 minute,
what concentration would remain after 3
minutes?1. 5 M
2. 4 M
3. 2 M
4. 1 M
5. 0.5 M
A first-order reaction has a rate constant of 3.0 10-3 s-1.The time required for the reaction to be 75% completeis?
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What if the question were:
A first-order reaction has a rate constant of 3.0 10-3 s-1.The time required for the reaction to be 30% completeis?
Second-Order Reactions
Aproducts
Setting each equation equal to each other and usingcalculus gives:
7
ktoA][
1
A][
1
o
A][
1
A][
1kt
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What will the slope
equal?
y = mx + b
oA][
1
A][
1 kt1. kt
2. k
3. -k
4. 1/[A]o
1[A]
1[A]o
+ kt=
For the half-life equation, [A] = [A]o/2 whent = t1/2.
Substitute this into the above equation gives:
What about zero-order reactions?
Rate = k[A]0 or
A plot of [A] versus t is a straight line.
What would a plot of rate versus time look like?
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Using Plots to Determine Order
Collision Theory
What is the difference between baking a cake at250o versus 350oF?
8
Dependence of Rate Constant
on Temperature
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The Collision Theory of Chemical
Kinetics
What is occurring on the molecular level that
causes rate to increase with concentration andtemperature?
Rate increases with the number of collisions persecond.
What happens to the number ofcollisions as the concentration
increases?
Concentration and Number of
Collisions
We must have a collision in order to have areaction.
If every collision resulted in a reaction, all reactionswould occur virtually instantaneously.
So, why do some reactions take minutes, hours,
even days to happen?
Activation Energy -
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Potential Energy Diagrams
Based on what we have learned, why does the
reaction rate increase with temperature?
The Arrhenius Equation
k= Ae-Ea/RT
What unit would
temperature be in?
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k= Ae-Ea/RT
If we take the natural log of both sides we get:
RTAlnln Eak A plot of lnk
vs 1/T gives a
straight line
with slope = ?
As Ea goes ,
As T goes ,
ln k vs. 1/T
Take the Arrhenius equation:
and derive a two point equation for two differenttemperatures (T1 and T2) and two different rateconstants (k1 and k2)
AlnT
1
R
Eln a
k
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The activation energy for the following first-order reactionis 102 kJ/mol.
N2O5(g) 2NO2(g) + 1/2O2(g)
The value of the rate constant (k) is 1.35 10-4
s-1
at 35o
C.What is the value of kat 0oC?
The quantity A is thefrequency factor.
This takes into accounttwo factors:
1.
2.
Reaction Mechanisms
A chemical equation does not give us a goodpicture of how the atoms rearrange themselves toform products. It is a sum of several
Elementary steps -
Reaction mechanism -
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Lets consider the reaction:
2NO + O2 2NO2
Fact: While monitoring the reaction, it was found thatN2O2 existed for a brief time.
What does this mean?
Instead this is what is proposed:
NO + NO N2O2
N2O2 + O2 2NO2
Elementary step
Elementary step
N2O2 is an intermediate -
They are canceled as you add theelementary steps
unimolecular reaction - an elementary step inwhich only one reacting molecule participates
bimolecular reaction -
termolecular reaction - an elementary stepinvolving three molecules
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In thes mechanism for the formation
of NO 2, what type or types of
elementary step does it have?
1. Unimolecular
2. Bimolecular
3. termolecular
NO + NO N2O2
N2O2 + O2 2NO2
2NO + O2 2NO2
Rate Laws and Elementary Steps
The rate law of an elementary step canbedetermined by using the coefficients as the order.
Aproducts
A + B products
A + A products
NOTE: this is not true for the overall equation!only for the elementary step!
Remember: How do you determine theorders of an overall reaction?
Rate-determining step -
.
The rate of this step gives the rate of the overallreaction.
Lets look at a specific example:
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The rate law for the reaction:
H2O2 + 2H+ + 2I- I2 + 2H2O
is rate = k[H2O2][I-]. The following mechanism has
been suggested.H2O2 + I
- HOI + OH-
OH- + H+ H2O
HOI + H+ + I- I2 + H2O
Which step would be the rate-determining step?
slow
fast
fast
What is(are) the intermediate(s)
in the mechanism?
1. HOI
2. OH-
3. H+
4. HOI and OH-
5. I- and H2O H2O2 + I- HOI + OH-
OH- + H+ H2O
HOI + H+ + I- I2 + H2O
slow
fast
fast
Catalysis
Catalyst -
The substance reacts within an elementary step ofthe mechanism but is regenerated in a subsequentstep.
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Uncatalyzed vs. Catalyzed
There are three general types of catalysts.
Heterogeneous Catalyst
Homogeneous Catalyst
Enzyme Catalyst
Heterogeneous and
Homogeneous Catalysts
These are simply defined by the state of the catalyst.
Often a solid catalyst that a gas is passed through
Catalytic converter on a car is an example
All aqueous or all gases, for example.
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Enzymes
Often made up of very large and complexmolecules with molar masses in the thousands.
All aspects of a catalyst apply to enzymes.
Enzyme
UbiquitinActivatedEnzyme
End of Kinetics Unit