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Kinetics The study of reaction rates. Spontaneous reactions are reactions
that will happen - but we can’t tell how fast.
Diamond will spontaneously turn to graphite – eventually.
Reaction mechanism- the steps by which a reaction takes place.
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Reaction Rate
Rate = Conc. of A at t2 -Conc. of A at t1
t2- t1
Rate =[A]t
Change in concentration per unit time For this reaction N2 + 3H2 2NH3
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As the reaction progresses the concentration H2 goes down
Concentration
Time
[H[H22]]
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As the reaction progresses the concentration N2 goes down 1/3 as fast
Concentration
Time
[H[H22]]
[N[N22]]
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As the reaction progresses the concentration NH3 goes up.
Concentration
Time
[H[H22]]
[N[N22]]
[NH[NH33]]
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Calculating Rates Average rates are taken over long
intervals Instantaneous rates are determined by
finding the slope of a line tangent to the curve at any given point because the rate can change over time
Derivative.
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Average slope method
Concentration
Time
[H[H22]]
tt
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Instantaneous slope method.
Concentration
Time
[H[H22]]
tt
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Defining RateWe can define rate in terms of the
disappearance of the reactant or in terms of the rate of appearance of the product.
In our example N2 + 3H2 2NH3
-[N2] = -3[H2] = 2[NH3] t t t
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Rate Laws Reactions are reversible. As products accumulate they can begin
to turn back into reactants. Early on the rate will depend on only the
amount of reactants present. We want to measure the reactants as
soon as they are mixed. This is called the Initial rate method.
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Two key points The concentration of the products do
not appear in the rate law because this is an initial rate.
The order must be determined experimentally,
can’t be obtained from the equation
Rate LawsRate Laws
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You will find that the rate will only depend on the concentration of the reactants.
Rate = k[NO2]n
This is called a rate law expression. k is called the rate constant. n is the order of the reactant -usually a
positive integer.
2 NO2 2 NO + O2
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The rate of appearance of O2 can be said to be.
Rate' = [O2] = k'[NO2] t
Because there are 2 NO2 for each O2
Rate = 2 x Rate' So k[NO2]
n = 2 x k'[NO2]n
So k = 2 x k'
2 NO2 2 NO + O2
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Types of Rate Laws Differential Rate law - describes how
rate depends on concentration. Integrated Rate Law - Describes how
concentration depends on time. For each type of differential rate law
there is an integrated rate law and vice versa.
Rate laws can help us better understand reaction mechanisms.
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Determining Rate Laws The first step is to determine the form of
the rate law (especially its order). Must be determined from experimental
data. For this reaction
2 N2O5 (aq) 4NO2 (aq) + O2(g)
The reverse reaction won’t play a role
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[N[N22OO55] (mol/L) ] (mol/L) Time (s) Time (s)
1.001.00 00
0.880.88 200200
0.780.78 400400
0.690.69 600600
0.610.61 800800
0.540.54 10001000
0.480.48 12001200
0.430.43 14001400
0.380.38 16001600
0.340.34 18001800
0.300.30 20002000
Now graph the data
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00.10.20.30.40.50.60.70.80.9
1
0 200
400
600
800
1000
1200
1400
1600
1800
2000
To find rate we have to find the slope at two points
We will use the tangent method.
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00.10.20.30.40.50.60.70.80.9
1
0 200
400
600
800
1000
1200
1400
1600
1800
2000
At .90 M the rate is (.98 - .76) = 0.22 =- 5.5x 10 -4 (0-400) -400
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00.10.20.30.40.50.60.70.80.9
1
0 200
400
600
800
1000
1200
1400
1600
1800
2000
At .40 M the rate is (.52 - .31) = 0.22 =- 2.7 x 10 -4 (1000-1800) -800
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Since the rate at twice the concentration is twice as fast the rate law must be..
Rate = -[N2O5] = k[N2O5]1 = k[N2O5] t
We say this reaction is first order in N2O5
The only way to determine order is to run the experiment.
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The method of Initial Rates This method requires that a reaction be
run several times. The initial concentrations of the
reactants are varied. The reaction rate is measured bust after
the reactants are mixed. Eliminates the effect of the reverse
reaction.
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An example For the reaction
BrO3- + 5 Br- + 6H+ 3Br2 + 3 H2O
The general form of the Rate Law is
Rate = k[BrO3-]n[Br-]m[H+]p
We use experimental data to determine the values of n,m,and p
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Initial concentrations (M)
Rate (M/s)
BrOBrO33-- BrBr-- HH++
0.100.10 0.100.10 0.100.10 8.0 x 108.0 x 10--
44
0.200.20 0.100.10 0.100.10 1.6 x 101.6 x 10--
33
0.200.20 0.200.20 0.100.10 3.2 x 103.2 x 10--
33
0.100.10 0.100.10 0.200.20 3.2 x 103.2 x 10--
33
Now we have to see how the rate changes with concentration
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Integrated Rate Law Expresses the reaction concentration as
a function of time. Form of the equation depends on the
order of the rate law (differential). Changes Rate = [A]n
t We will only work with n=0, 1, and 2
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First Order For the reaction 2N2O5 4NO2 + O2
We found the Rate = k[N2O5]1
If concentration doubles rate doubles. If we integrate this equation with respect
to time we get the Integrated Rate Law ln[N2O5] = - kt + ln[N2O5]0
ln is the natural log [N2O5]0 is the initial concentration.
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General form Rate = [A] / t = k[A] ln[A] = - kt + ln[A]0
In the form y = mx + b y = ln[A] m = -k x = t b = ln[A]0
A graph of ln[A] vs time is a straight line.
First Order
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By getting the straight line you can prove it is first order
Often expressed in a ratio
First Order
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By getting the straight line you can prove it is first order
Often expressed in a ratio
First Order
lnA
A = kt0
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Half Life The time required to reach half the
original concentration. If the reaction is first order [A] = [A]0/2 when t = t1/2
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Half Life• The time required to reach half the
original concentration.
• If the reaction is first order
• [A] = [A]0/2 when t = t1/2
ln
A
A = kt0
01 2
2
ln(2) = kt1/2
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Half Life t1/2 = 0.693/k The time to reach half the original
concentration does not depend on the starting concentration.
An easy way to find k
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Second Order Rate = -[A] / t = k[A]2 integrated rate law 1/[A] = kt + 1/[A]0 y= 1/[A] m = k x= t b = 1/[A]0 A straight line if 1/[A] vs t is graphed Knowing k and [A]0 you can calculate [A]
at any time t
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Second Order Half Life [A] = [A]0 /2 at t = t1/2
1
20
2[ ]A = kt +
1
[A]10
22[ [A]
- 1
A] = kt
0 01
tk[A]1 =
1
02
1
[A] = kt
01 2
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Zero Order Rate Law Rate = k[A]0 = k Rate does not change with concentration. Integrated [A] = -kt + [A]0
When [A] = [A]0 /2 t = t1/2
t1/2 = [A]0 /2k
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Most often when reaction happens on a surface because the surface area stays constant.
Also applies to enzyme chemistry.
Zero Order Rate Law
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Time
Concentration
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Time
Concentration
A]/t
t
k =
A]
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More Complicated Reactions BrOBrO33
-- + 5 Br + 5 Br-- + 6H + 6H++ 3Br 3Br22 + 3 H + 3 H22OO
For this reaction we found the rate law For this reaction we found the rate law to beto be
Rate = k[BrORate = k[BrO33--][Br][Br--][H][H++]]22
To investigate this reaction rate we To investigate this reaction rate we need to control the conditions need to control the conditions
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Rate = k[BrORate = k[BrO33--][Br][Br--][H][H++]]22
We set up the experiment so that two of the reactants are in large excess.
[BrO[BrO33--]]00= 1.0 x 10= 1.0 x 10-3-3 M M
[Br[Br--]]0 0 = 1.0 M= 1.0 M [H[H++]]0 0 = 1.0 M= 1.0 M As the reaction proceeds [BrOAs the reaction proceeds [BrO33
--] ]
changes noticably changes noticably [Br[Br--] and [H] and [H++] don’t] don’t
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This rate law can be rewritten Rate = k[BrORate = k[BrO33
--][Br][Br--]]00[H[H++]]00
22
Rate = k[BrRate = k[Br--]]00[H[H++]]00
22[BrO[BrO33--]]
Rate = k’[BrORate = k’[BrO33--]]
This is called a pseudo first order rate This is called a pseudo first order rate law.law.
k =k = k’ k’
[Br[Br--]]00[H[H++]]00
22
Rate = k[BrORate = k[BrO33--][Br][Br--][H][H++]]22
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Reaction Mechanisms The series of steps that actually occur
in a chemical reaction. Kinetics can tell us something about the
mechanism A balanced equation does not tell us
how the reactants become products.
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2NO2 + F2 2NO2F Rate = k[NO2][F2] The proposed mechanism is NO2 + F2 NO2F + F (slow) F + NO2 NO2F (fast) F is called an intermediate It is formed
then consumed in the reaction
Reaction Mechanisms
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Each of the two reactions is called an elementary step .
The rate for a reaction can be written from its molecularity .
Molecularity is the number of pieces that must come together.
Reaction Mechanisms
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Unimolecular step involves one molecule - Rate is rirst order.
Bimolecular step - requires two molecules - Rate is second order
Termolecular step- requires three molecules - Rate is third order
Termolecular steps are almost never heard of because the chances of three molecules coming into contact at the same time are miniscule.
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A products Rate = k[A] A+A products Rate= k[A]2
2A products Rate= k[A]2
A+B products Rate= k[A][B] A+A+B Products Rate= k[A]2[B] 2A+B Products Rate= k[A]2[B] A+B+C Products Rate= k[A][B]
[C]
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How to get rid of intermediates Use the reactions that form them If the reactions are fast and irreversible
- the concentration of the intermediate is based on stoichiometry.
If it is formed by a reversible reaction set the rates equal to each other.
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Formed in reversible reactions 2 NO + O2 2 NO2
Mechanism 2 NO N2O2 (fast)
N2O2 + O2 2 NO2 (slow)
rate = k2[N2O2][O2]
k1[NO]2 = k-1[N2O2]
rate = k2 (k1/ k-1)[NO]2[O2]=k[NO]2[O2]
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Formed in fast reactions 2 IBr I2+ Br2 Mechanism IBr I + Br (fast) IBr + Br I + Br2 (slow)
I + I I2 (fast) Rate = k[IBr][Br] but [Br]= [IBr] Rate = k[IBr][IBr] = k[IBr]2
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Collision theory Molecules must collide to react. Concentration affects rates because
collisions are more likely. Must collide hard enough. Temperature and rate are related. Only a small number of collisions
produce reactions.
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Potential Energy
Reaction Coordinate
Reactants
Products
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Potential Energy
Reaction Coordinate
Reactants
Products
Activation Energy Ea
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Potential Energy
Reaction Coordinate
Reactants
Products
Activated complex
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Potential Energy
Reaction Coordinate
Reactants
ProductsE}
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Potential Energy
Reaction Coordinate
2BrNO
2NO + Br
Br---NO
Br---NO
2
Transition State
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Terms Activation energy - the minimum energy
needed to make a reaction happen. Activated Complex or Transition State -
The arrangement of atoms at the top of the energy barrier.
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Arrhenius Said the at reaction rate should
increase with temperature. At high temperature more molecules
have the energy required to get over the barrier.
The number of collisions with the necessary energy increases exponentially.
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Arrhenius Number of collisions with the required
energy = ze-Ea/RT
z = total collisions e is Euler’s number (opposite of ln) Ea = activation energy
R = ideal gas constant T is temperature in Kelvin
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Problems Observed rate is less than the number
of collisions that have the minimum energy.
Due to Molecular orientation written into equation as p the steric
factor.
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ON
Br
ON
Br
ON
Br
ON
Br
O N Br ONBr ONBr
O NBr
O N BrONBr No Reaction
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Arrhenius Equation
k = zpe-Ea/RT = Ae-Ea/RT
A is called the frequency factor = zp
ln k = -(Ea/R)(1/T) + ln A
Another line !!!!
ln k vs t is a straight line
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Activation Energy and Rates
The final saga
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Mechanisms and rates There is an activation energy for each
elementary step. Activation energy determines k. k = Ae- (Ea/RT)
k determines rate Slowest step (rate determining) must
have the highest activation energy.
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This reaction takes place in three steps
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Ea
First step is fast
Low activation energy
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Second step is slowHigh activation energy
Ea
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Ea
Third step is fastLow activation energy
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Second step is rate determining
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Intermediates are present
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Activated Complexes or Transition States
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Catalysts Speed up a reaction without being used
up in the reaction. Enzymes are biological catalysts. Homogenous Catalysts are in the same
phase as the reactants. Heterogeneous Catalysts are in a
different phase as the reactants.
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How Catalysts Work Catalysts allow reactions to proceed by
a different mechanism - a new pathway. New pathway has a lower activation
energy. More molecules will have this activation
energy. Do not change E
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Pt surface
HH
HH
HH
HH
Hydrogen bonds to surface of metal.
Break H-H bonds
Heterogenous Catalysts
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Pt surface
HH
HH
Heterogenous Catalysts
C HH C
HH
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Pt surface
HH
HH
Heterogenous Catalysts
C HH C
HH
The double bond breaks and bonds to the catalyst.
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Pt surface
HH
HH
Heterogenous Catalysts
C HH C
HH
The hydrogen atoms bond with the carbon
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Pt surface
H
Heterogenous Catalysts
C HH C
HH
H HH
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Homogenous Catalysts Chlorofluorocarbons catalyze the
decomposition of ozone. Enzymes regulating the body
processes. (Protein catalysts)
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Catalysts and rate Catalysts will speed up a reaction but
only to a certain point. Past a certain point adding more
reactants won’t change the rate. Zero Order
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Catalysts and rate.
Concentration of reactants
Rate
Rate increases until the active sites of catalyst are filled.
Then rate is independent of concentration