Kinetics

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Kinetics

• The study of reaction rates.
• Spontaneous reactions are reactions that will
  happen - but we cant 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 DA Dt
• 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
H2
Time
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• As the reaction progresses the concentration N2
  goes down 1/3 as fast

Concentration
N2
H2
Time
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• As the reaction progresses the concentration NH3
  goes up.

Concentration
N2
H2
NH3
Time
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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
DH2
Dt
Time
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• Instantaneous slope method.

Concentration
DH2 D t
Time
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Defining Rate

• We 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
• -DN2 -3DH2 2DNH3
  Dt Dt Dt

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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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Rate Laws

• 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,
• cant be obtained from the equation

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2 NO2 2 NO O2

• You will find that the rate will only depend on
  the concentration of the reactants.
• Rate kNO2n
• This is called a rate law expression.
• k is called the rate constant.
• n is the order of the reactant -usually a
  positive integer.

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2 NO2 2 NO O2

• The rate of appearance of O2 can be said to be.
• Rate' DO2 k'NO2 Dt
• Because there are 2 NO2 for each O2
• Rate 2 x Rate'
• So kNO2n 2 x k'NO2n
• So k 2 x k'

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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 wont play
  a role

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N2O5 (mol/L) Time
(s) 1.00 0 0.88 200 0.78 400 0.69
600 0.61 800 0.54 1000 0.48 1200 0.43
1400 0.38 1600 0.34 1800 0.30 2000

• Now graph the data

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• To find rate we have to find the slope at two
  points
• We will use the tangent method.

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At .90 M the rate is (.98 - .76) 0.22 -
5.5x 10 -4 (0-400) -400
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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 -DN2O5 kN2O51 kN2O5 Dt
• 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
  kBrO3-nBr-mHp
• We use experimental data to determine the values
  of n,m,and p

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Initial concentrations (M)
Rate (M/s)
BrO3-
Br-
H
0.10 0.10 0.10 8.0 x 10-4
0.20 0.10 0.10 1.6 x 10-3
0.20 0.20 0.10 3.2 x 10-3
0.10 0.10 0.20 3.2 x 10-3

• 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 DAn Dt
• We will only work with n0, 1, and 2

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First Order

• For the reaction 2N2O5 4NO2 O2
• We found the Rate kN2O51
• If concentration doubles rate doubles.
• If we integrate this equation with respect to
  time we get the Integrated Rate Law
• lnN2O5 - kt lnN2O50
• ln is the natural log
• N2O50 is the initial concentration.

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First Order

• General form Rate DA / Dt kA
• lnA - kt lnA0
• In the form y mx b
• y lnA m -k
• x t b lnA0
• A graph of lnA vs time is a straight line.

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First Order

• By getting the straight line you can prove it is
  first order
• Often expressed in a ratio

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First Order

• By getting the straight line you can prove it is
  first order
• Often expressed in a ratio

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Half Life

• The time required to reach half the original
  concentration.
• If the reaction is first order
• A A0/2 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 A0/2 when t t1/2

• 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 -DA / Dt kA2
• integrated rate law
• 1/A kt 1/A0
• y 1/A m k
• x t b 1/A0
• A straight line if 1/A vs t is graphed
• Knowing k and A0 you can calculate A at any
  time t

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Second Order Half Life

• A A0 /2 at t t1/2

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Zero Order Rate Law

• Rate kA0 k
• Rate does not change with concentration.
• Integrated A -kt A0
• When A A0 /2 t t1/2
• t1/2 A0 /2k

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Zero Order Rate Law

• Most often when reaction happens on a surface
  because the surface area stays constant.
• Also applies to enzyme chemistry.

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Concentration
Time
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Concentration
DA/Dt
k
DA
Dt
Time
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More Complicated Reactions

• BrO3- 5 Br- 6H 3Br2 3 H2O
• For this reaction we found the rate law to be
• Rate kBrO3-Br-H2
• To investigate this reaction rate we need to
  control the conditions

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Rate kBrO3-Br-H2

• We set up the experiment so that two of the
  reactants are in large excess.
• BrO3-0 1.0 x 10-3 M
• Br-0 1.0 M
• H0 1.0 M
• As the reaction proceeds BrO3- changes
  noticably
• Br- and H dont

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Rate kBrO3-Br-H2

• This rate law can be rewritten
• Rate kBrO3-Br-0H02
• Rate kBr-0H02BrO3-
• Rate kBrO3-
• This is called a pseudo first order rate law.
• k k Br-0H02

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Summary of Rate Laws
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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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Reaction Mechanisms

• 2NO2 F2 2NO2F
• Rate kNO2F2
• 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

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Reaction Mechanisms

• 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.

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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 kA
• AA products Rate kA2
• 2A products Rate kA2
• AB products Rate kAB
• AAB Products Rate kA2B
• 2AB Products Rate kA2B
• ABC Products Rate kABC

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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 k2N2O2O2
• k1NO2 k-1N2O2
• rate k2 (k1/ k-1)NO2O2kNO2O2

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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 kIBrBr but Br IBr
• Rate kIBrIBr kIBr2

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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
Reactants
Products
Reaction Coordinate
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Potential Energy
Activation Energy Ea
Reactants
Products
Reaction Coordinate
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Activated complex
Potential Energy
Reactants
Products
Reaction Coordinate
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Potential Energy

Reactants
DE
Products
Reaction Coordinate
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Br---NO
Potential Energy
Br---NO
Transition State
2BrNO
2NO Br
2
Reaction Coordinate
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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 Eulers 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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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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Ea
Second step is slow High activation energy
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Ea
Third step is fast Low 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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Heterogenous Catalysts

• Hydrogen bonds to surface of metal.
• Break H-H bonds

Pt surface
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Heterogenous Catalysts
Pt surface
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Heterogenous Catalysts

• The double bond breaks and bonds to the catalyst.

Pt surface
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Heterogenous Catalysts

• The hydrogen atoms bond with the carbon

Pt surface
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Heterogenous Catalysts
Pt surface
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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 wont
  change the rate.
• Zero Order

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Catalysts and rate.
Rate

• Rate increases until the active sites of catalyst
  are filled.
• Then rate is independent of concentration

Concentration of reactants
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