Chapter 14 Chemical Kinetics

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Chapter 14Chemical Kinetics
CHEM 160September 13, 2006
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Factors that Affect Reaction Rates

• Kinetics is the study of how fast chemical
  reactions occur.
• There are 4 important factors which affect rates
  of reactions
• reactant concentration,
• temperature,
• action of catalysts, and
• surface area.
• Goal to understand chemical reactions at the
  molecular level.

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Reaction Rates

• Speed of a reaction is measured by the change in
  concentration with time.
• For a reaction A ? B
• Suppose A reacts to form B. Let us begin with
  1.00 mol A.

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Reaction Rates
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Reaction Rates

• At t 0 (time zero) there is 1.00 mol A (100 red
  spheres) and no B present.
• At t 20 min, there is 0.54 mol A and 0.46 mol
  B.
• At t 40 min, there is 0.30 mol A and 0.70 mol
  B.
• Calculating,

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Reaction Rates

• For the reaction A ? B there are two ways of
  measuring rate
• the speed at which the products appear (i.e.
  change in moles of B per unit time), or
• the speed at which the reactants disappear (i.e.
  the change in moles of A per unit time).

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Reaction Rates

• Change of Rate with Time
• For the reaction A ? B there are two ways of
• Most useful units for rates are to look at
  molarity. Since volume is constant, molarity and
  moles are directly proportional.
• Consider
• C4H9Cl(aq) H2O(l) ? C4H9OH(aq) HCl(aq)

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Reaction Rates

• Change of Rate with Time
• C4H9Cl(aq) H2O(l) ? C4H9OH(aq) HCl(aq)
• We can calculate the average rate in terms of the
  disappearance of C4H9Cl.
• The units for average rate are mol/Ls or M/s.
• The average rate decreases with time.
• We plot C4H9Cl versus time.
• The rate at any instant in time (instantaneous
  rate) is the slope of the tangent to the curve.
• Instantaneous rate is different from average
  rate.
• We usually call the instantaneous rate the rate.

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Reaction Rates

• Reaction Rate and Stoichiometry
• For the reaction
• C4H9Cl(aq) H2O(l) ? C4H9OH(aq) HCl(aq)
• we know
• In general for
• aA bB ? cC dD

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Concentration and Rate

• In general rates increase as concentrations
  increase.
• NH4(aq) NO2-(aq) ? N2(g) 2H2O(l)

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Concentration and Rate

• For the reaction
• NH4(aq) NO2-(aq) ? N2(g) 2H2O(l)
• we note
• as NH4 doubles with NO2- constant the rate
  doubles,
• as NO2- doubles with NH4 constant, the rate
  doubles,
• We conclude rate ? NH4NO2-.
• Rate law
• The constant k is the rate constant.

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Concentration and Rate

• Exponents in the Rate Law
• For a general reaction with rate law
• we say the reaction is mth order in reactant 1
  and nth order in reactant 2.
• The overall order of reaction is m n .
• A reaction can be zeroth order if m, n, are
  zero.
• Note the values of the exponents (orders) have to
  be determined experimentally. They are not
  simply related to stoichiometry.

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Concentration and Rate

• Using Initial Rates to Determines Rate Laws
• A reaction is zero order in a reactant if the
  change in concentration of that reactant produces
  no effect.
• A reaction is first order if doubling the
  concentration causes the rate to double.
• A reacting is nth order if doubling the
  concentration causes an 2n increase in rate.
• Note that the rate constant does not depend on
  concentration.

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The Change of Concentration with Time

• First Order Reactions
• Goal convert rate law into a convenient equation
  to give concentrations as a function of time.
• For a first order reaction, the rate doubles as
  the concentration of a reactant doubles.

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The Change of Concentration with Time

• First Order Reactions
• A plot of lnAt versus t is a straight line with
  slope -k and intercept lnA0.
• In the above we use the natural logarithm, ln,
  which is log to the base e.

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The Change of Concentration with Time

• First Order Reactions

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The Change of Concentration with Time

• Second Order Reactions
• For a second order reaction with just one
  reactant
• A plot of 1/At versus t is a straight line with
  slope k and intercept 1/A0
• For a second order reaction, a plot of lnAt vs.
  t is not linear.

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The Change of Concentration with Time
Second Order Reactions
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The Change of Concentration with Time

• Half-Life
• Half-life is the time taken for the concentration
  of a reactant to drop to half its original value.
• For a first order process, half life, t½ is the
  time taken for A0 to reach ½A0.
• Mathematically,

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The Change of Concentration with Time

• Half-Life
• For a second order reaction, half-life depends in
  the initial concentration

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Temperature and Rate

• The Collision Model
• Most reactions speed up as temperature increases.
  (E.g. food spoils when not refrigerated.)
• When two light sticks are placed in water one at
  room temperature and one in ice, the one at room
  temperature is brighter than the one in ice.
• The chemical reaction responsible for
  chemiluminescence is dependent on temperature
  the higher the temperature, the faster the
  reaction and the brighter the light.

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Temperature and Rate

• The Collision Model
• As temperature increases, the rate increases.

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Temperature and Rate

• The Collision Model
• Since the rate law has no temperature term in it,
  the rate constant must depend on temperature.
• Consider the first order reaction CH3NC ? CH3CN.
• As temperature increases from 190 ?C to 250 ?C
  the rate constant increases from 2.52 ? 10-5 s-1
  to 3.16 ? 10-3 s-1.
• The temperature effect is quite dramatic. Why?
• Observations rates of reactions are affected by
  concentration and temperature.

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Temperature and Rate

• The Collision Model
• Goal develop a model that explains why rates of
  reactions increase as concentration and
  temperature increases.
• The collision model in order for molecules to
  react they must collide.
• The greater the number of collisions the faster
  the rate.
• The more molecules present, the greater the
  probability of collision and the faster the rate.

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Temperature and Rate

• The Collision Model
• The higher the temperature, the more energy
  available to the molecules and the faster the
  rate.
• Complication not all collisions lead to
  products. In fact, only a small fraction of
  collisions lead to product.
• The Orientation Factor
• In order for reaction to occur the reactant
  molecules must collide in the correct orientation
  and with enough energy to form products.

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Temperature and Rate

• The Orientation Factor
• Consider
• Cl NOCl ? NO Cl2
• There are two possible ways that Cl atoms and
  NOCl molecules can collide one is effective and
  one is not.

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Temperature and Rate
The Orientation Factor
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Temperature and Rate

• Activation Energy
• Arrhenius molecules must posses a minimum amount
  of energy to react. Why?
• In order to form products, bonds must be broken
  in the reactants.
• Bond breakage requires energy.
• Activation energy, Ea, is the minimum energy
  required to initiate a chemical reaction.

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Temperature and Rate

• Activation Energy
• Consider the rearrangement of methyl isonitrile
• In H3C-N?C, the C-N?C bond bends until the C-N
  bond breaks and the N?C portion is perpendicular
  to the H3C portion. This structure is called the
  activated complex or transition state.
• The energy required for the above twist and break
  is the activation energy, Ea.
• Once the C-N bond is broken, the N?C portion can
  continue to rotate forming a C-C?N bond.

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Temperature and Rate

• Activation Energy
• The change in energy for the reaction is the
  difference in energy between CH3NC and CH3CN.
• The activation energy is the difference in energy
  between reactants, CH3NC and transition state.
• The rate depends on Ea.
• Notice that if a forward reaction is exothermic
  (CH3NC ? CH3CN), then the reverse reaction is
  endothermic (CH3CN ? CH3NC).

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Temperature and Rate

• Activation Energy
• How does a methyl isonitrile molecule gain enough
  energy to overcome the activation energy barrier?
• From kinetic molecular theory, we know that as
  temperature increases, the total kinetic energy
  increases.
• We can show the fraction of molecules, f, with
  energy equal to or greater than Ea is
• where R is the gas constant (8.314 J/molK).

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Temperature and Rate
Activation Energy
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Temperature and Rate

• The Arrhenius Equation
• Arrhenius discovered most reaction-rate data
  obeyed the Arrhenius equation
• k is the rate constant, Ea is the activation
  energy, R is the gas constant (8.314 J/K-mol) and
  T is the temperature in K.
• A is called the frequency factor.
• A is a measure of the probability of a favorable
  collision.
• Both A and Ea are specific to a given reaction.

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Temperature and Rate

• Determining the Activation Energy
• If we have a lot of data, we can determine Ea and
  A graphically by rearranging the Arrhenius
  equation
• From the above equation, a plot of ln k versus
  1/T will have slope of Ea/R and intercept of ln
  A.

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Temperature and Rate
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Temperature and Rate

• Determining the Activation Energy
• If we do not have a lot of data, then we
  recognize

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Reaction Mechanisms

• The balanced chemical equation provides
  information about the beginning and end of
  reaction.
• The reaction mechanism gives the path of the
  reaction.
• Mechanisms provide a very detailed picture of
  which bonds are broken and formed during the
  course of a reaction.
• Elementary Steps
• Elementary step any process that occurs in a
  single step.

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Reaction Mechanisms

• Elementary Steps
• Molecularity the number of molecules present in
  an elementary step.
• Unimolecular one molecule in the elementary
  step,
• Bimolecular two molecules in the elementary
  step, and
• Termolecular three molecules in the elementary
  step.
• It is not common to see termolecular processes
  (statistically improbable).

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Reaction Mechanisms

• Multistep Mechanisms
• Some reaction proceed through more than one step
• NO2(g) NO2(g) ? NO3(g) NO(g)
• NO3(g) CO(g) ? NO2(g) CO2(g)
• Notice that if we add the above steps, we get the
  overall reaction
• NO2(g) CO(g) ? NO(g) CO2(g)

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Reaction Mechanisms

• Multistep Mechanisms
• If a reaction proceeds via several elementary
  steps, then the elementary steps must add to give
  the balanced chemical equation.
• Intermediate a species which appears in an
  elementary step which is not a reactant or
  product.

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Reaction Mechanisms

• Rate Laws for Elementary Steps
• The rate law of an elementary step is determined
  by its molecularity
• Unimolecular processes are first order,
• Bimolecular processes are second order, and
• Termolecular processes are third order.

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Reaction Mechanisms
Rate Laws for Elementary Steps
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Reaction Mechanisms

• Rate Laws for Multistep Mechanisms
• Rate-determining step is the slowest of the
  elementary steps.
• Therefore, the rate-determining step governs the
  overall rate law for the reaction.
• Mechanisms with an Initial Fast Step
• It is possible for an intermediate to be a
  reactant.
• Consider
• 2NO(g) Br2(g) ? 2NOBr(g)

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Reaction Mechanisms

• Mechanisms with an Initial Fast Step
• 2NO(g) Br2(g) ? 2NOBr(g)
• The experimentally determined rate law is
• Rate kNO2Br2
• Consider the following mechanism

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Reaction Mechanisms

• Mechanisms with an Initial Fast Step
• The rate law is (based on Step 2)
• Rate k2NOBr2NO
• The rate law should not depend on the
  concentration of an intermediate (intermediates
  are usually unstable).
• Assume NOBr2 is unstable, so we express the
  concentration of NOBr2 in terms of NOBr and Br2
  assuming there is an equilibrium in step 1 we have

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Reaction Mechanisms

• Mechanisms with an Initial Fast Step
• By definition of equilibrium
• Therefore, the overall rate law becomes
• Note the final rate law is consistent with the
  experimentally observed rate law.

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Catalysis

• A catalyst changes the rate of a chemical
  reaction.
• There are two types of catalyst
• homogeneous, and
• heterogeneous.
• Chlorine atoms are catalysts for the destruction
  of ozone.
• Homogeneous Catalysis
• The catalyst and reaction is in one phase.

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Catalysis

• Homogeneous Catalysis
• Hydrogen peroxide decomposes very slowly
• 2H2O2(aq) ? 2H2O(l) O2(g)
• In the presence of the bromide ion, the
  decomposition occurs rapidly
• 2Br-(aq) H2O2(aq) 2H(aq) ? Br2(aq)
  2H2O(l).
• Br2(aq) is brown.
• Br2(aq) H2O2(aq) ? 2Br-(aq) 2H(aq) O2(g).
• Br- is a catalyst because it can be recovered at
  the end of the reaction.

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Catalysis

• Homogeneous Catalysis
• Generally, catalysts operate by lowering the
  activation energy for a reaction.

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Catalysis
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Catalysis

• Homogeneous Catalysis
• Catalysts can operate by increasing the number of
  effective collisions.
• That is, from the Arrhenius equation catalysts
  increase k be increasing A or decreasing Ea.
• A catalyst may add intermediates to the reaction.
• Example In the presence of Br-, Br2(aq) is
  generated as an intermediate in the decomposition
  of H2O2.

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Catalysis

• Homogeneous Catalysis
• When a catalyst adds an intermediate, the
  activation energies for both steps must be lower
  than the activation energy for the uncatalyzed
  reaction. The catalyst is in a different phase
  than the reactants and products.
• Heterogeneous Catalysis
• Typical example solid catalyst, gaseous
  reactants and products (catalytic converters in
  cars).
• Most industrial catalysts are heterogeneous.

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Catalysis

• Heterogeneous Catalysis
• First step is adsorption (the binding of reactant
  molecules to the catalyst surface).
• Adsorbed species (atoms or ions) are very
  reactive.
• Molecules are adsorbed onto active sites on the
  catalyst surface.

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Catalysis
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Catalysis

• Heterogeneous Catalysis
• Consider the hydrogenation of ethylene
• C2H4(g) H2(g) ? C2H6(g), ?H -136 kJ/mol.
• The reaction is slow in the absence of a
  catalyst.
• In the presence of a metal catalyst (Ni, Pt or
  Pd) the reaction occurs quickly at room
  temperature.
• First the ethylene and hydrogen molecules are
  adsorbed onto active sites on the metal surface.
• The H-H bond breaks and the H atoms migrate about
  the metal surface.

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Catalysis

• Heterogeneous Catalysis
• When an H atom collides with an ethylene molecule
  on the surface, the C-C ? bond breaks and a C-H ?
  bond forms.
• When C2H6 forms it desorbs from the surface.
• When ethylene and hydrogen are adsorbed onto a
  surface, less energy is required to break the
  bonds and the activation energy for the reaction
  is lowered.
• Enzymes
• Enzymes are biological catalysts.
• Most enzymes are protein molecules with large
  molecular masses (10,000 to 106 amu).

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Catalysis

• Enzymes
• Enzymes have very specific shapes.
• Most enzymes catalyze very specific reactions.
• Substrates undergo reaction at the active site of
  an enzyme.
• A substrate locks into an enzyme and a fast
  reaction occurs.
• The products then move away from the enzyme.

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Catalysis

• Enzymes
• Only substrates that fit into the enzyme lock can
  be involved in the reaction.
• If a molecule binds tightly to an enzyme so that
  another substrate cannot displace it, then the
  active site is blocked and the catalyst is
  inhibited (enzyme inhibitors).
• The number of events (turnover number) catalyzed
  is large for enzymes (103 - 107 per second).

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Catalysis
Enzymes
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End of Chapter 14Chemical Kinetics