Kinetics Overview

1
Kinetics Overview

• Lets look at the big picture
• Chemical Kinetics is the area of chemistry that
  deals with reaction rates.
• Why do we study chemical kinetics?
• -Determine how fast a reaction takes place/how
  long we need reaction to go to reach certain
  completion (or to reach equilibrium).
• -Figure out the mechanism of the reaction
  (helpful when trying to make a reaction work
  better/shut it off).

2
Kinetics Overview

• What do we mean by reaction rates?
• What do we mean by the rate of a reaction?
• How the concentration of a reactant or product
  changes over time.
• Reaction rates are things that we can easily
  measure in the lab
• All you need is a stopwatch and a way to look at
  the reaction

3
Kinetics Overview

• What determines what the rate of a reaction will
  be?
• Reaction Rates Depend on
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• We describe how a reaction is influenced by these
  different factors using a Rate Law.
• There are two different types of rate laws
• Differential how rate is dependent on
  concentration
• Integrated how concentration depends on time
• Differential Rate Laws are what we typically
  think of when we say rate law

4
Kinetics Overview

• What determines what the rate of a reaction will
  be?
• Reaction Rates Depend on
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• In a rate law one of the factors above is easily
  manipulated, which one is it?
• Concentration of the reacting species
• The other factors are rolled into the rate
  constant (k)which means that a rate constant is
  only good for a certain temperature (because of
  the Arrhenius equation).

5
Kinetics Overview

• What does a rate law look like?
• Differential rate laws have the general form
• Rate k reactant speciesn
• Where k the rate constant for that reaction at
  a given temperature
• n the order of the reaction with respect to a
  given reactant species
• Rate the rate of the reaction
• There are many different ways we can describe the
  rate of a given reaction. We MUST be careful to
  clearly define the rate (it can have a big effect
  on the value we determine for the rate constant).
  

6
Kinetics Overview

• Defining the rate we are looking at
• A 2B ? 3C 4D
• Rate of reaction - D A -1 D B 1 D
  C 1 D D kAmBn
• Dt 2 Dt 3 Dt
  4 Dt
• These are all valid ways to describe the rate of
  this reaction.
• If we look at the coefficients of the balanced
  reaction, 4 molecules of D will be formed for
  each molecule of A that is consumed. The rate
  of formation of D over time would then be 4x
  that of the consumption of A. To make these
  two rates equal to each other we must multiply
  the rate of formation of D over time by (1/4).

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Kinetics Overview

• Example of relating k and rate of reaction
• 2 NO2 (g) ? 2 NO (g) O2 (g)
• If we studied this reaction in the lab would
  could define the rate law in the following
  fashion
• Rate -1 D NO2 kNO2n
• 2 Dt
• Rate D O2 kNO2n
• Dt
• in this example 2 k k or k k/2
• The value of k can vary for a reaction depending
  on our
• definition of rate of the reaction.

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Kinetics Overview

• What do we do once weve proposed a rate law?
• Once weve looked at a reaction and proposed a
  rate law we have to determine the order of the
  reaction. There are a couple of ways to do that
  
• -Plotting data from integrated rate laws (see
  Buret Kinetics Power Point presentation from
  class)
• -Isolation method with initial rates. You will
  be given a table of data with different
  concentrations of reactants and the initial rate
  of the reaction. (The book does a good job of
  demonstrating how to do these problems if you
  are still a bit shaky. See section 12.3 of
  Zumdahl)
• Once we know the order of the reaction we can use
  the integrated rate law which allows us to relate
  concentration to time. Also opens the doors to
  calculating the half life of a reaction.

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Kinetics Overview

• Rate Laws for different orders
• Zero Order
• Differential Rate kAo k
• Integrated A -kt Ao
• First Order
• Differential Rate kA1
• Integrated lnA -kt lnAo
• Second Order
• Differential Rate kA2 or kAB if A
  B
• Integrated 1/A kt 1/Ao
• For each integrated rate law you should know what
  to plot for each order and what you would expect
  the graph to look like.

10
Kinetics Overview

• Half lifes for different order reactions
  (assuming 1 reagent)
• Another very useful application of integrated
  rate laws is the ability to determine the half
  life for a reaction (time where A Ao/2).
  This is very useful in looking at how long drugs
  will stay in a system, how long environmental
  waste will be present, and how long a given
  compound will be stable.
• Zero Order
• t1/2 Ao/2k (depends on Ao, half life gets
  shorter over time)
• First Order
• t1/2 ln 2/k (no Ao dependence, half life
  stays constant over time)
• Second Order
• t1/2 1/kAo (depends on Ao, half life gets
  longer over time)

11
Kinetics Overview

• Pseudo 1st order kinetics
• What do you do when you have more than 1 reagent
  and everything is too complicated???
• To this point all rate laws have been of the
  form
• rate kAn
• However, this simple form will not work for a
  reaction like
• A B ? C D (where A is not B
• The rate law for this reaction would be
• Rate kAmBn
• This leads to a more complicated integrated rate
  law that doesnt fit the simple y mx b form.

12
Kinetics Overview

• Pseudo 1st order kinetics
• A B ? C D
• To simplify this problem we use pseudo 1st order
  kinetics.
• First, remember that the rate constant k, is a
  constant for this reaction.
• If we use a large enough relative concentration
  of one of the reactants in the rate law (lets
  choose B), such that B Bo the
  concentration of B is essentially constant
  through the reaction.
• We can then say the rate constant times the
  essentially constant B equals a new constant
  k.
• k B k

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Kinetics Overview

• Pseudo 1st order kinetics
• A B ? C D
• If we substitute this new constant k into the
  original rate law
• Rate kAmBn ? Rate kAm
• The rate of the reaction is now essentially a
  first order process which we can solve using
  either an integrated rate law. But when we
  determine k for this pseudo 1st order process,
  we still must do some work to calculate k for the
  reaction.
• Remember that k k B, so if we know the Bo
  of the reaction we can easily solve for k of the
  overall reaction.
• This is a very useful tool to make really
  complicated problems simple.

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Kinetics Overview

• What does order tell us?
• Other then telling us what integrated rate law to
  use to find k, what does the order of a
  reaction tell us?
• Allows us to experimentally determine which step
  is rate determining. Why do we care about that?
• Because of molecularity, we have a snap-shot of
  the number and kind of molecules that are
  colliding in the transition state of the rate
  determining step! We can see the reaction
  taking place,
• The order of a reaction gives us a virtual
  snapshot into what the transition state of the
  reaction looks like!
• Allows us to gain information about the
  mechanism of the reaction that we are studying.

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Kinetics Overview

• Reaction mechanisms
• Reaction mechanisms are the written descriptions
  of the series of steps that take place in a
  chemical reaction.
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• Tells stoichiometry, but no info on reaction
  mechanism.
• NO2 (g) NO2 (g) ? NO3 (g) NO (g) k1 (slow
  step)
• NO3 (g) CO (g) ? NO2 CO2 (g) k2 (fast
  step)
• Each of these steps is an elementary step, a
  reaction whose rate law can be written from its
  molecularity.
• NO3 is produced in formed and consumed in the
  overall reaction, but isnt starting material or
  product intermediate.

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Kinetics Overview

• Reaction mechanisms
• Reaction mechanisms must obey two requirements
• 1. The sum of the overall elementary steps must
  give the overall balanced equation
• 2. The mechanism must agree with experimentally
  determined rate law.
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• NO2 (g) NO2 (g) ? NO3 (g) NO (g) k1(slow
  step)
• NO3 (g) CO (g) ? NO2 CO2 (g) k2 (fast
  step)
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• Given that the experimental rate k NO22. We
  know that the kinetics of this reaction will be
  based on RDS (slow step).

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Kinetics Overview

• Reaction mechanisms
• Reaction mechanisms must obey two requirements
• 1. The sum of the overall elementary steps must
  give the overall balanced equation
• 2. The mechanism must agree with experimentally
  determined rate law.
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• NO2 (g) NO2 (g) ? NO3 (g) NO (g) k1(slow
  step)
• NO3 (g) CO (g) ? NO2 CO2 (g) k2 (fast
  step)
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• Because each step in the mechanism is an
  elementary step, we can write the rate law from
  the initial step of the reaction.
• Rate (step 1) k NO22 Rate (experimental)
  k NO22

18
Kinetics Overview

• Reaction mechanisms
• Reaction mechanisms must obey two requirements
• 1. The sum of the overall elementary steps must
  give the overall balanced equation
• 2. The mechanism must agree with experimentally
  determined rate law.
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• NO2 (g) NO2 (g) ? NO3 (g) NO (g) k1(slow
  step)
• NO3 (g) CO (g) ? NO2 CO2 (g) k2 (fast
  step)
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• This is a valid reaction mechanism and MAY be the
  how the reaction takes place.

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Kinetics Overview

• Collision Model/Arrhenius Equation
• Why do reaction rates depend on
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• In order to answer these questions, scientists
  have proposed a collision model which says
• Reactions can take place when we have collisions
  of molecules.
• Sothe more concentrated the solution, the more
  collisions, and more reactions can take place
• But why dont all collisions lead to a reaction?

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Kinetics Overview

• Collision Model/Arrhenius Equation
• Why do reaction rates depend on
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• Each reaction has a certain energy
  barrier that must be reached for a reaction
  to take place (Ea)
• Not enough energy? no reaction, wrong
  conformation?
• no reaction. Higher Temp? More energy
  to get over barrier

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Kinetics Overview

• Collision Model/Arrhenius Equation
• Why do reaction rates depend on
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• The Collision Model can be summed up by one of
  the greatest equations in all of the land
  Arrhenius equation
• k A e -Ea/RT
• Where A is the frequency factor (which takes the
  nature of the reacting species into account) and
  Ea is the activation energy.
• This equation also shows why a rate constant is
  only valid for 1 temp.

22
Kinetics Overview

• Catalysts
• Why do reaction rates depend on?
• 1. The nature of the reacting species
• 2. The concentration of the reacting species
• 3. The temperature of the reaction
• 4. The presence or absence of a catalyst
• The last thing that will effect the rate of a
  reaction is a catalyst.
• Catalysts speed up the rate of reaction without
  being consumed (it will get consumed, it just
  gets regenerated later)
• There are two types of catalysts
• -Heterogeneous different phase
• -Homogeneous same phase (Enzymes are the
  ultimate cat.)
• Both types work using the same principle
• Lower the activation energy of a reaction (giving
  a lower energy pathway for the reaction to take
  place)

23
Kinetics Overview

• Collision Model/Arrhenius Equation
• The easiest way to see how a catalyst works is to
  look at an energy diagram
• The catalyst offers an alternative pathway which
  has a lower EaArrhenius equation tells us that
  this will have a faster rate

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Kinetics Overview

• Conclusion
• When I think about kinetics, it helps me to break
  it into a series of different steps that we can
  use to answer questions.
• -What is the rate Im looking at? How have I
  defined the rate law?
• -What is the order of the reaction? What does
  that tell me?
• -What is the rate constant in this reaction?
  That will let me determine the concentration of
  reactants at different times (which is really
  useful).
• -What mechanism does this kinetic data support?
• -How can I improve/change the reaction rate?
  Increase concentrations? Increase temperature?
  Add a catalyst?
• -Are there other questions being asked?