Chem 1310: Introduction to physical chemistry Part 2: Chemical Kinetics

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Chem 1310 Introduction to physical chemistry
Part 2 Chemical Kinetics

• Peter H.M. Budzelaar

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Kinetics vs Thermodynamics

• Thermodynamics show why a reaction wants to
  proceed.
• Kinetics can explain how it proceeds.
• The two topics are complementaryyou will need
  both to understand chemistry.

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Kinetics -the rates of chemical reactions

• How fast does a reaction go?
• Does the rate change over time?
• Can it be influenced?
• What does all this sayabout how the reaction
  proceeds?

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Convoluted reaction paths

• Most reactions follow a complicated course.
• You might see (on paper)
• CH4 Cl2 CH3Cl HCl
• But what actually happens is
• Cl2 hn 2 Cl start ("initiation")
• Cl CH4 HCl CH3 production
• CH3 Cl2 CH3Cl Cl ("propagation")
• 2 Cl Cl2 stop
• CH3 Cl CH3Cl ("termination")
• 2 CH3 C2H6

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Convoluted reaction paths

• Kinetics, the study of the rates of reactions,
  can help us establish mechanisms and predict what
  will happen in "new" circumstances.

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What is a rate?

• Rate of a reactionthe number of moles L-1 s-1
  of reactants passing into products.
• Why the unitstwice the volume, same
  concentration twice as many molecules go.same
  volume, concentrations, wait twice as long twice
  as many molecules go (approx...).

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What is a rate?

• We usually mean the rate at any given moment (the
  instantaneous rate, Dt very small) rather than
  over a whole second or other time spin (the
  average rate, a larger Dt).
• Don't forget stoichiometry here! If not all
  components in a reaction have coefficient 1, we
  define the "rate of the reaction" as the rate of
  (dis)appearance of the components divided by
  their coefficients.

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What is a rate? (2)
Example 4 NH3 3 O2 2 N2 6 H2O (using
smallest possible integer coefficients)

• The rate belongs to the reaction as written.
• Compare with DH calculations, where we also give
  the result for the equation as written.

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Rates, rate lawsand elementary steps

• A "rate law" expresses the dependence of the rate
  on the concentrations of reactants.
• For an elementary step
• A X ...
• we would expect an expression like
• rate k A
• Similarly, for
• A B X ...
• one would expect
• rate k AB

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Rates, rate lawsand elementary steps

• The k values ("rate constants") depend on the
  temperature, and are different for different
  reactions.
• Most "real" reactions consist of many steps. If
  we would know them, we could construct an
  expression for the overall rate. This can depend
  on concentrations in a complicated fashion, as we
  will see.
• Catalysts, compounds that accelerate reactions,
  work by enabling alternative paths (new
  elementary steps), not by affecting rate
  constants of existing elementary steps.

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Measuring rate laws

• The dependence of rate on concentrations may be
  simple, as in
• rate k A
• or it can be complicated, as in
• In practice, you measure the dependence of the
  rate on concentrations, then fit to various
  reasonable "laws".

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Measuring rate lawsfrom initial rates

• Start reaction at a certain concentration.
• Measure conversion in the first 0.1 or so
  seconds.
• Þ initial rate at the original concentration
• Do the same at 0.5, 0.25, 0.125 etc times the
  original concentration(s).
• Þ initial rates at different concentrations
• If there is more than one reactant, vary the
  concentration of each one independently.

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Measuring rate lawsfrom initial rates

• Test for first-order kinetics
• if rate µ A, then etc
• or plot rate vs A Þ straight line
• We write rate (in mol L-1 s-1) k A, k in s-1.
• If there are more components, the reaction may be
  first-order in each rate k AB, k in L
  mol-1 s-1.

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Measuring rate lawsfrom initial rates

• If first-order doesn't work, test for
  second-order kinetics
• if rate µ A2, then
  etc
• or plot rate vs A2 (or Örate vs A) Þ straight
  line
• We write rate (in mol L-1 s-1) k A2, k in L
  mol-1 s-1.
• If the rate does not depend on a particular
  reactant, we say it is zero-order in that
  reactant.

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Measuring rate lawsfrom reaction progress
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Measuring rate lawsfrom reaction progress

• Follow reaction in time, try to fit the curve
  with various models.
• Do this for several initial concentrations, to
  verify the model!
• For a first-order reaction
• Limit for small Dt
• This is a differential equation.
• The solution is
• (verify by differentiation)
• To check for this model plot ln A vs t

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Measuring rate lawsfrom reaction progress

• For a second-order reaction
• Solution
• To check for this model plot 1/A vs t
• For a zero-order reaction
• Solution
• (obviously not valid for large t!)

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First-order reactions and half-life

• Half-life time to go from a certain initial
  reactant concentration to half this initial
  value.
• This does not mean that after two half-lifes all
  reactant has been consumed! Rather, every
  half-life reduces the concentration by a factor
  of 2.

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First-order reactions and half-life
This is called exponential decay.
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Back to the microscopic model

• Why are some reactions faster than others?
• At any given moment, only asmall fraction of the
  moleculeshave enough energy to hopover the
  barrier. The fractionbecomes larger if the
  barrieris reduced (easier, faster reaction)or
  if the temperature is raised(more of the
  molecules haveenough energy).

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Intermezzo explosive reactions

• Once a few molecules hop over, the reaction
  produces so much energy that many more can
  follow. Heat is produced faster than it can
  dissipate even via diffusion of the gaseous
  products.
• A detonator is used to provide the initial bit of
  energy.
• Ammonium nitrate can decompose explosively.
• To what?
• Why would adding kerosene improve the explosive
  power?

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The Arrhenius expression

• Nearly all reactions have a similar temperature
  dependence

Frequency factor what fraction of
collisions could in principle lead to a reaction.
Energy term what fraction of molecules will have
enough energy to pass the barrier.
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The Arrhenius plot

• Plot ln k vs 1/T
• ln k ln A -Ea/RT

intercept ln A
slope -Ea/R
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The rate-limiting step

• The slowest step in a sequence of elementary
  steps
• (the "bottleneck").
• The overall rate is determined by this step.
• Typically corresponds to the highest barrier
  (activation energy) on the path, since frequency
  factors are usually not too different.

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The rate-limiting step

• Overall rate rate of RLS

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Rates and mechanisms

• Single-step mechanism
• rate rate of single step
• e.g. rate kAB, no problem
• Multi-step mechanism
• if first step is RLS,treat as single-step
  (remaining steps don't matter)
• if later step is RLS, things get complicated
• rate k2B, but we don't know B. What now?

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Steady-state approximation

• When the reaction starts, we have B 0. It
  builds up from A, then starts to deplete as also
  A decreases. For a long time it will be nearly
  constant.

this is what we obtain as kin a first-order rate
law
Question what wouldan Arrhenius plotof "k"
produce now?
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Catalysis

• Not faster reactions but new reactions made
  possible by reaction with the catalyst.
• The catalyst does react!It might be
  regeneratedat the end of the reaction,but it is
  not chemically inert.
• Catalysis is not "homeopathic"!

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The best catalyst?

• What is the most common, most versatile
  catalystin chemistry?

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The best catalyst?

• What is the most common, most versatile
  catalystin chemistry?

H
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Enzymes - the catalysts of nature

• Enzymes are proteins containing one or more
  regions or groups specifically adapted to promote
  a chemical reaction. This may be a single H/OH-
  catalyzed reaction of something more complicated,
  including transition-metal catalysis.
• The protein provides a semi-rigid environment
  where the reaction can take place. It is usually
  (shape-)selective, able to distinguish between
  subtly different substrates and to produce
  products with high selectivity.

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Enzymes - the catalysts of nature

• Enzymes require water to be stable.
• They will irreversibly denature at high
  temperatures.
• This is an example of catalyst deactivation.
• Enzymes can get poisoned by molecules that bind
  to them but do not undergo the desired reaction.

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Enzyme kinetics

• Typical behaviour
• Steady-state (assume ES is constant,
  EESE0)
• For small S (like a
  regular two-step reaction)
• For large S (all
  enzyme present as E-S
  complex, rate limited by
  E0)
• "Saturation kinetics"

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Man-made catalysts

• Homogeneous in same phase as reactants(usually
  solution)
• Heterogeneous different phases(usually solid
  catalyst, gaseous reactants)

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Homogeneous catalysts

• Typically small, well-defined transition-metal
  complexes. Designed to do a specific type of
  reaction on a specific type of functional group,
  for a class of substrates.
• Not as specific/selective as enzymes.
• Work under mild conditions (0-120C).
• Used for synthesis of fine chemicals/pharmaceutica
  ls.

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An example ofa homogeneous catalyst
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Heterogeneous catalysts

• Typically metals, metal oxides or silicate-like
  materials with a range of "active sites".
• Tend to produces mixtures of products, with
  distributions determined by product stabilities.
• Used in petrochemical industry and oil refining.

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An example ofa heterogeneous catalyst

• Via dissociation to atoms.
• Works equally well for all NxOy compounds.
• Products are N2 and O2 because N-O bond is weak.
• Requires high temperature to work.
• Can be poisoned lead in gasoline precipitates on
  surfaces, blocks active sites.