Determining rate: Isolation Method

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Determining rate Isolation Method

• For multiple reactants the integrated rate
  equation can get quite complex
• Simplify things by having all reactants except
  one, A, present in great excess so their
  concentrations can be considered constant
  (usually 10 100 x A)
• A B ? products

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• (i) Solve to find a
• (ii) ß can be obtained by varying b0 and plotting
  log k versus log b0
• slope
• log k log k ß log b0
• intercept

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Half-Life Method

• Recall, we define the half-life of a reaction to
  be the time at which
• a ½ a0
• ? Plug in a ½ a0 into the integrated rate
  equations and solve for t

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Half-Life Method

• Can use these expressions to determine reaction
  order and rate coefficient
• (i) Follow a reaction over several half-lives and
  examine the dependence of the t½s on
  concentration at the start of the t½
• (ii) Perform several different experiments with
  different initial concentrations and determine
  the first t½ for each.

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Differential Method

• Look at the generalized rate law at t 0 (method
  of initial rates)
• By varying the values of a0 (holding b0 etc.
  constant) and measuring the initial rates, we can
  find a
• Similarly, by varying b0 (holding a0 etc.
  constant) ... one can find ß

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Alternatively, for Take tangents to the
concentration vs. time plot at various points.
Plot log (tangents) vs. log a
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Comparison of the Techniques

• (i) Isolation method means many reactions can be
  studied under pseudo-first order conditions
• with the integral method we do not need to know
  the absolute concentration of A, but only
  relative values.
• half-life technique also doesnt require
  absolute concentrations
• 1st order reaction, t½ is independent of
  concentration

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Comparison of the Techniques

• (ii) Order of reaction can be determined in one
  plot using the differential method but....
• rate constant is found by extrapolation to an
  intercept, increasing the error in k
• tangents by eye are subject to considerable
  uncertainty.

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Dependence on Temperature

• Rate constant ? Rate Coefficient
• The rate coefficient is found experimentally to
  depend on temperature (sometimes very strongly)
• activation energy
• k A exp (-EA / R T) (Arrhenius)
• pre-exponential factor

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Dependence on Temperature

• Physical interpretation
• A - collision frequency factor
• - rate of collisions
• exp (-EA / R T) - fraction of collisions with
  energy in excess of EA
• - (Boltzmann factor)
• A exp (-EA / R T) is a measure of the rate of
  successful collisions
• Analysis of temperature dependence is via
• ln k ln A - EA / RT

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Parallel and Consecutive Reactions

• Combinations of elementary reactions

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Parallel Reactions

• reactants can be removed by two or more reactions
• overall rate of removal?
• fraction removed by each channel?
• e.g. Chlorine atoms generated by UV photolysis
  of chlorofluorocarbons (CFCs) in the
  stratosphere. Chlorine is then reactive.

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Parallel Reactions
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Consecutive Reactions

• A ? B ? C
• two consecutive first order reactions
• The concentration profiles will depend on the
  relative rate constants for 1 and 2
• For k1 gtgt k2
• conversion of A into B before much C is formed.
• growth of C matches the decay of B (B ? C
  rate-determining)
• For k2 gtgt k1
• B is a very reactive intermediate and never
  builds up to a large concentration (reacts
  quickly to give C)
• (Growth of C matches decay of A)

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Explicit kinetic expressions are not always
straightforward !
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Photochemical Kinetics

• Thermal reaction kinetics are initiated by
  intermolecular collisions and defined by (simple)
  rate laws but,
• Many atmospheric processes are initiated by
  photons.
• How can we quantify their photochemical
  kinetics?

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Photochemical Kinetics

• Write the photochemical reaction just as a
  normal reaction and substitute hn as one of the
  reactants.
• e.g. NO2 hn ? NO O
• Second order rate constant

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Photochemical Kinetics

• Unfortunately, not so useful ....
• rate will vary dramatically with photon energy
• also easier to consider 2nd order processes in
  pseudo-first order conditions
• How to fix?
• take a constant flux of photons with a fixed
  wavelength distribution

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• Where
• J is a special photochemical rate constant which
  includes
• absorption coefficient of reactant,
• quantum yield of reaction and
• intensity of the solar spectrum under conditions
  of interest.

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Photochemical Kinetics

• It is relatively easy to estimate Js
• (i) need to know spectral characteristics of
  absorption (lab experiments)
• (ii) amount of incoming radiation
• (iii) estimate (fit) quantum yield for the
  photoreaction (lab experiments)

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Photochemical Kinetics

• e.g. mid-latitude mid-day values of JNO2 5 x
  10-3 sec-1
• Recall also that
• Where k is the assumed 1st order rate constant
• So that t (200 sec)

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