Summary of concepts so far

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Summary of concepts so far

• Stoichiometry (Conservation of mass)
  quantitative relation between reactants and
  products
• Thermodynamics predicts ratio of products to
  reactants at equilibrium. However, we are rarely
  at equilibrium. If there is a net rate of
  reaction, we are not at equilibrium.
• Kinetics Quantitative description of observed
  reaction rate (its temperature and concentration
  dependency)
• Mechanism postulated interactions between
  components (reactants, products, and
  intermediates) that explain the observed kinetics

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Reading assignment

• Review section 2.3 (Levenspiel) which summarizes
  the relationship between stoichiometry, kinetics,
  and mechanism

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How do we observe the kinetics

• Physical arrangements in the laboratory
• Batch reactors
• Flow reactors
• Ways of analyzing data
• Integral
• Differential

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How do we observe the kinetics in a batch
reactor

• As a function of time, observe
• Concentration
• Pressure (at constant volume)
• Volume (at constant pressure)
• Some other property that can be related to
  concentration.
• Establish concentration dependency at constant
  temperature
• Then establish temperature dependency by
  repeating experiment at different temperatures

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Concentration dependency in a constant volume
batch reactor

• Integrate this expression to get C vs t
  expression, compare with C vs t data to obtain
  constants k, a, b ? Integral method of
  analysis
• OR,
• Find dCi/dt from C vs t data, compare with
  expression to obtain k, a, b
• ? Differential method of analysis

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Integral method of analysis

• Say we postulate a unimolecular, irreversible
  reaction
• Plotting ln(CA/CA0) vs t should give straight
  line with slope k.

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Notation and conventions

• CA/CA0 is the fraction of reactant remaining
  (unreacted) at time t
• Define conversion as the fraction reacted
• Thus,

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Zero order kinetics
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nth order kinetics

• n is not necessarily an integer
• Plot L.H.S vs t, if straight line results, k is
  the slope

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n 2

• 1/CA vs t should give straight line
• Or, using XA insead of CA

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nth order kinetics

• Plot L.H.S vs t, if straight line results, k is
  the slope (n is not necessarily an integer)
• PROBLEM we do not know n, this becomes a trial
  and error procedure with an infinite number of
  possibilities for n
• The half-life method provides a systematic
  approach

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The half-life method

• nth order kinetics result rewritten
• Let CA 0.5CA0 at t t1/2, the half-life of
  A

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The half-life method

• Plot log t1/2 vs logCA0 to get 1-n from slope
• Will also work with fractions other than 0.5,
  e.g. t0.8
• Problem we do not know the times at which to
  take CA measurements a priori
• Solution take CA measurements at pretty much
  regular intervals and then fit a curve to CA vs
  time data so that CA at any required time can be
  estimated.

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Recap Integral method of analysis

• determining concentration dependency in a
  constant volume batch reactor
• Integrate this expression to get C vs t
  expression, compare with C vs t data to obtain
  constants k, a, b
• Example 3.1

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Differential method of analysis

• determining concentration dependency in a
  constant volume batch reactor 1) postulate
• 2) Obtain dC/dt vs C relationship from C vs t
  data
• 3) Compare with postulated expression on
  appropriate coordinates to determine order and
  obtain parameters
• Step 2 will require appropriate methodology

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Differential method of analysis

• Obtaining dC/dt vs C from discrete C vs t data
• Alternatives
• Use ?C/ ?t from adjacent points, attribute them
  to the mid-point
• Fit a curve to the C vs t data, draw tangents to
  the curve at the data points and measure dC/dt
  (manually, or using computer programs like Excel)
• Beware of curve fitting pitfalls!
• Example 3.2

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Recap Examples 3.1 and 3.2

• We have used the integral and differential
  methods of analysis for the unimolecular type
  reaction
• A ? products
• We came up with the rate expression
• What does this say about the reaction?
• Not elementary, i.e. not really unimolecular
• We now need a mechanism to explain how this
  reaction takes place.

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• Now look at

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• What is the relation between CA0 and CB0 ?
• Could be CA0 CB0 , but does not have to be
• Let M CB0 / CA0 initial molar ratio

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• M CB0 / CA0 the initial molar ratio
• What value should we aim at?
• If CB0 gtgt CA0 (i.e. M is large), CB would not
  deviate much from CB0 as reaction proceeds,
  CB(t)? CB0

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Case M gtgt 1

• In plain English, when there is a lot of excess
  of one reactant, the rate appears to be dependent
  only on the limiting reactant. Our second order
  (overall) reaction appears to be first order!
• This could be useful in determining the orders in
  a reaction rate like
• by providing excess of two reactants while
  seeking the order with respect to the limiting
  reactant

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Case M 1 (stoichiometric)

• The general solution we obtained
• becomes indeterminate.
• But, if CA0 CB0, and we have AB? products,
  stoichiometry tells us CA(t) CB (t) , and we
  have
• This would also apply to 2A ? products

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What about A2B? products ?

• M CB0 / CA0 2 for stoichiometry now
• Say we still look for a second order (overall)
  reaction rate

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• A2B? products but M ? 2
• We can obtain, similar to the A B case,

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Reversible reactions
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Reversible reactions
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Reversible reactions
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Reversible reactions
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Reversible reactions
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Reaction rate parameters from batch data - Summary

• Batch reactor experiments give us concentration
  vs time data.
• With either the integral or differential method
  of analysis we seek to test the reaction rate
  expression against the data in an appropriate
  linear form
• If we get agreement in the linear form we also
  get the values of the reaction rate constant
• The linear forms are specific to each case and
  require some ingenious algebraic manipulation

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Cases analyzed in Chapter 3

• By the integral method
• Irreversible unimolecular-type first-order
  reactions
• Irreversible bimolecular-type second-order
  reactions
• Irreversible trimolecular-type third-order
  reactions
• Empirical rate equations of nth order
• Zero order reactions
• Overall order of irreversible reactions from the
  half-life
• Irreversible reactions in parallel
• Homogeneous catalyzed reactions
• Autocatalyic reactions
• Irreversible reactions in series
• First-order reversible reactions
• Second-order reversible reactions
• Reversible reactions in general
• Reactions of shifting order

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Cases analyzed in Chapter 3

• By the differential method
• Empirical rate equations of nth order
• In a variable volume batch reactor
• Zero order reactions
• First-order reactions
• Second-order reactions

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Pressure and concentration

• Gas phase composition often reported by pi
  partial pressure of component i
• Ideal gas law PVnRT
• n/V C, concentration, e.g. mol/L CP/RT
• ni/V Cipi/RT
• Example 3.4 demonstrates the correct use of p in
  rate expressions

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