Rates of Reactions

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Rates of Reactions
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Factors affecting rates

• Temperature
• Increasing temperature increases rate.
• More molecules have sufficient energy to react.
• Reactant concentrations
• Dependence on concentration must be determined
  experimentally.
• Can be used to deduce mechanism.
• Catalysts
• speed up reactions
• heterogeneous (e.g. solids) or homogeneous (same
  phase)

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Dependence of concentration on time, in solution

• For the simple reaction A ? C,
• starting with A 1.0 and C 0
• Concentration of A decreases.
• Concentration of C increases at the same rate.
• Reaction slows, but continues until A runs out,
  or until equilibrium is established.
• At completion, or equilibrium, concentrations of
  A and C are constant.

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Dependence of concentration on time, in solution

• Rate of reaction can be expressed
• as the rate of disappearance of A or
• as the rate of appearance of C.
• For the reaction A ? C,
• Rate -DA/D t
• DC/Dt
• Once we see how the rate of reaction
• depends on the concentrations, we will
• write mathematical expressions for the
• concentrations as a function of time,
• these are the integrated rate laws.

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Dependence of concentration on time, in solution

• For the reaction A ? 2C,
• The rate of appearance of C is
• twice the rate of disappearance of A
• DC/ D t 2(- DA/ D t )
• In general, for any reaction
• a A b B ? c C
• - DA - DB DC
• a D t b D t c D t

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Measuring the rate of a reaction

• The rate is often measured as DX/Dt, where X
  may be a reactant or product.
• Depending on the nature of X, the change in
  concentration may be monitored by a change in
• colour (intensity of some wavelength)
• pressure (for gases)
• pH (for OH- or H3O)
• conductivity (ions)
• radioactivity, etc.

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Measuring the initial rate

• The rate of the forward reaction depends on the
  concentration of reactants, not products.
• The dependence may be linear, quadratic, etc.,
  this must be determined experimentally.
• The rate is measured at the beginning of the
  reaction (the initial rate), as a function of the
  initial reactant concentrations
• This determines the reaction order.

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Initial reaction rates2 NO (g) 2 H2 (g) ? N2
(g) 2 H2O (g)
Rate k NO2 H21
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Initial reaction rates reaction order
Rate k A2 B1 Reaction is second order in
A, first order in B and third order overall
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CONSIDER THE RATE DATA FOR THE REACTION 2NO
O2 2NO2
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Reaction order the rate law

• The rate law is Rate kAxBy
• The order of a reaction is equal to the value of
  the exponent in the rate law.
• The reaction has an order with respect to each
  reactant (and each catalyst).
• The overall reaction order is the sum of the
  individual orders.
• k is the rate constant, which depends on T.

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The rate constant

• Once the form of the rate law is known, we can
  fill in the data from any one run of our
  determination to find the rate constant.
• e.g. 2 NO (g) 2 H2 (g) ? N2 (g) 2 H2O (g)
• Rate 0.0339 Ms-1 k (.210 M)2(.122 M)
• k 6.30 M-2 s-1
• The units of k depend on the order of the reaction

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The rate constant

• The value of k depends on the nature of the
  reactants and on the temperature.
• Arrhenius found that the temperature dependence
  could be expressed as
• k Ae-Ea / RT
• The preexponential factor A, and the activation
  energy, Ea, are relatively independent of
  temperature.
• What are these parameters?
• Why does k have this dependence?

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Rate Law Determination

• Consider the combination reaction of NO and O2 to
  produce NO2
• 2 NO(g) O2(g) ? 2 NO2 (g)
• Determination of the Rate Law (via Methods of
  Initial Rates)
• Initial Concentrations
• (mol/ L) Initial Rate Experiment
  NO O2 (mol/L s)
• 1 0.020 0.010 0.028
• 2 0.020 0.020 0.057
• 3 0.020 0.040 0.114
• 4 0.040 0.020 0.227
• 5 0.010 0.020 0.014
• Based on these data, what is the rate equation?
  What is the value of the rate constant k?

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Rate Law Solving for rate Constant
The general rate law is Rate law k NO2
O2 the rate constant k is determine by
selecting one of the experiments and solving the
equation. Consider experiment1 Rate 0.028
k 0.0202 0.010 k 0.028 / (410-4)(0.010)
7.1103 M-2 s-1 Rate Law Rate 7.1103
NO2 O2
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Microscopic view

• In order to understand our macroscopic
  observations about temperature and concentration
  dependence, we should look at the reaction
  microscopically - on the size scale of atoms and
  molecules.
• The rates of chemical reactions are explained by
  collision theory, which is based on kinetic
  theory.
• Collision theory views a reaction as the result
  of a successful collision between two or more
  reactants and/or catalysts.
• A few reactions occur without any collision.

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Collision Theory

• The number of collisions between two or more
  species is proportional to the product of their
  concentrations.
• When the reaction is the result of a single
  collision an elementary step then the
  concentration dependence is directly related to
  the stoichiometry of that collision.
• The probability that A will collide with B is
  proportional to AB.
• The probability that A will collide with A is
  proportional to A2
• For more complicated processes, the rate law is
  some combination of these elementary steps.
• In order to react, the molecules must collide in
  a favourable orientation and with sufficient
  energy.
• These factors are accounted for in the rate
  constant.

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Molecularity of elementary steps

• For an elementary step (arising from one
  collision), the rate law depends on the
  stoichiometry of the collision.
• A step involving only one molecule is called
  unimolecular.
• Rate kA
• A step involving two molecules is called
  bimolecular.
• Rate kAB, or Rate kA2
• A step involving three molecules is called
  termolecular.
• Rate kABC, etc.
• Very few elementary steps involve more than 3
  molecules.

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Reaction progress Ea

• For an elementary process we can plot the
  potential (chemical) energy of the molecules as
  they approach each other, collide, react and move
  apart.
• For an elementary process which involves only one
  molecule, we can plot the potential energy as
  some internal coordinate, such as bond length or
  angle, changes.
• This plot is sometimes called a reaction
  coordinate diagram, or an energy plot. There is
  typically a maximum near the collision.
• Molecules move along this reaction coordinate
  with some initial kinetic energy. K.E. is
  converted to P. E. to overcome the energy
  barrier, the activation energy.
• Those molecular collisions starting with enough
  kinetic energy can overcome the barrier and react.

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Arrhenius and Boltzmann

• We saw in chapter 13 that only a certain
  proportion of molecules had enough energy to
  remain in the gas phase. The same type of energy
  distribution is at play here.
• The Boltzmann distribution tells us that at any
  particular temperature a certain percentage of
  the molecules are above some energy cut-off.
• The cut-off of interest in this case is the
  activation energy.
• The percentage of molecules with energy above Ea
  is related to the factor exp(-Ea/RT) in the
  Arrhenius expression in the rate.
• As the temperature increases, so does the
  percentage of molecules above the cut-off.

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Calculations with Ea T

• k Ae-Ea / RT ln k ln A (Ea/RT)
• Increasing the temperature from 300 K to 310 K
  increases the rate by a factor of 2. What is the
  activation energy?
• Given a set of T and k data, a plot of ln k vs.
  1/T has a slope of -Ea/R

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Rate determining step

• When the reaction is a series of elementary
  steps, rather than a single step, the rate of
  reaction is determined by the slowest step, which
  is typically the step with the highest activation
  barrier.
• This step is called the rate determining step,
  and the rate law for a known mechanism can be
  written in terms of the rate for this step.
• If the rate determining step is not the first
  step, the rate may depend on some species which
  do not appear as reactants in the overall
  reaction equation.

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Reaction mechanism

• Chemists often study reaction rates in order to
  deduce or confirm a reaction mechanism the
  stepwise progress of the reaction.
• A proposed mechanism is written as a sum of
  elementary steps, which may be reversible.
• If the rate law derived from the proposed
  mechanism matched the observed rate law, then we
  are more confident in our proposal, but still
  unsure.
• If the rate laws do not match, we must come up
  with a different proposal.

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2 NO (g) Br2 (g) ? 2 BrNO (g)

• Step 1 Rate k1Br2NO
• Br2 (g) NO (g) ? NOBr2 (g)
• Step 2 Rate 2 k2Br2NOBr2
• NOBr2 (g) NO (g) ? 2 BrNO (g)
• NOBr2 is an intermediate it is formed and then
  used up.
• The overall rate will depend on which step is
  rate determining, and on whether either step is
  reversible.

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2 NO2 (g) F2 (g) ? 2 FNO2 (g)

• Step 1 rate k1NO2F2
• NO2 F2 ? FNO2 F slow
• Step 2 rate k2NO2F
• NO2 F ? FNO2 fast
• Overall rate k1NO2F2
• Rate of reaction rate of the slowest step
• k2 gtgt k1

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2 NO (g) O2 (g) ? 2 NO2 (g)

• Step 1 is reversible K1 NO3 / NOO2
• NO O2 NO3 fast equilibrium
• Step 2 rate k2NO3NO
• NO3 NO ? 2 NO2 slow
• Overall rate k2 NO3NO
• Rate of reaction rate of the slowest step, but
  NO is an intermediate difficult to determine
  its concentration. Want to replace NO with
  known quantities
• K1 NO3 / NOO2 NO3 K1 NO O2
• Rate k2(K1 NO O2) NO k NO2O2

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Equilibria in reaction mechanisms

• Note that this topic is not covered in Kotz and
  Treichel
• In principle all reaction are reversible, but
  only some are reversible on a time scale relevant
  to the overall process.
• A reaction, or step, which is fast in both the
  forward and reverse direction will come to
  equilibrium rapidly.
• Dynamic equilibrium is reached when the rate of
  the forward reaction equals the rate of the
  reverse reaction.
• For an elementary step 2A B C, at
  equilibrium
• rate forward k1A2 k-1BC rate reverse
• equilibrium constant.