Chapter 15: Kinetics

1
Chapter 15 Kinetics

• The speed with which the reactants disappear and
  the products form is called the rate of the
  reaction
• A study of the rate of reaction can give detailed
  information about how reactants change into
  products
• The series of individual steps that add up to the
  overall observed reaction is called the reaction
  mechanism

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• There are five principle factors that influence
  reaction rates
• Chemical nature of the reactants
• Ability of the reactants to come in contact with
  each other
• Concentration of the reactants
• Temperature
• Availability of of rate-accelerating agents
  called catalysts

3

The progress of the reaction A ? B. The number of
A molecules (in red) decreases with time while
the number of B molecules (in blue) increases.
The steeper the concentration versus time curve,
the faster the reaction rate. The film strip
represents the relative number of A and B
molecules at each time.
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• Chemical nature of the reactants
• Bonds break and form during reactions
• The most fundamental difference in reaction rates
  lie in the reactants themselves
• Some reactions are fast by nature and others slow
• Ability of the reactants to meet
• Most reactions require that particles (atoms,
  molecules, or ions) collide before the reaction
  can occur
• This depends on the phase of the reactants

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• In a homogeneous reaction the reactants are in
  the same phase
• For example both reactants in the gas (vapor)
  phase
• In a heterogeneous reaction the reactants are in
  different phases
• For example one reactant in the liquid and the
  second in the solid phase
• In heterogeneous reactions the reactants meet
  only at the intersection between the phases
• Thus the area of contact between the phases
  determines the rate of the reaction

6

Effect of crushing a solid. When a single solid
is subdivided into much smaller pieces, the total
surface area on all of the pieces becomes very
large.
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• Concentration of the reactants
• Both homogeneous and heterogeneous reaction rates
  are affected by reactant concentration
• For example, red hot steel wool bursts into
  flames in the presence of pure oxygen
• Temperature of the system
• The rates for almost all chemical reactions
  increase as the temperature is increased
• Cold-blooded creatures, such as insects and
  reptiles, become sluggish at lower temperatures
  as their metabolism slows down

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• Presence of a catalyst
• A catalysts is a substance that increases the
  rate of a chemical reaction without being
  consumed
• Enzymes are biological catalysts that direct our
  body chemistry
• A rate is always expressed as a ratio
• One way to describe a reaction rate is to select
  one component of the reaction and describe the
  change in concentration per unit of time

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• Molarity (mol/L) is normally the concentration
  unit and the second (s) is the most often used
  unit of time
• Typically, the reaction rate has the units

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• By convention, reaction rates are reported as a
  positive number even when the monitored species
  concentration decreases with time
• If the rate is known with respect to one species,
  the coefficients of the balanced chemical
  equation can be used to find the rates with
  respect to the other species
• Consider the combustion of propane

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• Compared to the rate with respect to propane
• Rate with respect to oxygen is five times faster
• Rate with respect to carbon dioxide is three
  times faster
• Rate with respect to water is four times faster
• Since the rates are all related any may be
  monitored to determine the reaction rate

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• A reaction rate is generally not constant
  throughout the reaction
• Since most reactions depend on the concentration
  of reactants, the rate changes as they are used
  up
• The rate at any particular moment is called the
  instantaneous rate
• It can be calculated from a concentration versus
  time plot

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A plot of the concentration of HI versus time for
the reaction 2HI(g) ? H2(g) I2(g). The
slope is negative because we are measuring the
disappearance of HI. When used to express the
rate it is used as a positive number.
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• The rate of a homogeneous reaction at any instant
  is proportional to the product of the molar
  concentrations of the reactants raised to a power
  determined from experiment

15

• Consider the following reaction
• From experiment, the rate law (determined from
  initial rates) is
• At 0oC, k equals 5.0 x 105 L5 mol-5 s-1
• Thus, at 0oC

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• The exponents in the rate law are generally
  unrelated to the chemical equations coefficients
• Never simply assume the exponents and
  coefficients are the same
• The exponents must be determined from the results
  of experiments
• The exponent in a rate law is called the order of
  reaction with respect to the corresponding
  reactant

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• For the rate law
• We can say
• The reaction is first order with respect to
  H2SeO3
• The reaction is third order with respect to I-
• The reaction is second order with respect to H
• The reaction order is sixth order overall
• Exponents in a rate law can be fractional,
  negative, and even zero

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• Looking for patterns in experimental data provide
  way to determine the exponents in a rate law
• One of the easiest ways to reveal patterns in
  data is to form ratios of results using different
  sets of conditions
• This technique is generally applicable
• Again consider the hypothetical reaction

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• Suppose the experimental concentration-rate data
  for five experiments is

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• For experiments 1, 2, and 3 B is held constant,
  so any change in rate must be due to changes in
  A
• The rate law says that at constant B the rate
  is proportional to Am

Thus m1
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• This means that the reactions is first order with
  respect to reactant A
• For experiments 3, 4, and 5 A is held constant,
  so any change must be due to changes in B
• The rate law says that at constant A the rate
  is proportional to Bn
• Using the results from experiment 3 and 4

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• The reaction is second order in B and
• ratekAB2

Thus n2
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• The rate constant (k) can be determined using
  data from any experiment
• Using experiment 1
• Using data from a different experiment might give
  a slightly different value

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• The relationship between concentration and time
  can be derived from the rate law and calculus
• Integration of the rate laws gives the integrated
  rate laws
• Integrate laws give concentration as a function
  of time
• Integrated laws can get very complicated, so only
  a few simple forms will be considered

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• First order reactions
• Rate law is rate k A
• The integrate rate law can be expressed as
• A0 is A at t (time) 0
• At is A at t t
• e base of natural logarithms 2.71828

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• Graphical methods can be used to determine the
  first-order rate constant, note

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• A plot of lnAt versus t gives a straight line
  with a slope of -k

The decomposition of N2O5. (a) A graph of
concentration versus time for the decomposition
at 45oC. (b) A straight line is obtained from a
logarithm versus time plot. The slope is negative
the rate constant.
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• The simplest second-order rate law has the form
• The integrated form of this equation is

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• Graphical methods can also be applied to
  second-order reactions
• A plot of 1/Bt versus t gives a straight line
  with a slope of k

Second-order kinetics. A plot of 1/HI versus
time (using the data in Table 15.1).
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• The amount of time required for half of a
  reactant to disappear is called the half-life,
  t1/2
• The half-life of a first-order reaction is not
  affected by the initial concentration

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First-order radioactive decay of iodine-131. The
initial concentration is represented by I0.
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• The half-life of a second-order reactions does
  depend on the initial concentration

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• One of the simplest models to explain reactions
  rates is collision theory
• According to collision theory, the rate of
  reaction is proportional to the effective number
  of collisions per second among the reacting
  molecules
• An effective collision is one that actually gives
  product molecules
• The number of all types of collisions increase
  with concentration, including effective
  collisions

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• There are a number of reasons why only a small
  fraction of all the collisions leads to the
  formation of product
• Only a small fraction of the collisions are
  energetic enough to lead to products
• Molecular orientation is important because a
  collision on the wrong side of a reacting
  species cannot produce any product
• This becomes more important as the complexity of
  the reactants increases

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The key step in the decomposition of NO2Cl to NO2
and Cl2 is the collision of a Cl atom with a
NO2Cl molecules. (a) A poorly orientated
collision. (b) An effectively orientated
collision.
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• The minimum energy kinetic energy the colliding
  particles must have is called the activation
  energy, Ea
• In a successful collision, the activation energy
  changes to potential energy as the bonds
  rearrange to for products
• Activation energies can be large, so only a small
  fraction of the well-orientated, colliding
  molecules have it
• Temperature increases increase the average
  kinetic energy of the reacting particles

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Kinetic energy distribution for a reaction at two
different temperatures. At the higher
temperature, a larger fraction of the collisions
have sufficient energy for reaction to occur. The
shaded area under the curves represent the
reacting fraction of the collisions.
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• Transition state theory explains what happens
  when reactant particles come together
• Potential-energy diagrams are used to help
  visualize the relationship between the activation
  energy and the development of total potential
  energy
• The potential energy is plotted against reaction
  coordinate or reaction progress

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The potential-energy diagram for an exothermic
reaction. The extent of reaction is represented
as the reaction coordinate.
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A successful (a) and unsuccessful (b) collision
for an exothermic reaction.
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• Activation energies and heats of reactions can be
  determined from potential-energy diagrams

Potential-energy diagram for an endothermic
reaction. The heat of reaction and activation
energy are labeled.
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• Reactions generally have different activation
  energies in the forward and reverse direction

Activation energy barrier for the forward and
reverse reactions.
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• The brief moment during a successful collision
  that the reactant bonds are partially broken and
  the product bonds are partially formed is called
  the transition state
• The potential energy of the transition state is a
  maximum of the potential-energy diagram
• The unstable chemical species that exists
  momentarily is called the activated complex

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Formation of the activated complex in the
reaction between NO2Cl and Cl.
NO2ClCl?NO2Cl2
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• The activation energy is related to the rate
  constant by the Arrhenius equation
• k rate constant
• Ea activation energy
• e base of the natural logarithm
• R gas constant 8.314 J mol-1 K-1
• T Kelvin temperature
• A frequency factor or pre-exponential factor

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• The Arrhenius equation can be put in standard
  slope-intercept form by taking the natural
  logarithm
• A plot of ln k versus (1/T) gives a straight line
  with slope -Ea/RT

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• The activation energy can be related to the rate
  constant at two temperatures
• The reactions mechanism is the series of simple
  reactions called elementary processes
• The rate law of an elementary process can be
  written from its chemical equation

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• The overall rate law determined for the mechanism
  must agree with the observed rate law
• The exponents in the rate law for an elementary
  process are equal to the coefficients of the
  reactants in chemical equation

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• Multistep reactions are common
• The sum of the element processes must give the
  overall reaction
• The slow set in a multistep reaction limits how
  fast the final products can form and is called
  the rate-determining or rate-limiting step
• Simultaneous collisions between three or more
  particles is extremely rate

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• A reaction that depended a three-body collision
  would be extremely slow
• Thus, reaction mechanism seldom include
  elementary process that involve more than
  two-body or bimolecular collisions
• Consider the reaction
• The mechanism is thought to be

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• The second step is the rate-limiting step, which
  gives
• N2O2 is a reactive intermediate, and can be
  eliminated from the expression

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• The first step is a fast equilibrium
• At equilibrium, the rate of the forward and
  reverse reaction are equal

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• Substituting, the rate law becomes
• Which is consistent with the experimental rate law

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• A catalyst is a substance that changes the rate
  of a chemical reaction without itself being used
  up
• Positive catalysts speed up reactions
• Negative catalysts or inhibitors slow reactions
• (Positive) catalysts speed reactions by allowing
  the rate-limiting step to proceed with a lower
  activation energy
• Thus a larger fraction of the collisions are
  effective

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(a) The catalyst provides an alternate,
low-energy path from the reactants to the
products. (b) A larger fraction of molecules have
sufficient energy to react when the catalyzed
path is available.
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• Catalysts can be divided into two groups
• Homogeneous catalysts exist in the same phase as
  the reactants
• Heterogeneous catalysts exist in a separate phase
• NO2 is a homogeneous catalyst for the production
  of sulfuric acid in the lead chamber process
• The mechanism is

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• The second step is slow, but is catalyzed by NO2

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• Heterogeneous catalysts are typically solids
• Consider the synthesis of ammonia from hydrogen
  and nitrogen by the Haber process
• The reaction takes place on the surface of an
  iron catalyst that contains traces of aluminum
  and potassium oxides
• The hydrogen and nitrogen binds to the catalyst
  lowering the activation energy

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The Haber process. Catalytic formation of ammonia
molecules from hydrogen and nitrogen on the
surface of a catalyst.