Archer G11
Chemistry: The Central Science
Chapter 14: Chemical Kinetics
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Chemical kinetics – Area of chemistry concerned with the speeds, or rates, of
reactions
o Subject of broad importance
Rates of reactions span an enormous range
14.1: Factors that Affect Reaction Rates
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The speeds of reactions depend on the nature of the reactants themselves
Four factors allowing the change of rates at which particular reaction occur:
o The physical state of the reactants
 When reactants are in different phases, the reaction is limited to their
area of contact
o The concentrations of the reactants
 As concentration increases, the frequency with which the reactant
molecules collide increases, leading to increased rates
o The temperature at which the reaction occurs
 As temperature increases, the kinetic energy increases thus causing
the molecules to collide more frequently with higher energy, leading to
increased reaction rates
o The presence of a catalyst
 Catalysts are agents that increase reaction rates without being used up
Reaction rates depend on frequency of collisions
o A sufficient amount of energy is required for a collision to lead a reaction
14.2: Reaction Rates
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Reaction rate is the change in the concentration of reactants or products per
unit of time
o The units for reaction rate are usually molarity per second (M/s)
The rate of reaction can be expressed either as the rate of disappearance of
reactant or as the rate of appearance of product
o
o
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Bracket to indicate the concentration of the substance in
molarity
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 Negative sign in front of disappearance to make it positive
o Rates are always expressed as positive quantities
Change of Rate with Time
o Over time, it is typical for rates to decrease as a reaction proceeds,
because the concentration of reactants decreases
Instantaneous Rate
o Instantaneous rate is the rate at a particular moment in the reaction
o Can be determined from the slope of the tangent line at the point
o Instantaneous rate at t = 0 is called the initial rate
Reaction Rates and Stoichiometry
o The rate also depends on the stoichiometric relationship
o Rate of reaction
can be given by the equation
below
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14.3: Concentration and Rate
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Rate at the beginning of a reaction depends on the starting concentration
Equation which shows how the rate depends on the concentrations of reactants is
called a rate law
o
 k in the rate law is called the rate constant
 the magnitude of k depends on temperature
Reaction Orders: The Exponents in the Rate Law
o The exponent m and n in the rate law are called reaction orders
o Overall reaction order is the sum of the orders with respect to each reactant
in the rate law
 The exponents in a rate law indicate how the rate is affected by the
concentration of each reactant
o If a rate law is second order with respect to a reactant, [A]2, then doubling the
concentration of that substance causes the reaction rate to quadruple ([2]2 =
4), whereas tripling the concentration causes the rate to increase ninefold
([3]2 = 9)
o The values of these exponents must be determined experimentally
o In most rate laws, reaction orders are 0, 1, or 2
 Some rate laws have the reaction order as fraction or even negative
Units of Rate Constants
o Units of the rate constant depend on the overall reaction order of the rate law
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o E.g. Reaction that is second order overall
 Units of rate = (units of rate constant)(units of concentration)2
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Using Initial Rates to Determine Rate Laws
o Rate law for any chemical reaction must be determined experimentally
o The task of determining rate law becomes one of determining the reaction
orders, m and n
 Reaction order = 0, changing concentration have no effect on rate
 Reaction order = 1, rate change in proportion to concentration
 Reaction order = 2, changing concentration change rate by square of
that change
o Rate of a reaction depends on concentration but the rate constant does not
 Rate constant is affected by temperature and by the presence of a
catalyst
14.4: The Change of Concentration with Time
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Rate laws can be converted into equations that show the relationship between the
concentrations of the reactants or products and time
First-Order Reactions
o First-order reaction is one whose rate depends on the concentration of a
single reactant raised to the first power
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The form of a rate law that expresses how rate depends on
concentration is called the differential rate law
o Using an operation from calculus called integration, this relationship can be
transformed into an equation that relates the concentration of A at the start
of the reaction to its concentration at any other time
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or
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This form is called the integrated rate law
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Can be used to verify whether a reaction is first order and to
determine its rate constant
o A reaction that is not first order will not yield a straight
line
Has the slope-intercept form
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These two equation can be used with any concentration units as long
as the units are the same for both
and
Second-Order Reactions
o Second-order reaction is one whose rate depends on the reactant
concentration raised to the second power or on the concentrations of two
different reactants, each raised to the first power
o
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The integrated rate law is
 Also a slope-intercept form
o One way to distinguish between first- and second-order rate laws is to graph
both
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and
If the
against t
plot is linear, the reaction is first order; if the
plot is
linear, the reaction is second order
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Half-life
o Half-life of a reaction is the time required for the concentration of a reactant
to reach on-half of its initial value,
o Half-life of a first-order reaction can be determined by substituting
into
the integrated first-order rate law
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 Does not depend on the starting concentration
 Half-life remains constant throughout the reaction
In a first-order reaction, the concentration of the reactant decreases by
in each of a series of regularly spaced time intervals, namely,
o Half-life for second-order and other reactions depends on reactant
concentration
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The half-life depends on the initial concentration of reactant—the
lower the initial concentration, the greater the half-life
14.5: Temperature and Rate
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The faster rate at higher temperature is due to an increase in the rate constant with
increasing temperature
The Collision Model
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o Collision model accounts for the effect of both the concentration of reactants
and temperature at molecular level
o The central idea is that the molecules must collide to react
 Ac concentration increases, the number of collisions increases, leading
to an increase in reaction rate
 As temperature increases, the molecules collide more forcefully (with
more energy) and more frequently, increasing the reaction rates
o For a reaction to occur, more is required than a simple reaction
The Orientation Factor
o In most reactions, molecules must be oriented in a certain way during
collisions for a reaction to occur
 The relative orientations of the molecules during their collisions
determine whether the atoms are suitably positioned to form new
bonds
 E.g.
 To react, the Cl must collide with each other; if Cl collide with other
atom (as in N or O), the reaction will not occur
Activation Energy
o In 1888 the Swedish chemist Svante Arrhenius suggested that molecules must
possess a certain minimum amount of energy to react
o Upon collision, the kinetic energy is used to change the potential energy of
the molecule
o Activation Energy (Ea) is the minimum energy required to initiate a chemical
reaction
 Activation energy varies from reaction to reaction
o The energy difference between that of a starting molecule and the highest
energy along the reaction pathway is the activation energy
 The particular arrangement of atoms at the top of the barrier is called
the activation complex, or transition state
o The rate depends on the magnitude of Ea; generally, the lower Ea is, the faster
the reaction
o The fraction of molecules that has an energy equal to or greater than Ea is
given by the equation below
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 R is the gas constant
 T is absolute temperature
The Arrhenius Equation
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o Arrhenius found that most reaction-rate data obeyed an equation based on
three factors
 The fraction of molecules possessing an energy of Ea or greater
 The number of collisions occurring per second
 The fraction of collisions that have the appropriate orientation
o He made an Arrhenius equation based on the three factors
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 k is the rate constant
 Ea is the activation energy
 R is the gas constant
 T is the absolute temperature
 A is the frequency factor and is a constant, or nearly so, as
temperature is varied
o t is related to the frequency of collisions and the
probability that the collisions are favorably oriented
from reaction
 Reaction rates decrease as Ea increases
Determining the Activation Energy
o Taking the natural log of both sides of Arrhenius equation
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 Has the form of straight line
 Activation energy can be determined from graphing
o The equation can also be combined equation
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and
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14.6: Reaction Mechanisms
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Balanced equation indicates the substances present at the start of the reaction and
those produced as the reaction proceeds
The process by which a reaction occurs is called the reaction mechanism
Elementary Reactions
o Reactions that occur in a single event or step are called elementary reactions
o The number of molecules that participate as reactants in an elementary
reaction defines its molecularity
 If a single molecule is involved, the reaction is unimolecular
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The rearrangement of methyl isonitrile is a unimolecular
process
 Elementary reactions involving the collision of two reactant molecules
are bimolecular
 The reaction between NO and O3 (forming NO2 and O2) is
bimolecular
 Elementary reactions involving the simultaneous collision of three
molecules are termolecular
 Far less probably than unimolecular and bimolecular
Multistep Mechanisms
o The net change represented by a balanced chemical equation often occurs by
multistep mechanism, which consists of a sequence of elementary reactions
o E.g.
 Below 225°C, this reaction appears to proceed in two elementary
reactions (or two elementary steps)
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The chemical equations for the elementary reactions in a multistep
mechanism must always add to give the chemical equation of the over
all process
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o Simplifying this equation gives the initial equation
 Molecules that is neither a reactant nor a product in the overall
reaction is called an intermediate (NO3 in this case)
Rate Laws for Elementary Reactions
o If a reaction is an elementary reaction, then its rate law is based directly on its
molecularity
 The rate of a unimolecular process will be first order
 For bimolecular elementary steps, the rate law is second order
 If the reaction is “A + B  product” type, the rate law will be
first order in both [A] and [B], and second order overall
o The number of elementary steps cannot be determined by merely looking at a
balanced chemical equation
The Rate-Determining Step for a Multistep Mechanism
o Each elementary step in multistep mechanism has its own rate constant and
activation energy
o Often one of the steps is much slower than the others
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Because the slow step limits the overall reaction rate, it is called the
rate-determining step (or rate-limiting step)
o The slowest step in a multistep reaction limits the overall rate
 If the slow step is not the first one, the faster preceding steps produce
intermediate products that accumulate before being consumed in the
slow step
o The rate-determining step governs the rate law for the overall reaction
Mechanisms with a Slow Initial Step
o E.g.
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is the rate-determining step
 The rate law is
 CO is absent from the rate law because it reacts in a step that
follows the rate-determining step
Mechanisms with a Fast Initial Step
o E.g.
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 Step 2 is the rate-determining step
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 NOBr is an intermediate generate from part one
 Step 1 is a reaction in both way thus form equilibrium
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Rate of the reaction is given by substituting the step above
o
o In general, whenever a fast step precedes a slow one, we can solve for the
concentration of an intermediate by assuming that an equilibrium is
established in the fast step
14.7: Catalysis
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A catalyst is a substance that changes the speed of a chemical reaction without
undergoing a permanent chemical change itself in the process
Homogeneous Catalysis
o A catalyst that is present in the same phase as the reacting molecules is called
a homogeneous catalyst
o E.g.
 Br- is added to catalyze the reaction
 Turns to Br2 then back to Br-
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 Br- is the catalyst while Br2 is the intermediate
o The catalyst is there at the start of the reaction, whereas the intermediate is
formed during the course of the reaction
o As a general rule, a catalyst lowers the overall activation energy for a chemical
reaction
Heterogeneous Catalysis
o A heterogeneous catalyst exists in a different phase from the reactant
molecules
o The initial step in heterogeneous catalysis is usually adsorption, the binding of
molecules to a surface
o Surface atoms and ions have unused bonding capacity
o E.g.
 Upon adsorption, the H—H bond of H2 breaks, leaving two H atoms
 When a hydrogen encounters an adsorbed ethylene (C2H4) molecule,
it can form a σ bond to one of the carbon
 Destroy the C—C π bond, leaving an ethyl group (C2H5) bonded
to the surface via a metal-to-carbon σ bond
o This σ bond is relatively weak
 When the other carbon atom also encounters a hydrogen atom, a sixth
C—H σ bond is readily formed and an ethane molecule is released from
the metal surface
Enzyme
o Enzymes – Biological catalysts
 Mostly are large protein molecules
o The reaction is catalyzed at a very specific location in the enzyme, called the
active site
 Active site is often fairly flexible thus may change shape as it binds the
substrate
 The substances that undergo reaction at this site are called substrates
o The lock-and-key model provides a simple explanation for the specificity of an
enzyme
o In the process of fitting into the active site, the substrate molecule may be
distorted and thus made more reactive
o The activity of an enzyme is destroyed if some molecule in the solution is able
to bind strongly and block the entry of the substrate
 Such substances are called enzyme inhibitors
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o The number of individual catalyzed reaction events occurring at a particular
active site, called the turnover number, is generally in the range of 103 to 107
per second
 Such large turnover numbers correspond to very low activation
energies