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Prentice Hall © 2003 Chapter 14
Chapter 14Chapter 14Chemical KineticsChemical Kinetics
CHEMISTRY The Central Science
9th Edition
David P. White
Prentice Hall © 2003 Chapter 14
• Kinetics is the study of how fast chemical reactions occur.
• There are 4 important factors which affect rates of reactions:– reactant concentration,– temperature,– action of catalysts, and– surface area.
• Goal: to understand chemical reactions at the molecular level.
Factors that Affect Reaction Factors that Affect Reaction RatesRates
Prentice Hall © 2003 Chapter 14
• Speed of a reaction is measured by the change in concentration with time.
• For a reaction A B
• Suppose A reacts to form B. Let us begin with 1.00 mol A.
Reaction RatesReaction Rates
t
B of molesin time change
B of moles ofnumber in changerate Average
Prentice Hall © 2003 Chapter 14
Reaction RatesReaction Rates
Prentice Hall © 2003 Chapter 14
– At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present.
– At t = 20 min, there is 0.54 mol A and 0.46 mol B.– At t = 40 min, there is 0.30 mol A and 0.70 mol B.– Calculating,
Reaction RatesReaction Rates
mol/min 026.0min 0min 10mol 0 mol 26.0
min 0min 100at B of moles10at B of moles
B of molesrate Average
ttt
Prentice Hall © 2003 Chapter 14
• For the reaction A B there are two ways of measuring rate:– the speed at which the products appear (i.e. change in moles of
B per unit time), or– the speed at which the reactants disappear (i.e. the change in
moles of A per unit time).
Reaction RatesReaction Rates
t
A of molesA respect to with rate Average
Prentice Hall © 2003 Chapter 14
Change of Rate with Time• For the reaction A B there are two ways of• Most useful units for rates are to look at molarity. Since
volume is constant, molarity and moles are directly proportional.
• Consider:C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
Reaction RatesReaction Rates
Prentice Hall © 2003 Chapter 14
Change of Rate with TimeC4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
– We can calculate the average rate in terms of the disappearance of C4H9Cl.
– The units for average rate are mol/L·s or M/s.– The average rate decreases with time.– We plot [C4H9Cl] versus time.– The rate at any instant in time (instantaneous rate) is the slope
of the tangent to the curve.– Instantaneous rate is different from average rate.– We usually call the instantaneous rate the rate.
Reaction RatesReaction Rates
Prentice Hall © 2003 Chapter 14
Reaction Rate and Stoichiometry• For the reaction
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
we know
• In general foraA + bB cC + dD
Reaction RatesReaction Rates
tt
OHHCClHCRate 9494
tdtctbta
D1C1B1A1Rate
Prentice Hall © 2003 Chapter 14
• In general rates increase as concentrations increase.NH4
+(aq) + NO2-(aq) N2(g) + 2H2O(l)
Concentration and RateConcentration and Rate
Prentice Hall © 2003 Chapter 14
• For the reactionNH4
+(aq) + NO2-(aq) N2(g) + 2H2O(l)
we note – as [NH4
+] doubles with [NO2-] constant the rate doubles,
– as [NO2-] doubles with [NH4
+] constant, the rate doubles,
– We conclude rate [NH4+][NO2
-].
• Rate law:
• The constant k is the rate constant.
Concentration and RateConcentration and Rate
]NO][NH[Rate 24k
Prentice Hall © 2003 Chapter 14
Exponents in the Rate Law• For a general reaction with rate law
we say the reaction is mth order in reactant 1 and nth order in reactant 2.
• The overall order of reaction is m + n + ….• A reaction can be zeroth order if m, n, … are zero.• Note the values of the exponents (orders) have to be
determined experimentally. They are not simply related to stoichiometry.
Concentration and RateConcentration and Rate
nmk ]2reactant []1reactant [Rate
Prentice Hall © 2003 Chapter 14
Using Initial Rates to Determines Rate Laws
• A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.
• A reaction is first order if doubling the concentration causes the rate to double.
• A reacting is nth order if doubling the concentration causes an 2n increase in rate.
• Note that the rate constant does not depend on concentration.
Concentration and RateConcentration and Rate
Prentice Hall © 2003 Chapter 14
First Order Reactions• Goal: convert rate law into a convenient equation to give
concentrations as a function of time.• For a first order reaction, the rate doubles as the
concentration of a reactant doubles.
The Change of The Change of Concentration with TimeConcentration with Time
kt
kt
kt
t
t
0
0
AA
ln
AlnAln
]A[A][Rate
Prentice Hall © 2003 Chapter 14
First Order Reactions• A plot of ln[A]t versus t is a straight line with slope -k
and intercept ln[A]0.• In the above we use the natural logarithm, ln, which is
log to the base e.
The Change of The Change of Concentration with TimeConcentration with Time
Prentice Hall © 2003 Chapter 14
First Order Reactions
The Change of The Change of Concentration with TimeConcentration with Time
0AlnAln ktt
Prentice Hall © 2003 Chapter 14
Second Order Reactions• For a second order reaction with just one reactant
• A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0
• For a second order reaction, a plot of ln[A]t vs. t is not linear.
The Change of The Change of Concentration with TimeConcentration with Time
0A1
A1 kt
t
Prentice Hall © 2003 Chapter 14
Second Order Reactions
The Change of The Change of Concentration with TimeConcentration with Time
0A1
A1 kt
t
Prentice Hall © 2003 Chapter 14
Half-Life• Half-life is the time taken for the concentration of a
reactant to drop to half its original value.• For a first order process, half life, t½ is the time taken for
[A]0 to reach ½[A]0.• Mathematically,
The Change of The Change of Concentration with TimeConcentration with Time
kk
t 693.0ln 21
21
Prentice Hall © 2003 Chapter 14
Half-Life• For a second order reaction, half-life depends in the
initial concentration:
The Change of The Change of Concentration with TimeConcentration with Time
0A1
21 k
t
Prentice Hall © 2003 Chapter 14
The Collision Model• Most reactions speed up as temperature increases. (E.g.
food spoils when not refrigerated.)• When two light sticks are placed in water: one at room
temperature and one in ice, the one at room temperature is brighter than the one in ice.
• The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.
Temperature and RateTemperature and Rate
Temperature and RateTemperature and RateThe Collision
Model• As temperature
increases, the rate increases.
Prentice Hall © 2003 Chapter 14
The Collision Model• Since the rate law has no temperature term in it, the rate
constant must depend on temperature.• Consider the first order reaction CH3NC CH3CN.
– As temperature increases from 190 C to 250 C the rate constant increases from 2.52 10-5 s-1 to 3.16 10-3 s-1.
• The temperature effect is quite dramatic. Why?• Observations: rates of reactions are affected by
concentration and temperature.
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
The Collision Model• Goal: develop a model that explains why rates of
reactions increase as concentration and temperature increases.
• The collision model: in order for molecules to react they must collide.
• The greater the number of collisions the faster the rate.• The more molecules present, the greater the probability
of collision and the faster the rate.
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
The Collision Model• The higher the temperature, the more energy available to
the molecules and the faster the rate.• Complication: not all collisions lead to products. In fact,
only a small fraction of collisions lead to product.The Orientation Factor
• In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
The Orientation Factor• Consider:
Cl + NOCl NO + Cl2
• There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
The Orientation Factor
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
Activation Energy• Arrhenius: molecules must posses a minimum amount of
energy to react. Why?– In order to form products, bonds must be broken in the
reactants.– Bond breakage requires energy.
• Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
Activation Energy• Consider the rearrangement of methyl isonitrile:
– In H3C-NC, the C-NC bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state.
– The energy required for the above twist and break is the activation energy, Ea.
– Once the C-N bond is broken, the NC portion can continue to rotate forming a C-CN bond.
Temperature and RateTemperature and Rate
H3C N CC
NH3C H3C C N
Prentice Hall © 2003 Chapter 14
Activation Energy• The change in energy for the reaction is the difference in
energy between CH3NC and CH3CN.• The activation energy is the difference in energy between
reactants, CH3NC and transition state.
• The rate depends on Ea.
• Notice that if a forward reaction is exothermic (CH3NC CH3CN), then the reverse reaction is endothermic (CH3CN CH3NC).
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
Activation Energy• How does a methyl isonitrile molecule gain enough
energy to overcome the activation energy barrier?• From kinetic molecular theory, we know that as
temperature increases, the total kinetic energy increases.• We can show the fraction of molecules, f, with energy
equal to or greater than Ea is
where R is the gas constant (8.314 J/mol·K).
Temperature and RateTemperature and Rate
RTEa
ef
Prentice Hall © 2003 Chapter 14
Activation Energy
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
The Arrhenius Equation• Arrhenius discovered most reaction-rate data obeyed the
Arrhenius equation:
– k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K.
– A is called the frequency factor.– A is a measure of the probability of a favorable collision.– Both A and Ea are specific to a given reaction.
Temperature and RateTemperature and Rate
RTEa
Aek
Prentice Hall © 2003 Chapter 14
Determining the Activation Energy• If we have a lot of data, we can determine Ea and A
graphically by rearranging the Arrhenius equation:
• From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.
Temperature and RateTemperature and Rate
ARTEk a lnln
Temperature and RateTemperature and Rate
Prentice Hall © 2003 Chapter 14
Determining the Activation Energy• If we do not have a lot of data, then we recognize
Temperature and RateTemperature and Rate
1221
2121
22
11
11ln
lnlnlnln
lnln and lnln
TTRE
kk
ARTEA
RTEkk
ARTEkA
RTEk
a
aa
aa
Prentice Hall © 2003 Chapter 14
• The balanced chemical equation provides information about the beginning and end of reaction.
• The reaction mechanism gives the path of the reaction.• Mechanisms provide a very detailed picture of which
bonds are broken and formed during the course of a reaction.
Elementary Steps• Elementary step: any process that occurs in a single step.
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Elementary Steps• Molecularity: the number of molecules present in an
elementary step.– Unimolecular: one molecule in the elementary step,– Bimolecular: two molecules in the elementary step, and– Termolecular: three molecules in the elementary step.
• It is not common to see termolecular processes (statistically improbable).
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Multistep Mechanisms• Some reaction proceed through more than one step:
NO2(g) + NO2(g) NO3(g) + NO(g)
NO3(g) + CO(g) NO2(g) + CO2(g)• Notice that if we add the above steps, we get the overall
reaction:NO2(g) + CO(g) NO(g) + CO2(g)
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Multistep Mechanisms• If a reaction proceeds via several elementary steps, then
the elementary steps must add to give the balanced chemical equation.
• Intermediate: a species which appears in an elementary step which is not a reactant or product.
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Rate Laws for Elementary Steps• The rate law of an elementary step is determined by its
molecularity:– Unimolecular processes are first order,– Bimolecular processes are second order, and– Termolecular processes are third order.
Rate Laws for Multistep Mechanisms• Rate-determining step: is the slowest of the elementary
steps.
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Rate Laws for Elementary Steps
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Rate Laws for Multistep Mechanisms• Therefore, the rate-determining step governs the overall
rate law for the reaction.Mechanisms with an Initial Fast Step
• It is possible for an intermediate to be a reactant.• Consider
2NO(g) + Br2(g) 2NOBr(g)
Reaction MechanismsReaction Mechanisms
Prentice Hall © 2003 Chapter 14
Mechanisms with an Initial Fast Step2NO(g) + Br2(g) 2NOBr(g)
• The experimentally determined rate law isRate = k[NO]2[Br2]
• Consider the following mechanism
Reaction MechanismsReaction Mechanisms
NO(g) + Br2(g) NOBr2(g)k1
k-1
NOBr2(g) + NO(g) 2NOBr(g)k2
Step 1:
Step 2:
(fast)
(slow)
Prentice Hall © 2003 Chapter 14
Mechanisms with an Initial Fast Step• The rate law is (based on Step 2):
Rate = k2[NOBr2][NO]• The rate law should not depend on the concentration of
an intermediate (intermediates are usually unstable).• Assume NOBr2 is unstable, so we express the
concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have
Reaction MechanismsReaction Mechanisms
]NO][Br[]NOBr[ 21
12
kk
Prentice Hall © 2003 Chapter 14
Mechanisms with an Initial Fast Step• By definition of equilibrium:
• Therefore, the overall rate law becomes
• Note the final rate law is consistent with the experimentally observed rate law.
Reaction MechanismsReaction Mechanisms
]NOBr[]NO][Br[ 2121 kk
][BrNO][NO][]NO][Br[Rate 22
11
221
12
kkk
kkk
Prentice Hall © 2003 Chapter 14
• A catalyst changes the rate of a chemical reaction.• There are two types of catalyst:
– homogeneous, and– heterogeneous.
• Chlorine atoms are catalysts for the destruction of ozone.Homogeneous Catalysis
• The catalyst and reaction is in one phase.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Homogeneous Catalysis• Hydrogen peroxide decomposes very slowly:
2H2O2(aq) 2H2O(l) + O2(g)• In the presence of the bromide ion, the decomposition
occurs rapidly:– 2Br-(aq) + H2O2(aq) + 2H+(aq) Br2(aq) + 2H2O(l).
– Br2(aq) is brown.
– Br2(aq) + H2O2(aq) 2Br-(aq) + 2H+(aq) + O2(g).– Br- is a catalyst because it can be recovered at the end of the
reaction.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Homogeneous Catalysis• Generally, catalysts operate by lowering the activation
energy for a reaction.
CatalysisCatalysis
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Homogeneous Catalysis• Catalysts can operate by increasing the number of
effective collisions.• That is, from the Arrhenius equation: catalysts increase k
be increasing A or decreasing Ea.• A catalyst may add intermediates to the reaction.• Example: In the presence of Br-, Br2(aq) is generated as
an intermediate in the decomposition of H2O2.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Homogeneous Catalysis• When a catalyst adds an intermediate, the activation
energies for both steps must be lower than the activation energy for the uncatalyzed reaction. The catalyst is in a different phase than the reactants and products.
Heterogeneous Catalysis• Typical example: solid catalyst, gaseous reactants and
products (catalytic converters in cars).• Most industrial catalysts are heterogeneous.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Heterogeneous Catalysis• First step is adsorption (the binding of reactant molecules
to the catalyst surface).• Adsorbed species (atoms or ions) are very reactive.• Molecules are adsorbed onto active sites on the catalyst
surface.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Heterogeneous Catalysis• Consider the hydrogenation of ethylene:
C2H4(g) + H2(g) C2H6(g), H = -136 kJ/mol.– The reaction is slow in the absence of a catalyst.– In the presence of a metal catalyst (Ni, Pt or Pd) the reaction
occurs quickly at room temperature.– First the ethylene and hydrogen molecules are adsorbed onto
active sites on the metal surface.– The H-H bond breaks and the H atoms migrate about the metal
surface.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Heterogeneous Catalysis– When an H atom collides with an ethylene molecule on the
surface, the C-C bond breaks and a C-H bond forms.– When C2H6 forms it desorbs from the surface.– When ethylene and hydrogen are adsorbed onto a surface, less
energy is required to break the bonds and the activation energy for the reaction is lowered.
Enzymes• Enzymes are biological catalysts.• Most enzymes are protein molecules with large molecular
masses (10,000 to 106 amu).
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Enzymes• Enzymes have very specific shapes.• Most enzymes catalyze very specific reactions.• Substrates undergo reaction at the active site of an
enzyme.• A substrate locks into an enzyme and a fast reaction
occurs.• The products then move away from the enzyme.
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Enzymes• Only substrates that fit into the enzyme lock can be
involved in the reaction.• If a molecule binds tightly to an enzyme so that another
substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors).
• The number of events (turnover number) catalyzed is large for enzymes (103 - 107 per second).
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
Enzymes
CatalysisCatalysis
Prentice Hall © 2003 Chapter 14
End of Chapter 14End of Chapter 14Chemical KineticsChemical Kinetics