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C h a p t e r 12C h a p t e r 12
Chemical KineticsChemical Kinetics
Reaction Rates 01Reaction Rates 01
• Reaction Rate: The change in the concentration of a reactant or a product with time (M/s).
Reactant Products aA bB
Rate [A]t
Rate [B]t
Reaction Rates 02Reaction Rates 02
• Consider the decomposition of N2O5 to give NO2 and O2: 2 N2O5(g) 4 NO2(g) + O2(g)
Reaction Rates 03Reaction Rates 03
Rate Law & Reaction Order 01Rate Law & Reaction Order 01
• Rate Law: Shows the relationship of the rate of a
reaction to the rate constant and the concentration
of the reactants raised to some powers.
• For the general reaction: aA + bB cC + dD
rate = k[A]x[B]y
• x and y are NOT the stoichiometric coefficients.• k = the rate constant
Rate Law & Reaction Order 02Rate Law & Reaction Order 02
• Reaction Order: The sum of the powers to which
all reactant concentrations appearing in the rate
law are raised.
• Reaction order is determined experimentally:
1. By inspection.
2. From the slope of a log(rate) vs. log[A] plot.
Rate Law & Reaction Order 03Rate Law & Reaction Order 03
• Determination by inspection:
aA + bB cC + dD
Rate = R = k[A]x[B]y Use initial rates (t = 0)
yx
yx
yx
B
B
A
A
BAk
BAk
R
R
1
2
1
2
11
22
1
2
][
][
][
][
][][
][][
121
2
1
2 [B][B]if][
][
x
A
A
R
R
Rate Law & Reaction Order 04Rate Law & Reaction Order 04
• Determination by plot of a log(rate) vs. log[A]:
aA + bB cC + dD
Rate = R = k[A]x[B]y
Log(R) = log(k) + x·log[A] + y·log[B]
= const + x·log[A] if [B] held constant
Rate Law & Reaction Order 05Rate Law & Reaction Order 05
• The reaction of nitric oxide with hydrogen at
1280°C is: 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g)
• From the following data determine the rate law and
rate constant.Experiment [NO] [H2] Initial Rate (M/s)
1 5.0 x 10–3 2.0 x10–3 1.3 x 10–5
2 10.0 x 10–3 2.0 x 10–3 5.0 x 10–5
3 10.0 x 10–3 4.0 x 10–3 10.0 x 10–5
Rate Law & Reaction Order 06Rate Law & Reaction Order 06
• The reaction of peroxydisulfate ion (S2O82-) with
iodide ion (I-) is:
S2O82-
(aq) + 3 I-(aq) 2 SO4
2-(aq) + I3
-(aq)
• From the following data, determine the rate law and rate constant.
Experiment [S2O82-] [I-] Initi al Rate (M/s)
1 0.080 0.034 2.2 x 10-4
2 0.080 0.017 1.1 x 10-4
3 0.16 0.017 2.2 x 10-4
Rate Law & Reaction Order 07Rate Law & Reaction Order 07
• Rate Constant: A constant of proportionality between the reaction rate and the concentration of reactants.
rate [Br2]
rate = k[Br2]
First-Order Reactions 01First-Order Reactions 01
• First Order: Reaction rate depends on the reactant
concentration raised to first power.
Rate = k[A]
Rate = - A t
First-Order Reactions 02First-Order Reactions 02
• Using calculus we obtain the integrated rate equation:
• Plotting ln[A]t against t gives a straight line of slope –k.
An alternate expression is:
[A]t [A]0e kt exponential decay law
ln[A]t
[A]0
kt or ln[A]t ln[A]o kt
First-Order Reactions 03First-Order Reactions 03
• Identifying First-Order Reactions:
First-Order Reactions 04First-Order Reactions 04
• Show that the decomposition of N2O5 is first order and calculate the rate constant.
First-Order Reactions 06First-Order Reactions 06
• Half-Life: Time for reactant concentration to decrease by halfits original value.
t12
ln2k
Second-Order Reactions 01Second-Order Reactions 01
•Second-Order Reaction:
A Products A + B Products
Rate = k[A]2 Rate = k[A][B]
•These can then be integrated to give:
1[A]t
kt 1[A]0
Second-Order Reactions 02Second-Order Reactions 02
• Half-Life: Time for reactant concentration to decrease by halfits original value.
t12
1k[A]
0
Second-Order Reactions 03Second-Order Reactions 03
• Iodine atoms combine to form molecular iodine in the gas
phase.
I(g) + I(g) I2(g)
• This reaction follows second-order kinetics and k
= 7.0 x 10–1 M–1s–1 at 23°C. (a) If the initial concentration of I
was 0.086 M, calculate the concentration after 2.0 min. (b)
Calculate the half-life of the reaction if the initial concentration
of I is 0.60 M and if it is 0.42 M.
Reaction Mechanisms 01Reaction Mechanisms 01
• A reaction mechanism
is a sequence of
molecular events, or
reaction steps, that
defines the pathway
from reactants to
products.
Reaction Mechanisms 02Reaction Mechanisms 02
• Single steps in a mechanism are called elementary steps (reactions).
• An elementary step describes the behavior of individual molecules.
• An overall reaction describes the reaction stoichiometry.
Reaction Mechanisms 03Reaction Mechanisms 03
• NO2(g) + CO(g) NO(g) + CO2(g) Overall
• NO2(g) + NO2(g) NO(g) + NO3(g) Elementary
• NO3(g) + CO(g) NO2(g) + CO2(g) Elementary
• The chemical equation for an elementary reaction is a description of an individual molecular event that involves the breaking and/or making of chemical bonds.
Reaction Mechanisms 04Reaction Mechanisms 04
• Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation.
• Unimolecular: Single reactant molecule.
Reaction Mechanisms 05Reaction Mechanisms 05
• Bimolecular: Two reactant molecules.
• Termolecular: Three reactant molecules.
Reaction Mechanisms 06Reaction Mechanisms 06
• Determine the overall reaction, the reaction intermediates, and the molecularity of each individual elementary step.
Rate Laws and Reaction Mechanisms 01Rate Laws and Reaction Mechanisms 01
• Rate law for an overall reaction must be determined experimentally.
• Rate law for elementary step follows from its molecularity.
Rate Laws and Reaction Mechanisms 02Rate Laws and Reaction Mechanisms 02
• The rate law of each elementary step follows its molecularity.
• The overall reaction is a sequence of elementary steps called the reaction mechanism.
• Therefore, the experimentally observed rate law for an overall reaction must depend on the reaction mechanism.
Rate Laws and Reaction Mechanisms 03Rate Laws and Reaction Mechanisms 03
• The slowest elementary step in a multistep reaction is called the rate-determining step.
• The overall reaction cannot occur faster than the speed of the rate-determining step.
• The rate of the overall reaction is therefore determined by the rate of the rate-determining step.
Rate Laws and Reaction Mechanisms 04Rate Laws and Reaction Mechanisms 04
Rate Laws and Reaction Mechanisms 05Rate Laws and Reaction Mechanisms 05
• The following reaction has a second-order rate law:H2(g) + 2 ICl(g) I2(g) + 2 HCl(g) Rate = k[H2][ICl]
• Devise a possible mechanism.
• The following substitution reaction has a first-order rate law:
Co(CN)5(H2O)2–(aq) + I– Co(CN)5I3–(aq) + H2O(l)
Rate = k[Co(CN)5(H2O)2–]
• Suggest a mechanism in accord with the rate law.
The Arrhenius Equation01The Arrhenius Equation01
• Collision Theory: A bimolecular reaction occurs when two correctly oriented molecules collide with sufficient energy.
• Activation Energy (Ea): The potential energy
barrier that must be surmounted before reactants can be converted to products.
The Arrhenius Equation02The Arrhenius Equation02
The Arrhenius Equation03The Arrhenius Equation03
The Arrhenius Equation04The Arrhenius Equation04
• This relationship is summarized by the Arrhenius equation.
• Taking logs and rearranging, we get:
lnk Ea
R
1T
lnA
k Ae Ea RT
The Arrhenius Equation05The Arrhenius Equation05
Temp(°C)
k(M-1 s-1)
283 3.52e-7
356 3.02e5
393 2.19e-4
427 1.16e-3
508 3.95e-2
The Arrhenius Equation07The Arrhenius Equation07
The second-order rate constant for the decomposition of nitrous oxide (N2O) into nitrogen molecule and oxygen atom has been measured at different temperatures:
Determine graphicallythe activation energyfor the reaction.
k (M -1s-1) t (°C)
1.87x10-3 6000.0113 6500.0569 7000.244 750
The second-order rate constant for the decomposition of nitrous oxide (N2O) into nitrogen molecule and oxygen atom has been measured at different temperatures:
Determine graphicallythe activation energyfor the reaction.
k (M -1s-1) t (°C)
1.87x10-3 6000.0113 6500.0569 7000.244 750
The Arrhenius Equation09The Arrhenius Equation09
• A simpler way to use this is by comparing the rate
constant at just two temperatures:
• If the rate of a reaction doubles by increasing the
temperature by 10°C from 298.2 K to 308.2 K, what is
the activation energy of the reaction?
lnk2k1
EaR
1T2
1T1
• A catalyst is a substance that increases the rate of a reaction without being consumed in the reaction.
Catalysis 01Catalysis 01
Catalysis 02Catalysis 02
• The relative rates of the reaction A + B AB in vessels a–d are 1:2:1:2. Red = A, blue = B, yellow = third substance C.
(a) What is the order of reaction in A, B, and C?(b) Write the rate law.(c) Write a mechanism that agrees with the rate law.(d) Why doesn’t C appear in the overall reaction?
Catalysis 03Catalysis 03
• Homogeneous Catalyst: Exists in the same phase as the reactants.
• Heterogeneous Catalyst: Exists in different phase to the reactants.
Catalysis 04Catalysis 04
• Catalytic Hydrogenation:
Catalysis 05Catalysis 05