c h a p t e r 12 chemical kinetics. reaction rates01 reaction rate: the change in the concentration...

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


• Consider the decomposition of N2O5 to give NO2 and O2: 2 N2O5(g) 4 NO2(g) + O2(g)

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


• 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.


• 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


• 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


• 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


• 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 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


• 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


• Identifying First-Order Reactions:


• Show that the decomposition of N2O5 is first order and calculate the rate constant.


• 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


• Half-Life: Time for reactant concentration to decrease by halfits original value.

t12

1k[A]

0


• 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.


• 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.


• 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.


• Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation.

• Unimolecular: Single reactant molecule.


• Bimolecular: Two reactant molecules.

• Termolecular: Three reactant molecules.


• 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.


• 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.


• 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.


• 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.


• This relationship is summarized by the Arrhenius equation.

• Taking logs and rearranging, we get:

lnk Ea

R

1T

lnA

k Ae Ea RT


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 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


• 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


• 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?


• Homogeneous Catalyst: Exists in the same phase as the reactants.

• Heterogeneous Catalyst: Exists in different phase to the reactants.


• Catalytic Hydrogenation:

c h a p t e r 12 chemical kinetics. reaction rates01 reaction rate: the change in the concentration...

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