Chemical Kinetics

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# Chemical Kinetics - PowerPoint PPT Presentation

Chemical Kinetics. Chapter 15. A B. ___ = . D [A]. D [B]. ___ = -. D t. D t. Chemical Kinetics. ____________________ – does a reaction take place? ____________________– how fast does a reaction proceed?.

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A B

___ =

D[A]

D[B]

___ = -

Dt

Dt

Chemical Kinetics

____________________ – does a reaction take place?

____________________– how fast does a reaction proceed?

____________ ____________ is the change in the concentration of a reactant or a product with time (M/s).

D[A] = change in concentration of A over

time period Dt

D[B] = change in concentration of B over

time period Dt

Because [A] decreases with time, D[A] is __________ .

A B

Rate =

D[A]

D[B]

Rate =- -

Dt

Dt

Chemical Kinetics

Thermodynamics – does a reaction take place?

Kinetics – how fast does a reaction proceed?

Reaction Rate is the change in the concentration of a reactant or a product with time (M/s).

D[A] = change in concentration of A over

time period Dt

D[B] = change in concentration of B over

time period Dt

Because [A] decreases with time, D[A] is negative.

A B

time

rate =

D[A]

D[B]

rate = -

Dt

Dt

Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)

time

Br2(aq)

393 nm

393 nm

Detector

light

Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)

slope of

tangent

slope of

tangent

slope of

tangent

[Br2]final – [Br2]initial

D[Br2]

_________________ = -

= -

Dt

tfinal - tinitial

_________________ = rate for specific instance in time

Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)

slope of

tangent

slope of

tangent

slope of

tangent

[Br2]final – [Br2]initial

D[Br2]

Average Rate = -

= -

Dt

tfinal - tinitial

Instantaneous Rate = rate for specific instance in time

rate

k =

[Br2]

Rates of the Reaction Between Molecular Bromine and Formic Acid at 25ºC

rate a [Br2]

rate = k [Br2]

= ____ _________

= 3.50 x 10-3 s-1

rate

k =

[Br2]

Rates of the Reaction Between Molecular Bromine and Formic Acid at 25ºC

rate a [Br2]

rate = k [Br2]

= Rate Constant

= 3.50 x 10-3 s-1

2H2O2 (aq) 2H2O (l) + O2 (g)

[O2] = P

n

V

1

1

D[O2]

P = RT = [O2]RT

RT

RT

DP

rate =

=

Dt

Dt

measure DP over time

PV = nRT

2A B

aA + bB cC + dD

rate = -

=

=

rate = -

= -

D[C]

D[B]

D[A]

D[B]

D[D]

D[A]

rate =

1

1

1

1

1

Dt

Dt

Dt

Dt

Dt

Dt

c

d

a

2

b

Reaction Rates and Stoichiometry

Two moles of A disappear for each mole of B that is formed.

Write the rate expression for the following reaction:

CH4(g) + 2O2(g) CO2(g) + 2H2O (g)

D[CH4]

D[CO2]

D[O2]

D[H2O]

rate = -

=

=

=

Dt

Dt

Dt

Dt

Which relationship correctly compares the rates of the following reactants and products?

C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l)

a)

b)

c)

d)

e)

aA + bB cC + dD

The Rate Law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers.

Rate =

reaction is _______ order in A

reaction is _______ order in B

reaction is _______________ order overall

aA + bB cC + dD

The Rate Law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers.

Rate = k [A]m [B]n

reaction is mth order in A

reaction is nth order in B

reaction is (m + n)th order overall

F2(g) + 2ClO2(g) 2FClO2(g)

Rate Data for the Reaction between F2 and ClO2

rate =

Double [F2] with [ClO2] constant

Rate _____________

x = 1

Rate ______________

y = 1

rate =

F2(g) + 2ClO2(g) 2FClO2(g)

Rate Data for the Reaction between F2 and ClO2

rate = k [F2]m[ClO2]n

Double [F2] with [ClO2] constant

Rate doubles

m = 1

n = 1

rate = k [F2]1[ClO2]1

F2(g) + 2ClO2(g) 2FClO2(g)

1

Rate Laws

• Rate laws are always determined _______________.
• Reaction order is always defined in terms of ________ (not _____________) concentrations.
• The order of a reactant is not related to the ___________________ ____________________ of the reactants in the balanced chemical equation.

rate = k [F2][ClO2]

F2(g) + 2ClO2(g) 2FClO2(g)

1

Rate Laws

• Rate laws are always determined experimentally.
• Reaction order is always defined in terms of reactant (not product) concentrations.
• The order of a reactant is not related to the reaction coefficient of the reactant in the balanced chemical equation.

rate = k [F2][ClO2]

Determine the rate law and calculate the rate constant for the following reaction from the following data:

S2O82-(aq) + 3I-(aq) 2SO42-(aq) + I3-(aq)

rate

k =

M/s

=

[S2O82-][I-]

( M)( M)

rate =

y =

x =

rate =

Double [I-], rate ___________ (experiment 1 & 2)

Double [S2O82-], rate ___________ (experiment 2 & 3)

= ______ /M•s

Determine the rate law and calculate the rate constant for the following reaction from the following data:

S2O82-(aq) + 3I-(aq) 2SO42-(aq) + I3-(aq)

rate

k =

1.1 x 10-4 M/s

=

[S2O82-][I-]

( 0.08 M)( 0.017 M)

rate=k[S2O82-]m[I-]n

m = 1

n = 1

rate=k[S2O82-][I-]

Double [I-], rate doubles (experiment 1 & 2)

Double [S2O82-], rate doubles (experiment 2 & 3)

= 0.081 /M•s

A product

rate

=

[A]

M/s

D[A]

-

M

= k [A]

Dt

[A] = [A]0exp(-kt)

ln[A] = ln[A]0 - kt

D[A]

rate = -

Dt

First - Order Reactions

rate = k [A]

= 1/s or s-1

k =

[A] is the concentration of A at any time t

[A]0 is the concentration of A at time t=0

0.88 M

ln

The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ?

0.14 M

=

2.8 x 10-2 s-1

ln

ln[A]0 – ln[A]

=

k

k

[A]0

[A]

[A]0 = 0.88 M

ln[A] = ln[A]0 - kt

[A] = 0.14 M

kt = ln[A]0 – ln[A]

= 66 s

t =

[A]0

What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1?

ln

[A]0/2

0.693

=

=

=

=

k

k

ln2

ln2

0.693

=

k

k

5.7 x 10-4 s-1

First - Order Reactions

The half-life, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration.

t½ = t when [A] = [A]0/2

= 1216 s = 20 minutes

How do you know decomposition is first order?

units of k (s-1)

A product

# of

half-lives

[A] = [A]0/n

First-order reaction

1

2

2

4

3

8

4

16

A product

rate

=

[A]2

M/s

D[A]

1

1

-

M2

= k [A]2

=

+ kt

Dt

[A]

[A]0

t½ =

D[A]

rate = -

Dt

1

k[A]0

Second - Order Reactions

rate = k [A]2

= 1/M•s

k =

[A] is the concentration of A at any time t

[A]0 is the concentration of A at time t = 0

t½ = t when [A] = [A]0/2

A product

rate

[A]0

D[A]

-

= k

Dt

[A]0

t½ =

D[A]

2k

rate = -

Dt

Zeroth - Order Reactions

rate = k [A]0 = k

Reminder: what is the value of any number raised to the zero power? x0= ??

= M/s

k =

[A] is the concentration of A at any time t

[A] = [A]0 - kt

[A]0 is the concentration of A at time t=0

t½ = t when [A] = [A]0/2

Concentration-Time Equation

Order

Rate Law

Half-Life

1

1

=

+ kt

[A]

[A]0

=

[A]0

t½ =

t½ =

ln2

2k

k

1

k[A]0

Summary of the Kinetics of Zero-Order, First-Order and Second-Order Reactions

[A] = [A]0 - kt

rate = k

0

ln[A] = ln[A]0 - kt

1

rate = k [A]

2

rate = k [A]2

Implications of the Collision Theory of Chemical Kinetics

Rate 

The ____________ ____________ (Ea ) is the minimum amount of energy required to initiate a chemical reaction.

Implications of the Collision Theory of Chemical Kinetics

Rate  1/Ea

The Activation Energy (Ea ) is the minimum amount of energy required to initiate a chemical reaction.

A + B C + D

__________ Reaction

__________ Reaction

The __________ __________ (___)is the minimum amount of energy required to initiate a chemical reaction.

A + B C + D

Endothermic Reaction

Exothermic Reaction

The Activation Energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.

The Rate Constant Depends on Temperature

What happens to the rate of a chemical reaction as the temperature increases?

Why does this happen?

Explain this observation in terms of the Collision Theory of Kinetics.

We express this dependence of rate on temperature in the ___________ equation.

The Rate Constant Depends on Temperature

What happens to the rate of a chemical reaction as the temperature increases?

Why does this happen?

Explain this observation in terms of the Collision Theory of Kinetics.

We express this dependence of rate on temperature in the Arrhenius Equation.

lnk = -

+ lnA

Ea

1

T

R

The Rate Constant Depends on Temperature

Arrhenius equation

k =

Ea= the activation energy (J/mol)

R = the gas constant (8.314 J/K•mol)

T = the absolute temperature

A = frequency factor/collision frequency

e = the base of the natural log scale

Why do we write it in this form?

lnk = -

+ lnA

Ea

1

T

R

Why do we rewrite the equation in this form?

y = m x + b

slope

Now a plot of lnkversus 1/T is a __________ line,Ea/R is the _________, and the _____________________is lnA.

lnk = -

+ lnA

Ea

1

T

R

Why do we rewrite the equation in this form?

y = m x + b

slope

Now a plot of lnkversus 1/T is a straight line,Ea/R is the slope, and the y-intercept is lnA.

lnk = -

+ lnA

Ea

1

T

R

Ex.14.6, p.451

A balanced chemical equation does not tell us how the reaction actually takes place.

Usually it just represents the sum of a series of simpler elementary steps or elementary reactions.

We try to deduce these steps and propose a _______________ _______________ .

A balanced chemical equation does not tell us how the reaction actually takes place.

Usually it just represents the sum of a series of simpler elementary steps or elementary reactions.

We try to deduce these steps and propose a reaction mechanism.

2NO (g) + O2 (g) 2NO2 (g)

Elementary step:

NO + NO N2O2

+

Elementary step:

N2O2 + O2 2NO2

Overall reaction:

2NO + O2 2NO2

Reaction Mechanisms

The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions.

The sequence of elementary steps that leads to product formation is the reaction mechanism.

N2O2 is detected during the reaction!

Elementary step:

NO + NO N2O2

+

Elementary step:

N2O2 + O2 2NO2

Overall reaction:

2NO + O2 2NO2

Species that appear in a reaction mechanism but not in the overall balanced equation are called ___________.

An ___________ is always formed in an early elementary step and consumed in a later elementary step.

• The _______________ of a reaction is the number of molecules reacting in an elementary step.
• ____________ reaction – elementary step with 1 molecule
• ___________ reaction – elementary step with 2 molecules
• ___________ reaction – elementary step with 3 molecules

Unimolecular reaction

Bimolecular reaction

Bimolecular reaction

A + B products

A + A products

A products

Rate Laws and Elementary Steps

rate = k [A]

rate = k [A][B]

rate = k [A]2

• Writing plausible reaction mechanisms:
• The sum of the elementary steps must give the overall balanced equation for the reaction.
• The rate-determining step should predict the same rate law that is determined experimentally.

The rate-determining step is the __________step in the sequence of steps leading to product formation

Step 1:

Step 2:

NO2 + NO2 NO + NO3

The experimental rate law for the reaction between NO2 and CO to produce NO and CO2 is rate = k[NO2]2. The reaction is believed to occur via two steps:

NO3 + CO NO2 + CO2

What is the equation for the overall reaction?

What is the intermediate?

What can you say about the relative rates of steps 1 and 2?

rate = is the rate law for step 1 so

step 1 must be ___________ than step 2

uncatalyzed

catalyzed

Ea

k

'

Ea< Ea

A _____________ is a substance that increases the rate of a chemical reaction without itself being consumed.

k = A •exp( -Ea/RT )

ratecatalyzed > rateuncatalyzed

In ____________________________________ catalysis, the reactants and the catalysts are in different phases.

• Haber synthesis of ammonia
• Ostwald process for the production of nitric acid
• Catalytic converters

In ________________________ catalysis, the reactants and the catalysts are dispersed in a single phase, usually liquid.

• Acid catalyses
• Base catalyses

Fe/Al2O3/K2O

N2 (g) + 3H2 (g) 2NH3 (g)

catalyst

Haber Process

4NH3(g) + 5O2(g) 4NO (g) + 6H2O (g)

2NO (g) + O2(g) 2NO2(g)

2NO2(g) + H2O (l) HNO2(aq) + HNO3(aq)

Pt-Rh catalysts used

in Ostwald process

Hot Pt wire

over NH3 solution

Ostwald Process

Pt catalyst

catalytic

CO + Unburned Hydrocarbons + O2

CO2 + H2O

converter

catalytic

NO + NO2

N2 + O2

converter

Catalytic Converters

enzyme

catalyzed

uncatalyzed