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Chemical Kinetics Ch 13. We have learned that enthalpy is the sum of the internal energy plus the energy associated with the work done by the system (PV) on the atmosphere In addition, entropy and Gibb’s Free Energy predict whether a reaction will occur or not

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chemical kinetics ch 13
Chemical Kinetics Ch 13
  • We have learned that enthalpy is the sum of the internal energy plus the energy associated with the work done by the system (PV) on the atmosphere
  • In addition, entropy and Gibb’s Free Energy predict whether a reaction will occur or not
  • Now we will examine the rate at which a reaction will proceed
slide2

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.

13.1

slide3

A B

time

rate =

D[A]

D[B]

rate = -

Dt

Dt

13.1

slide4

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

time

Br2(aq)

393 nm

393 nm

Detector

light

D[Br2] aDAbsorption

13.1

slide5

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

13.1

slide6

rate

k =

[Br2]

rate a [Br2]

rate = k [Br2]

= rate constant

= 3.50 x 10-3 s-1

13.1

slide7

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

13.1

slide9

2A B

aA + bB cC + dD

rate = -

=

=

rate = -

= -

D[D]

D[B]

D[A]

D[B]

D[C]

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.

13.1

slide10

D[CO2]

=

Dt

D[CH4]

rate = -

Dt

Write the rate expression for the following reaction:

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

D[H2O]

=

Dt

D[O2]

= -

1

1

Dt

2

2

13.1

slide11

aA + bB cC + dD

The Rate Law

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]x[B]y

reaction is xth order in A

reaction is yth order in B

reaction is (x +y)th order overall

13.2

slide12

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

rate = k [F2]x[ClO2]y

Double [F2] with [ClO2] constant

Rate doubles

x = 1

rate = k [F2][ClO2]

Quadruple [ClO2] with [F2] constant

Rate quadruples

y = 1

13.2

slide13

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 stoichiometric coefficient of the reactant in the balanced chemical equation.

rate = k [F2][ClO2]

13.2

slide14

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 =

2.2 x 10-4 M/s

=

[S2O82-][I-]

(0.08 M)(0.034 M)

rate = k [S2O82-]x[I-]y

y = 1

x = 1

rate = k [S2O82-][I-]

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

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

= 0.08/M•s

13.2

definitions 1 st order reaction
Definitions: 1st Order Reaction
  • First Order Reaction: The reaction that occurs first, not always the one desired. For example, the formation of brown gunk in an organic prep.
slide16

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

13.3

definitions physical chemistry
Definitions: Physical Chemistry
  • The pitiful attempt to apply y=mx+b to everything in the universe.
an example
An Example
  • A reaction is 25% complete in 42 seconds. Calculate the half life.

Ln 1/.75=-.287, Div by 42 and k=6.84x10-3

T1/2 =0.693/k=101 s

slide21

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 =

13.3

slide22

[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

= 1200 s = 20 minutes

How do you know decomposition is first order?

units of k (s-1)

13.3

slide23

A product

# of

half-lives

[A] = [A]0/n

First-order reaction

1

2

2

4

3

8

4

16

13.3

slide26

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

13.3

slide27

A + B C + D

Endothermic Reaction

Exothermic Reaction

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

13.4

slide28

lnk = -

+ lnA

Ea

1

T

R

Temperature Dependence of the Rate Constant also known as the Arrhenius equation

k = A •exp( -Ea/RT )

(Arrhenius equation)

Eais the activation energy (J/mol)

R is the gas constant (8.314 J/K•mol)

T is the absolute temperature

A is the frequency factor

13.4

activation energy
Activation Energy
  • The useful quantity of energy available in one cup of coffee
slide30

A product

rate

[A]0

D[A]

-

= k

Dt

[A]0

t½ =

D[A]

2k

rate = -

Dt

Zero-Order Reactions

rate = k [A]0 = k

= 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

13.3

slide31

lnk = -

+ lnA

Ea

1

T

R

13.4

slide33

uncatalyzed

catalyzed

Ea

k

Ea< Ea

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

k = A •exp( -Ea/RT )

ratecatalyzed > rateuncatalyzed

13.6

slide34

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

  • Acid catalysis
  • Base catalysis

13.6

slide35

Fe/Al2O3/K2O

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

catalyst

Haber Process

13.6

slide36

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

13.6

slide37

catalytic

CO + Unburned Hydrocarbons + O2

CO2 + H2O

converter

catalytic

2NO + 2NO2

2N2 + 3O2

converter

Catalytic Converters

13.6

slide39

enzyme

catalyzed

uncatalyzed

D[P]

rate =

Dt

rate = k [ES]

13.6

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