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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

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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

• Now we will examine the rate at which a reaction will proceed

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

A B

time

rate =

D[A]

D[B]

rate = -

Dt

Dt

13.1

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

time

Br2(aq)

393 nm

393 nm

Detector

light

13.1

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

rate

k =

[Br2]

rate a [Br2]

rate = k [Br2]

= rate constant

= 3.50 x 10-3 s-1

13.1

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

13.1

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

13.1

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

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

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

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

y = 1

13.2

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

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: 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.

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

• The pitiful attempt to apply y=mx+b to everything in the universe.

Decomposition of N2O5

13.3

### 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

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

[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

A product

# of

half-lives

[A] = [A]0/n

First-order reaction

1

2

2

4

3

8

4

16

13.3

13.3

Second-Order Reactions- ignore

13.3

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

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

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

• The useful quantity of energy available in one cup of coffee

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

lnk = -

+ lnA

Ea

1

T

R

13.4

13.4

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

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

Fe/Al2O3/K2O

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

catalyst

Haber Process

13.6

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

catalytic

CO + Unburned Hydrocarbons + O2

CO2 + H2O

converter

catalytic

2NO + 2NO2

2N2 + 3O2

converter

Catalytic Converters

13.6

Enzyme Catalysis

13.6

enzyme

catalyzed

uncatalyzed

D[P]

rate =

Dt

rate = k [ES]

13.6