Kinetics-2

13.4-13.6; 13.11; 13.141-December

Assigned HW13.22, 13.24, 13.26, 13.34, 13.36, 13.58, 13.62

Due: Monday 6-Dec

Lecture 33

1

Concentration vs. Time – 0th Order

2

0Akt

Arate

The rate of 0th order reactions are independent of concentration

Decreasing Concentration

aA Products

k

t

Arate

Time

[A]

Since the reaction rate does NOT change as [A] changes, [A] decreases linearly.

Slope = k

Concentration vs. Time – 1st Order

3

1Akt

Arate

The rate of 1st order

reactions are dependent on concentration

aA Products

As [A] decreases,

the rate decreases

Rea

ctio

n R

ate

Rate 1

Rate 2

Rate 3

Rate 1 > Rate 2 > Rate 3

Integrated Rate Law - st Order

4

1Akt

Arate

aA Products

kt

A

A

t

eAA

AktA

ktA

A

tkA

A

tkA

A

Akt

Arate

0

0

0

0

lnln

ln

0

Sample Problem

5

How long does it take for the concentration of A to decrease to 1.0% of its initial value in a the reaction (k = 1.0 Ms-1)

A Products

1. Determine the order of the reaction.

2. Use to solve for time. 001.0 AA

k

t

Arate

kt

AA

t

A

0

0

Sample Problem

6

How long does it take for the concentration of A to decrease to 1.0% of its initial value in a the reaction (k = 1.0 s-1)

A Products

1. Determine the order of the reaction.

2. Use to solve for time. 001.0 AA

Half Life for a 1st Order Reaction

7

How long does it take for the concentration of A to decrease to 50.0% of its initial value in a first order reaction.

A Products

05.0 AA

ktA

A

0

ln

kt

ktA

A

5.0ln

5.0ln

0

0

kt

2ln2/1

For a first order reaction, the time it takes for half of the

reactants to decompose to

products

The half life is INDEPENDENT of CONCENTRATION

for a 1st order reaction

Half Life for a 1st Order Reaction

8

A Products

kt

2ln2/1

Each t1/2 is the same for 1st order reactions.

Half Life for a 1st Order Reaction

9

A Products

kt

2ln2/1

The half life is ONLY dependent on k for a 1st order reaction

Half Life for a 1st Order Reaction

10

kt

2ln2/1

For the reaction: C2H6 2 CH3 k = 5.5 x 10-4 s-1

How long will it take for [C2H6] to fall to 1/16th it’s original concentration?

Half Life for a 1st Order Reaction

11

kt

2ln2/1

For the reaction: C2H6 2 CH3 k = 5.5 x 10-4 s-1

Calculate how long it will take for 1.5 M CH3 to be produced if the reaction begins with 1 M C2H6.

Concentration vs. Time – 2nd Order

12

2Akt

Arate

The rate of 2nd order reactions are dependent on

concentration

aA Products

Bigger k faster rate

Integrated Rate Law – 2nd Order

13

2Akt

Arate

aA Products

011

Akt

A

A couple math steps

Integrated Rate Law Summary

14

011

Akt

A

2Akrate Akratekrate

kteAA 0 0AktA

RateLaw

IntegratedRate Law

0th Order 1st Order 2nd Order

Rates and Temperature – the link to Thermodynamics

15

RT

EAk alnln

Arrhenius Equation

RT

Ea

Aek

Arrhenius parameters:

Temperature independent

A pre-exponential factorEa activation energy

Y-int = lnASlope = -Ea/R

Rates and Temperature – the link to Thermodynamics

16

RT

EAk alnln

Arrhenius Equation

RT

Ea

Aek

The rate constant for the decomposition of N2O5 at 45 °C is k = 5.1 x 10-4 s-1. Determine the value of the rate constant at 50 °C if the activation energy is 103 kJ mol-1.

Rates and Temperature – the link to Thermodynamics

17

RT

EAk alnln

Arrhenius Equation

RT

Ea

Aek

Arrhenius parameters:

Temperature independent

A pre-exponential factorEa activation energy

The reverse reaction has a much larger Energy Barrier (Ea)

Activation Energy and Catalysis

18