1

1

Lecture 2Professor Hicks

Inorganic Chemistry (CHE152)

• Rate Law relates the rate of reaction to

concentrations

• Integrated Rate Law relates concentrations

and time

Rate law Integrated Rate Law

Rate = k [A] [A] = [A]oe-kt

Rate = k [A]2

Integrated Rate Laws

2

1

[A]= kt +

1

[A]o

3

1

2

1

8

Half life (t½ )

and doubling time

the time it takes for the

amount of a reactant go

down 50% is called the

half life (t½)

Time it takes a product

Concentration to double

is the dobling time

for many reactions

half- life and doubling

time change as the reaction

proceeds

900 s 1200 s 3600 s

9

half life (t½ ) for first order reaction

• For a first order reaction half lives of reactants

and doubling times of products are constant

• This is only true for first order reactions

10

First-order processes• half life/doubling time is constant for a first order process

• Applies to some chemical reactions

• Applies to radioactive decay (nuclear reactions)

• Applies to the growth of populations of cells, people, animals, before they get too crowded

- sterilization works by making initial amount of cells zero

• Applies to compounding of interest

• When a process has not been studied in enough detail to know if it is first order it is often treated as if it is first order

- Called a pseudo-first order analysis

- Like a cheap suit – one size fits all

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100 110

Time (s)

[N2O]

Rate data for the reaction

N2 + ½ O2 N2O

12Concentration of Nitrogen Oxide vs Time

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (s)

[NO

]

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14 16 18 20

A B

Time (s)

[A]

Example: a) Measure the first four half lives.

b) Is this a first-order process?

c) What is the half life?

1

13

14

[CH3CHO] vs Time (problem 13.48)

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200 250

Time (s)

[CH

3C

HO

] (M

)

1

How chemical reactions occur:

the collision model

molecules must collide with:

1) correct orientation and

2) enough energy (the activation energy or more)

effective collisions

orientation effect

effective collisions• collisions that meet the two conditions are called

effective collisions and lead to reaction

• the higher the frequency of effective collisions, the faster the reaction rate

• during an effective collision, a temporary, high energy chemical species is formed called atransition state

2

19

effect of temperature on rate

• increasing the temperature increases the rate of

a reaction by increasing the rate constant k

• Svante Arrhenius investigated this relationship

and showed that:

RT

Ea

eAk

R is the gas constant in energy units, 8.314 J/(mol∙K)

where T is the temperature in Kelvins

A is called the frequency factor

Ea is the activation energy, the energy needed for

the molecules to react

20

Arrhenius equation

RT

Ea

eAk

RT has units, J/mol it reflects the energy per mole of matter

Ea/RT compares the activation energy to the available energy

Reflects efficiency of collisions for different reactions

reflects the energy requirement

much less 1 when Ea >> RT

close to 1 when Ea << RT

Svante Arrhenius

Arrhenius equation

• Activation energy best determined graphically

• Rate constant measured at different temperatures

• Graphs of ln (k) vs 1/T (T must be in Kelvins)

ln (k) = ln(A) – Ea/RT

Slope = -Ea/RT and

Intercept = ln (a)21

RT

Ea

eAk Svante Arrhenius

3

22

Arrhenius equation:

two-point form

• if you only have two k values at two temperatures this form of the Arrhenius equation can be used:

121

2

T

1

T

1ln

R

E

k

k a

the A factor is eliminated from this equation

Boltzmann speed/energy

distribution

Ludwig Boltzmann

• increasing temperature

increases average speed

• higher speeds higher energy

- kinetic energy = ½ mv2

higher

temperature

% m

ole

cule

s

wit

h a

sp

eed

0 300 600 900 1200

speed (m/s)

lower

temperature

50% 50%

average

speed

• superior teaching

increases students understanding

• better understanding higher MCAT scores

Boltzmann energy distribution

like the Hicks grade distribution

other

classes

Hicks’

class

% s

tud

ents

wit

h a

sco

re

0 10 20 30 40 45

MCAT Score

Charles Hicks

class averages

on MCAT medical school

MCAT requirement

class

Hicks’

all

others

20%

4%

% students with

required grade

20%4%

4

0 300 600 900 1200

speed (m/s)%

mo

lecu

les

with

a s

pe

ed

0 300 600 900 1200

speed (m/s)

% m

ole

cu

les

with

a s

pe

ed

Boltzmann speed/energy

distribution

• higher speeds = higher energy

• reactions have energy requirements

higher

temperature

% m

ole

cule

s

wit

h a

spee

d

0 300 600 900 1200

speed (m/s)

lower

temperature

every speed has a kinetic energy

KE = ½mv2

higher

temperature

lower

temperature

55%

80%20%

45%

at the higher temperature larger

% of molecules have enough

kinetic energy to react

Ludwig BoltzmannLudwig Boltzmann

20% have

enough

energy

80% don’t

have enough

energy

55% have

enough

energy

45% don’t

have enough

energy

reaction requires

this speed (energy)

or greater

increasing temperature

increases rate two ways:

1) increasing the number of

molecules with activation

energy or greater

2) increasing the frequency

of collisions

Boltzmann energy

distribution

Ludwig Boltzmann

Study these facts

They could be T/F

exam questions

highest potential energy

lower potential energy

high point is like the

transition state

activation energy

5

heat

released

overall

reaction

(energy absorbed)

reactants

transition state

activation energy

(energy released)

transition state

products

Catalysts

• catalysts are substances that affect the rate of a reaction without being consumed

• catalysts work by lowering activation energy

Example

O3 (g)+ O (g) 2O2 (g)

ozone

• very slow without Cl catalyst

• catalyzed by Cl

• catalysts appear in rate law because they must get “bumped into”

rate law rate = k[O3][O][Cl]

enzymes

• most biological reactions require a catalyst to proceed at a reasonable rate

• protein molecules that catalyze biological reactions are called enzymes

• enzymes work by binding reactants and orienting them for reaction

6

enzymatic hydrolysis of sucrose

1

32

Arrhenius plot for problem 13.79

-9

-8.5

-8

-7.5

-7

-6.5

-6

-5.5

-5

1.45E-03 1.55E-03 1.65E-03 1.75E-03

1/T (K-1)

ln (k

)