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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
)