Chemical Kinetics 4 lectures Dr' Paul T' Maragh Tue' 5:00 p'm' Wed' 9:00 a'm' 1 full question on C10

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Chemical Kinetics(4 lectures)Dr. Paul T.
MaraghTue. 500 p.m. / Wed. 900 a.m.1 full
question on C10K Paper 1
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What is Chemical Kinetics?
The study of the speed or RATE at which a
chemical reaction occurs.
What are some of the factors that affect the
RATE of a chemical reaction?

• The nature of the reactants and products

• Temperature

• Catalysts

• The concentrations of the reacting species.

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Homogeneous reactionsgas phase H2(g) I2(g)
2HI(g)liquid phase NaOH(aq) HCl(aq)
NaCl(aq) H2O(l)

• Heterogeneous reactions
• Fe(s) 2H(aq) Fe2(aq) H2(g)

Irreversible reaction
Reversible reaction (equilibrium)
e.g. N2O4(g) 2NO2(g)
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The factors mentioned will affect the composition
of the reaction mixture at any given time.
Therefore
The change in composition of the reaction mixture
with time is the rate of reaction, denoted by R,
r or ?. R is the same whether monitoring
reactants or products Generally,

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Example 2H2 O2 2H2O
Then,
Compare rate of loss of H2 and rate of loss of O2.

• R has fixed dimensionality ratio of
  concentration upon time, i.e. (amount of
  material)(volume)-1 time-1 common units
  mol dm-3 s-1

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Graphically
C
Conc. / M
A
Time / s
The tangents to the curve are the slopes Rate
All reaction rates are positive
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Rate laws, rate constants, reaction order

• Consider the simple reaction A B P

R (AB) And, R ? Am Bn With
the use of a proportionality constant k, which is
the rate constant (independent of conc. but
dependent on temp.), R -dA/dt k Am
Bn Such an equation is called the rate law
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The exponents m and n are the order of the
reaction with respect to reactant A and
the order of the reaction with respect to
reactant B respectively.

• The order of the reaction m n

• If m n 1, then the reaction is first-order in
  A and first-order in B, but second-order
  overall, therefore R k AB

Hence,
Units for rate constant for 2nd order reaction
If first-order overall????
Units for rate constant for 1st order reaction
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Molecularity

• Molecularity is the number of molecules coming
  together to react in an elementary step.
• Elementary reactions are simple reactions
  (described by molecularity)
• (a) A Products UNI-molecular
  reaction
• e.g.

(b) A A Products or A B
Products BI-molecular e.g. CH3I
CH3CH2O- CH3OCH2CH3 I-
(c) 2A B P or A B C P
Ter-molecular
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Molecularity Order of reaction

• Reaction order is determined by experiment only
• Reaction order is an empirical quantity (values
  range -2 to 3).
• Can be fractional found mainly in gas phase
• Can be negative,

A is an inhibitor (decreases the rate)
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Mechanism, Rate determining step and
Intermediates

• Assembly of elementary steps (to give
  products(s)) is called the reaction mechanism.
• e.g. H2 Cl2 2HCl. HCl is NOT formed
  in this one step, but proceeds by a series of
  elementary steps
• Cl2 2Cl
• Cl H2 HCl H
• Cl H HCl
• H2 Cl2 2HCl Overall reaction

Mechanism arrived at from theory and experiment
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• Rate-determining step (RDS) is the slowest
  elementary reaction in the mechanism and controls
  the overall rate of the reaction.
• e.g. A 2B D E
• mechanism A B C E fast
• B C D slow rate
  determining step
• A 2B D E

C is an intermediate formed, and then used up
in the reaction
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Intermediates A B C
Products
Equilibrium is dynamic, this means Rf
Rr. Assume k ltlt kr, then slow step is A B
C C Prod. (Slow RDS)
R kC
Rate kKAB
Rate kAB
k kK
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Deriving the Integrated Rate Expressions

• First-order reactions
• A B, then the rate of disappearance
  of A is

Rearranging gives
At time t 0, A A0 And when t t, A
At
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Integrating
lnAt lnA0 - kt
y c mx
Integrated form of the 1st order rate expression
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Intercept lnA0
-slope -k
lnAt
t / s
Other useful forms
t / s
-slope -k
ln(At/A0)
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Recall lnAt lnAo - kt
Antilog gives
Intercept A0
At A0 e-kt
At
t / s
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• Second-order reactions

Two possible cases
Case I A A Products OR 2A
Products
Case II A B Products
Rearranging gives
At time t 0, A A0 And when t t, A
At
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Integrating
OR
Integrated form of the 2nd order rate expression
y c mx
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y c mx
slope 2k
(1/At) / dm3 mol-1
Intercept 1/A0
t / s
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What can we conclude about RATE LAWS versus
INTEGRATED RATE EXPRESSSIONS??

• a rate law can tell us the rate of a reaction,
• once the composition of the reaction mixture
  is known
• An integrated rate expression can give us the
  concentration
• of a species as a function of time. It can
  also give us the
• rate constant and order of the reaction by
  plotting the
• appropriate graph

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The Study of Half-Lives

• The half-life, t½, of a reaction is the time
  taken for the concentration of a reactant to fall
  to half its initial value.
• It is a useful indication of the rate of a
  chemical reaction.

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• First-order reactions

Remember that for a 1st order reaction lnAt
lnA0 - kt
At time t 0, A A0 Then at time t t½
(half-life), At½ A0/2 Substituting into
above equation, ln(A0/2) lnAo
kt½ ln(A0/2) lnA0 -kt½
ln 1 ln 2 -kt½, where ln 1 0 Therefore, ln
2 kt ½
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Hence,
or
What is/are the main point(s) to note from this
expression??

• For a 1st order reaction, the half-life is
  independent of reactant
• concentration

but dependent on k.

• The half-life is constant for a 1st order reaction

A0
Recall At A0e-kt
concentration
t1/2
A0/2
t1/2
A0/4
t1/2
A0/8
time
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• Second-order reactions

At time t 0, A A0 And when t t½, At½
A0/2
So t1/2 for 2nd order reactions depends on
initial concentration
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Therefore, larger initial concentrations imply
shorter half-lives (so faster the reaction).
A0
concentration
t1/2
A0/2
t1/2
A0/4
t1/2
A0/8
time
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Determining Rate Laws
Rate laws have to be determined experimentally.
Techniques for monitoring the progress of a
reaction include

• Absorption measurements (using a
  spectrophotometer)

• Conductivity (reaction between ions in solution)

• Polarimetry (if reactants/products are optically
  active, e.g. glucose)

• Aliquot method (employing titration technique)

Recall A B P, r kAmBn
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(A) Isolation MethodThis technique simplifies
the rate law by making all the reactants except
one, in large excess.
Therefore,
The dependence of the rate on each reactant can
be found by isolating each reactant in turn and
keeping all other substances (reactants) in
large excess.
Using as example r kAtm Btn
Make B in excess, so BgtgtA.
Hence, by the end of the reaction B would not
have changed that much, although all of A has
been used up
And we can say, B ? B0
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Since A is the reactant that changes, then the
rate becomes dependent on A, and we can say
r kAtm , where k kB0n
Created a false first-order (imitating
first-order) PSEUDO-FIRST-ORDER,
where k is the pseudo-first-order rate constant
Logging both sides gives
log r log k m log At
y c m x
A plot of log r vs log At gives a straight line
with slope m, and intercept log k
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If m 1, the reaction is said to be
pseudo-first-order
With the roles of A and B reversed, n can be
found in a similar manner
k can then be evaluated using any data set along
with the known values of m and n
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(B) Initial Rate Method - often used in
conjunction with the isolation method,
-The rate is measured at the beginning of the
reaction for several different initial
concentrations of reactants.
Initial rate
Follow reaction to 10 completion
At
t / s
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Recall A B P, Rate0 kA0aB0b
Taking logs
log Rate0 log k a log A0 b logB0
y
m
x
c
Keep A0 constant for varying values of B0
to find b
slope b
Log Ro
Intercept log k a logA0
logB0
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Keep B0 constant for varying values of A0
to find a from the slope of the graph, log R0
vs log A0
Substitute values of a, b, A0, B0 to find
k.
However, in some cases, there may be no need to
use the plots as shown previously.
EXAMPLE R1 kAaBb R2 knAaBb
For these experiments, B is kept constant while
A is varied and R1 and R2 are known.
Dividing R2 by R1
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(a) If R2 2R1, and n2, then a 1, so 1st
order with respect to A
(b) If R2 4R1, and n2, then a 2, so 2nd
order with respect to A
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Concluding if n2, and
Rate doubles 1st order Rate
increases by a factor of 4 2nd order
Rate increases by a factor of 9
3rd order
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COLLISION THEORY ARRHENIUS EQUATION
According to the Collision Theory Model a
bimolecular reaction occurs when two properly
oriented reactant molecules come together in a
sufficiently energetic collision.
i.e. for a reaction to occur, molecules, atoms or
ions must first collide.
Consider the hypothetical reaction A BC
AB C
A BC A----B----C AB C
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Potential Energy Profile
A---B---C

• The height of the barrier is called the
• activation energy, Ea.
• The configuration of atoms at the
• maximum in the P.E. profile is called
• the transition state.

Ea
Potential Energy
A BC
Reactants
AB C
Products
Reaction Progress
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If the collision energy lt Ea, the reactant
molecules cannot surmount the barrier and
they simply bounce apart.
If the collision energy is ? Ea, the reactants
will be able to surmount the barrier and be
converted to products.
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Very few collisions are productive because very
few occur with a collision energy as large as the
activation energy. Also, proper orientation is
necessary for product formation.
There must be some effect by Temperature on
reaction systems.
Temperature can result in an increase in energy.
This leads us to say The average kinetic energy
of a collection of molecules is proportional to
the absolute temperature.
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At a temperature T1, a certain fraction of the
reactant molecules have sufficient K.E., i.e.
K.E. gt Ea.
At a higher temperature T2, a greater fraction of
the molecules possess the necessary activation
energy, and the reaction proceeds at a faster
rate.
In fact it has been found that reaction rates
tend to double when the temperature is increased
by 10 oC.
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Maxwell-Boltzmann distribution curve
T2 gt T1
Fraction of molecules
T2
T1
Ea
Kinetic Energy

• The total area under the curve is proportional to
  
• the total molecules present.

(ii) Total area is the same at T1 and T2.

• The shaded areas represent the number of
  particles
• that exceed the energy of activation, Ea.

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It was observed by Svante Arrhenius that almost
all of the reaction rates (obtained from
experiments) accumulated over a period showed
similar dependence on temperature.
This observation led to the development of the
Arrhenius Equation
k Ae-Ea/RT
Collectively, A and Ea are called the Arrhenius
parameters of the reaction.

• Ea activation energy (kJ mol-1), and is the
• minimum kinetic energy required to allow
  reaction to occur

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The exponential term e-Ea/RT is simply the
fraction of collisions that have sufficient
energy to react.
This fraction goes up when T is increased because
of the negative sign in the exponential term.
However, most of the collisions calculated by
e-Ea/RT do not lead to products, and so

• A the frequency factor or pre-exponential
  factor (same units as k),
• is the fraction of sufficiently
  energetic collisions that actually
• lead to reaction.

• T Kelvin temperature
• R ideal gas constant (8.314 J mol-1 K-1)
• k is the rate constant

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Logarithmic form of the Arrhenius equation
Recall k Ae-Ea/RT
y
mx
c
A plot of ln k versus 1/T gives slope Ea/R and
intercept ln A
Cannot extrapolate for intercept. Obtain A by
substituting one of the data values along with
value of Ea into equation.
ln k
? y
?x
1/T
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High activation energy corresponds to a reaction
rate that is very sensitive to temperature (the
Arrhenius plot has a steep slope). Converse also
applies.
ln k
Low activation energy
High activation energy
1/T
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Manipulation of Arrhenius equation

• Once the activation energy of a reaction is
  known, it is a simple
• matter to predict the value of a rate
  constant k at a temperature,
• T from another value of k at another
  temperature, T.

ln k ln A Ea/RT
Subtract these equations
ln k ln A Ea/RT
ln k ln k ln A ln A Ea/RT (-Ea/RT)
(ii) Can also find Ea if k, k, T and T are
known.