Equilibrium and Kinetics

1
KINETICS
"Thermodynamics Warrants Kinetics Prohibits"
2
Kinetics

• In the chapter on Equilibrium we had seen that
  the thermodynamic feasibility of processes is
  dictated by Thermodynamic Potentials (e.g.
  Gibbs Free Energy, at constant T, P, Ni).
• If (say) the Gibbs Free Energy for a process is
  negative then the process CAN take place
  spontaneously.
• However, IF the process WILL actually take place
  (and if it will take place- how long will it take
  to occur?) ? will be determined by the Kinetics
  of the process.
• Deeper the metastable energy well, higher will
  be activation energy required to pull the system
  out of the well and take it to the equilibrium
  state (or some other metastable state).
• To give an example the window pane glass is in a
  metastable state ? there is a tendency for it to
  crystallize and to lower the Gibbs Free Energy of
  the system. However, at room temperature the
  crystallization is very slow and the glass pane
  can remain amorphous for hundreds of years.?
  Case of Thermodynamics warrants, Kinetics
  delays
• For a given process to occur heat and mass
  transfer may have to take place and this would
  take time ? hence in kinetics we deal with time
  and rates (1/t)

defined in an upcoming slide (must have read it
in school as well) All glasses are considered
to be metastable and there exists at least one
crystalline state with a lower G. The terms
glass and amorphous material are more often used
synonymously
3
Some basics

• A homogenous reaction is one which involves only
  one phase.? E.g. a reaction involving only
  gaseous phase
• In a heterogeneous reaction more than one phase
  is present.

Let us consider a homogenous balanced chemical
reaction, occurring in a single step
Rate of consumption of a reactant is proportional
to the stoichiometric coefficient in a balanced
reaction

• nA ? number of moles of A present at time t
• J ? Rate of conversion
• r ? rate of reaction ( J/V)

Rate of Conversion (J) is defined as
A, B are being consumed and hence dn/dt for these
species is negative and J is positive
J depends on system size and is an extensive
quantity, the conversion rate per unit volume
(J/V) is the reaction rate is an intensive
quantity
The reaction rate (r) is a function of P, T and
the concentration of species
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In many of the reactions the volume is constant.
If the volume is constant during the reaction

• nA ? number of moles of A present at time t
• J ? Rate of conversion
• r ? Rate of reaction ( J/V)
• A ? Molar concentration of A ( cA)

For many reactions it is seen that the rate can
be related to the concentration of species by a
reaction of the form
Partial orders Integer or half integer

• The rate constant k is a function of T and P?
  The pressure dependence is usually small
• The exponents ?, ? are usually integers or half
  integers (1, ½, 3/2, ) and are the partial
  orders (i.e. the reaction has got an order ? wrt
  to A and ? wrt B
• ? ? n is the order of the reaction (overall
  order)
• Units of k ? concentration1?n t?1

Order wrt A
Order wrt B
Rate Constant f(T,P)
Molar Concentrations
5
Some basics

• Gas phase reaction
• Overall Order as expected 2

• Gas phase reaction
• Partial and Overall Order as expected
• Overall order 3

The above are cases which are intuitively easy
to correlate with the concept of order. But,
reactions may have partial order as below or even
the cocept of order of a reaction may not apply!

• Gas phase reaction
• Partial overall order

• Gas phase reaction
• Catalyst NO appears in the order while reactant
  SO2 does not

• Gas phase reaction
• Concept of order does not apply

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• Looking at some of the examples in the previous
  slide it is clear that the exponents in the rate
  law can be different from the numerical
  coefficients in the balanced chemical reaction
  equation.
• Rate laws are to be determined from measurement
  of reaction rates and cannot be determined from
  reaction stoichiometry.
• Additionally, the use of concentrations in the
  rate equations is valid only for ideal systems.

7

• Rate constants depend strogely on temperature
  (usually increasing rapidly with increasing T).
• For many reactions in solution, a thumb rule can
  be used that near room temperature k doubles or
  triples every 10?C increase in temperature.
• In 1889 Arrhenius noted that for many reactions k
  f(T) fits an exponential function.

Arrhenius equation
Activation EnergyAffected by catalyst

• A ? pre-exponential factor units of k
• Q ? activation energy J/mole
• R ? gas constant

T in Kelvin
Frequency factor
A is a term which includes factors like the
frequency of collisions and their orientation. It
varies slightly with temperature, although not
much. It is often taken as constant across small
temperature ranges.
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Fraction of species having energyhigher than Q
(statistical result)
ln (Rate) ?
0 K
9
Reactants Products
A BC AB C
A BC (ABC) AB C
Activated complex
10
Activated complex
(ABC)
Preferable to use ?G
?H
Energy
A BC
AB C
Configuration
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• The average thermal energy is insufficient to
  surmount the activation barrier ( 1eV)
• The average thermal energy of any mode reaches
  1eV at 12000 K
• But reactions occur at much lower temperatures
• Fraction of species with energies above the
  activation barrier make it possible
• Lost species by reaction are made up by making
  up the distribution
• Rate ? fraction of species with sufficient
  energy Rate ? vibrational frequency
  (determines the final step)
• Rate ? n?