IIT-JEE 2010 - Career Point

As the reaction event proceeds, A and B come into
contact, distort, and begin to exchange or discard
atoms. The reaction coordinate is the collection of
motions, such as changes in interatomic distances and
bond angles, that are directly involved in the
formation of products from reactants. (The reaction
coordinate is essentially a geometrical concept and
quite distinct from the extent of reaction.) The
potential energy rises to a maximum and the cluster
of atoms that corresponds to the region close to the
maximum is called the activated complex. After the
maximum, the potential energy falls as the atoms
rearrange in the cluster and reaches a value
characteristic of the products. The climax of the
reaction is at the peak of the potential energy, which
corresponds to the activation energy E a . Here two
reactant molecules have come to such a degree of
closeness and distortion that a small further
distortion will send them in the direction of products.
This crucial configuration is called the transition
state of the reaction. Although some molecules
entering the transition state might revert to reactants,
if they pass through this configuration then it is
inevitable that products will emerge from the
encounter.
We also conclude from the preceding discussion that,
for a reaction involving the collision of two
molecules, the activation energy is the minimum
kinetic energy that reactants must have in order
to form products. For example, in a gas-phase
reaction there are numerous collisions each second,
but only a tiny proportion are sufficiently energetic to
lead to reaction. The fraction of collisions with a
kinetic energy in excess of an energy E a is given by
e −
E a / RT
the Boltzmann distribution as . Hence, we
can interpret the exponential factor in eqn(iii) as the
fraction of collision that have enough kinetic energy
to lead to reaction.
The pre-exponential factor is a measure of the rate at
which collisions occur irrespective of their energy.
Hence, the product of A and the exponential factor,
E a / RT
e − , gives the rate of successful collisions.
Kinetic and thermodynamic control of reactions :
In some cases reactants can give rise to a variety of
products, as in nitrations of mono-substituted
benzene, when various proportions of the ortho-,
meta-, and para- substituted products are obtained,
depending on the directing power of the original
substituent. Suppose two products, P 1 and P 2 , are
produced by the following competing reactions :
A + B ⎯→ P 1 Rate of formation of P 1 = k 1 [A][B]
A + B ⎯→ P 2 Rate of formation of P 2 = k 2 [A][B]
The relative proportion in which the two products
have been produced at a given state of the reaction
(before it has reached equilibrium) is given by the
ratio of the two rates, and therefore of the two rate
constants :
[P2]
k 2
=
[P1
] k1
This ratio represents the kinetic control over the
proportions of products, and is a common feature of
the reactions encountered in organic chemistry where
reactants are chosen that facilitate pathways
favouring the formation of a desired product. If a
reaction is allowed to reach equilibrium, then the
proportion of products is determined by
thermodynamic rather than kinetic considerations,
and the ratio of concentration is controlled by
considerations of the standard Gibbs energies of all
the reactants and products.
The kinetic isotope effect
The postulation of a plausible mechanism requires
careful analysis of many experiments designed to
determine the fate of atoms during the formation of
products. Observation of the kinetic isotope effect, a
decrease in the rate of a chemical reaction upon
replacement of one atom in a reactant by a heavier
isotope, facilitates the identification of bond-breaking
events in the rate-determining step. A primary
kinetic isotope effect is observed when the ratedetermining
step requires the scission of a bond
involving the isotope. A secondary isotope effect is
the reduction in reaction rate even though the bond
involving the isotope is not broken to form product.
In both cases, the effect arises from the change in
activation energy that accompanies the replacement
of an atom by a heavier isotope on account of
changes in the zero-point vibrational energies.
First, we consider the origin of the primary kinetic
isotope effect in a reaction in which the ratedetermining
step is the scission of a C–H bond. The
reaction coordinate corresponds to the stretching of
the C–H bond and the potential energy profile is
shown in figure. On deuteration, the dominant
change is the reduction of the zero-point energy of
the bond (because the deuterium atom is heavier).
The whole reaction profile is not lowered, however,
because the relevant vibration in the activated
complex has a very low force constant, so there is
little zero-point energy associated with the reaction
coordinate in either isotopomeric form of the
activated complex.
Potential energy
C–H
C–D
E a (C–H)
E a (C–D)
Reaction coordinate
XtraEdge for IIT-JEE 41 DECEMBER 2009