Activated Complex Theory Of Bimolecular Reaction Or Transition State Theory Or Eyring Equation Video Lecture - Chemistry

the transition state theory is based on
a model of how a reaction takes place at
a molecular level let's look at a
general elementary reaction a plus B C
goes to a B plus C the rate constant K
in the model the reaction pathway from
reactants to products passes through a
transition state at the highest point on
the energy profile this is shown in
Figure nine point two eight the red
curve shows the energy pathway from
reactants to products the transition
state ABC is at the highest point on the
pathway note the double dagger
superscript which is used to label the
transition state and also quantities
involved in its formation the theory
assumes that a pre equilibrium is first
established between the reactants and
the transition state ABC which then goes
on to form the products the large K
double dagger in blue is the equilibrium
constant for the pre equilibrium forming
the transition state and the small K
double dagger in red is the rate
constant for the formation of products
from the transition state now using the
ideas developed in Section 9.6 for this
type of reaction mechanism involving a
pre equilibrium it's possible to obtain
an expression for the overall rate
constant K in terms of the equilibrium
constant K double dagger and the
temperature T this term is constant KB
is the Boltzmann constant and H the
Planck constant
don't worry about the derivation and the
maths at this stage the important point
to note is that this equation links the
rate constant for the overall reaction
with the equilibrium constant for the
formation of the transition state now
you need to use some thermodynamics from
chapters 14 and 15 because K double
dagger is related to other thermodynamic
functions involved in the formation of
the transition state this is equation 15
point 4 which links an equilibrium
constant K with the standard Gibbs
energy change for the reaction it can be
rewritten in this form equilibrium
constant equals e to the minus Delta G
standard over RT so you can substitute
for K double dagger in equation 9.2 8 to
give this expression here where Delta G
double dagger is the Gibbs energy change
for the formation of the transition
state from the reactants and is called
the Gibbs energy of activation and since
Delta G equals Delta H minus T Delta s
equation nine point two eight can be
rewritten yet again into this form here
where Delta H double dagger is the
enthalpy of activation and Delta s
double dagger is the entropy of
activation now compare this equation
with the Iranian equation from section
nine point seven which shows the effect
of temperature on the rate constant
remember the equation on the left is
derived mathematically from a
theoretical model where as the Iranian
squashy
the right represents experimental
observations the enthalpy of activation
Delta H double dagger corresponds to e a
the activation energy and the term in
red which contains the entropy of
activation corresponds to a the a factor
in their Rania's equation a useful way
to follow the progress for reaction is
to plot the Gibbs energy G as the
reaction takes place this is called a
Gibbs energy profile we've seen that the
transition state Theory links the Gibbs
energy of activation directly to the
rate constant K for the reaction K the
rate constant is proportional to e to
the minus Delta G double dagger over RT
so the greater the value of Delta G
double dagger the smaller the value of K
the rate constant and the slower the
reaction also the Gibbs energy change
incorporates both an enthalpy term and
an entropy term which can be very
important for these reasons Gibbs energy
profiles rather than enthalpy profiles
are used extensively in organic
chemistry and in biochemistry to
illustrate the mechanisms of reactions
figure nine point two nine shows the
Gibbs energy profile for a concerted
single step reaction such as the
alkaline hydrolysis of a primary allergy
no alkane such as bromo methane which
takes place by sn2 mechanism and is an
elementary reaction
there's a single maximum corresponding
to the transition state for the reaction
Delta G double dagger is the Gibbs
energy change for the formation of the
transition state don't confuse this with
Delta G R which is the Gibbs energy
change for the reaction and its
difference in Gibbs energy between the
reactants and the products
figure 9.30 shows the Gibbs energy
profile for a complex reaction involving
two steps such as the alkaline
hydrolysis of a tertiary halogen no
alkane such as to bromo to methyl
propane which proceeds by sn1 mechanism
in this case the Gibbs energy profile
shows two Maxima corresponding to the
transition states of the two steps and
the minimum corresponding to the
formation of the intermediate this is
the first step via the first transition
state to form the intermediate and this
is the second step by the second
transition state to form the products
there is a Gibbs energy of activation
for each of the transition states and
this is the Gibbs energy change for the
reaction Delta G R in this example the
Gibbs energy change of formation for the
first transition state is much larger
than that for the formation of the
second so k1 the rate constant for the
first step is
very much less than k2 the rate constant
for the second step so the first step is
slow and is the rate determining step
from the rep for the reaction