CH221 CLASS 10
CHAPTER 5: AN OVERVIEW OF ORGANIC REACTIONS CONTINUED
Synopsis. Class 10 deals with the energetics and kinetics of organic reactions, beginning with an elementary consideration of thermodynamic reaction parameters (K eq
,

G o ,

H o and

S o ) and ending with the illustration of organic reaction kinetics, using energy diagrams. This introduces transition states and intermediates and shows clearly the relationship between thermodynamic (

G o ) and kinetic parameters (

G

).
Introduction
Two fundamental features of organic reactions are
Extent of reaction: how far the reaction equilibrium lies toward products. This is a measure of reaction feasibility and is expressed by thermodymanic parameters, such as the reaction equilibrium constant (K eq
) and the reaction standard Gibbs free energy change (

G o ) (and hence reaction enthalpy change,

H o , and entropy change,

S o ). No information on reaction rates can be deduced from these parameters.
Rate of reaction: how fast a reaction proceeds and how fast individual steps of a multi-step reaction occur. These are determined by kinetic parameters, such as
Gibbs free energy change of activation (

G

). No information regarding extent of reaction can be deduced from kinetic parameters.
Although thermodynamics and reaction kinetics are separate subjects, they can be inter-related in various ways, especially by the use of energy diagrams, as illustrated at the end of this class.
Reaction Energetics and Equilibria
All reactions can, in principal, proceed in forward (L

R) or backward (R

L) directions, the position of equilibrium (or extent of reaction) being given by the equilibrium constant:

For aA + bB cC + dD
Reactants Products
[C] c [D] d
K eq
=
[A] a [B] b
If K eq
>> 1, the overall direction of reaction is as written (L

R), but if K eq
<< 1, then the overall direction is backwards (R

L). In practice, if K eq
> ca. 10 3 , the reaction is said to “go to completion”, for all practical purposes, the equilibrium lies wholly to the right. The reverse is true when K eq
< 10 -3 .
The equilibrium constant is related to the standard Gibbs free energy change
(

G o ) for the reaction. Standard ( o ) means standard conditions of concentration
(1 M), pressure (1 atm) and temperature (298 K).

G o = - RT ln K eq
or K eq
= exp (-

G o / RT)
Take, as an example, the bromination of ethylene at 298 K:
CH
2
=CH
2
+ Br
2
CH
2
Br-CH
2
Br; K eq
= 7.5 x 10 7

G o = - 8.315 x 298 x ln (7.5 x 10 7 )
= - 44,800 J mol -1 or – 44.8 kJ mol -1
This negative value of

G o indicates that the reaction is “spontaneous”; that it is feasible as written. So, the values of K eq
and

G o both say that the reaction goes to completion.
Now,

G o is itself a composite thermodynamic parameter,

G o =

H o - T

S o
Enthalpy Entropy
Change Change
For the bromination of ethylene,

H o = -84.1 kJ mol -1 and

S o = -132 J K -1 mol -1 .
The enthalpy change of reaction is a measure of the change in total bonding energy that occurs as a result of the reaction. It is negative (the reaction is

exothermic) if the bonds of the products are stronger (more stable) than the bonds of the reactants (as in the bromination of ethylene).
The entropy change of reaction is a measure of the change in disorder that accompanies the reaction. The greater the freedom of motion (degrees of freedom) or the greater the number of microstates reactants and products can take up, the greater the entropy. If disorder increases in the forward direction, the entropy change is positive, but if disorder decreases (as in the bromination of ethylene), entropy change is negative.
Hence, compare:
Dissociative reaction A B + C

S o > 0
(e.g. elimination)
Associative reaction A + B C

S o < 0
(e.g. addition)
Bond Dissociation Energies as a Criterion of Reaction Feasibility
The bond dissociation energy, D, of a bond is defined as the energy needed (it is positive) to break one mole’s worth of bonds into radical fragments in the gas phase at 298 K.
E.g. for CH
4
CH
3
.
+ H .
;

H o (D) = 438.4 kJ mol -1
The bond dissociation energy of the C-H bond is 438.4 kJ mol -1 . Some important bond dissociation energies are given in the table below, but see textbook, p 154
(Table 5.3) for a more complete list.
Bond
H H
Cl Cl
H Cl
CH
3
Cl
D (kJ mol -1 )
436
243
432
351
Bond
CH
3
H
CH
3
CH
2
H
(CH
3
)
2
CH H
(CH
3
)
3
C H
D (kJ mol -1
438
420
401
)
390
With knowledge of bond dissociation energies, it should be possible to calculate

H o (reaction) for any reaction. For example, consider the monochlorination of methane at 298 K:

CH
3
H + Cl Cl CH
3
Cl + H Cl
Reactant bonds broken Product bonds formed
C-H D = 438 kJ mol -1 C-Cl D = 351 kJ mol -1
Cl-Cl D= 243 kJ mol -1 H-Cl D = 432 kJ mol -1

D = 681 kJ mol -1

D = 783 kJ mol -1

H o (reaction) =

D (reactants) -

D (products)
= 681 – 783
= - 102 kJ mol -1
Hence we have an example of a favorable reaction that has a negative standard enthalpy change (i.e. is exothermic). A similar result is obtained for the bromination of ethylene reaction that was considered previously, so it may be tempting to suppose that all feasible reactions are exothermic. However, this is not in full agreement with observations, and hence there are severe limitations on the use of

H o as a criterion of reaction feasibility. These limitations arise from two main flaws:

o
In practice, the big majority of organic reactions are carried out in the liquid phase, usually in solution. Under these conditions, solvation of at least some of the reaction species can result in values of

H o (reaction) that do not agree with the calculated value and, indeed, solvation is also known to influence

S o for the reaction. This means that

H o can only be used as an approximate criterion of reaction feasibility: better by far is

G o , as has already been suggested.
However, even

G o can only indicate reaction favorability, it says nothing about the rate of reaction: how fast the reaction proceeds. For example, the chlorination of methane, though favorable, is relatively slow in the absence of light. The rates of reactions, or more accurately of individual reaction steps, depend upon the activation energies (E
A
) of those steps, according to the
Årrhenius equation,
Rate constant k = A exp (-E
A
/ RT)

A is the Årrhenius constant.
The two main aspects of a reaction, extent (or direction) and rate, can be incorporated into an energy
– reaction progress diagram, as described next.
Energy Diagrams and Reaction Mechanism
The majority of organic reactions occur in a series of steps
– that is to say they are multi-step reactions. Consider a bimolecular reaction step. The combined initial energy of the two reactant molecules is comparatively low, but energy increases as the molecules approach each other and reaches a maximum value.
This maximum corresponds to the energy barrier of the reaction step and represents a transition state (symbol

) between reactants: a state where bonds are neither fully broken, nor fully made. Only molecules which have at least this combined energy are able to react, but once they have reacted the energy drops to a fixed value that represents the combined energies of the products. The change in energy for the whole of the step can be plotted on a diagram with some function of energy (often Gibbs function) as the y axis and the reaction coordinate (often simply the (non-numerical) reaction extent) as the x axis:
The above plot is known as an energy diagram and two important Gibbs free energy changes are evident from the plot:

G

is called the free energy of activation and

G o is known as the reaction free energy change . The former is inversely related to the rate constant k for the step: the higher the value of

G

, the lower the value of k (the slower the reaction step) at a fixed temperature
– see the Årrhenius equation, on the previous page. The latter is the familiar value of

G o for the reaction step: the particular example above is exergonic , because the products are lower in Gibbs free energy than the reactants. The reverse

reaction is therefore endergonic . Clearly, four different energy diagrams exist for a reaction step, the shape of the plot depending the relative values of

G
 and

G o , as illustrated below.
Describing a Reaction Mechanism using an Energy Diagram
The reaction to be illustrated here is the hydrobromination of ethylene. It is a typical electrophilic addition reaction of alkenes and it is known to occur in two steps: the first step is the rate-determining formation of a carbocation and the second step is the rapid reaction of the carbocation.
Step 1 CH
2
CH
2
+ H Br slow +
CH
2
CH
2
H + Brcarbocation
Step 2 Br+
+
CH
2
CH
2
H fast
Br CH
2
CH
2
Both steps must proceed through a transition state (energy maximum) and, according to the above mechanism,

G

(step 1) >

G

(step 2). Also, it has already been demonstrated that the reaction is exergonic (i.e.

G o < 0 or the
Gibbs free energy of the products is lower than that of the reactants. The carbocation is produced in the first step and consumed either in the backward step or in the second step and hence it is defined as a reaction
H

intermediate . It can be shown that the overall reaction lies much to the right
(as in the case of bromination of ethylene), hence the energy barrier for consumption of the carbocation intermediate in the second step must be lower than that in the backward step. With this knowledge, it is possible to construct an energy diagram:
Here the carbocation intermediate can be seen as a high-energy species: it is a distinct species that occupies the high valley or col in the mountain range represented by the energy profile. Similar diagrams can be drawn for other two step organic reactions, such as S
N
1 type nucleophilic substitutions, E1 type eliminations, electrophilic aromatic substitutions, etc. These diagrams are of similar shape to the one above, but differ principally in the relative values of free energies of activation for the different steps.
The Nature of the Transition State
The transition state has already been described as the energy maximum on the energy diagram for the reaction step. It is a bonding state somewhere between reactants (left hand side) and products (right hand side) and nothing else – it is not a species that can be isolated (unlike intermediates). For the

hydrobromination of ethylene, the two transition states can be represented as follows:
=

+
CH
2
CH
2
H Br

for step 1
 
+
Br CH
2
CH
3
= for step 2
Biological Reactions
A seemingly simple chemical reaction, like the combustion of glucose:
C
6
H
12
O
6
+ 3O
2
6CO
2
+ 6H
2
O, is an important source of energy for most living organisms. In the cell, instead of this reaction occurring in one step, thereby releasing all its energy at once, it occurs naturally in a series of steps, each of which is catalyzed by a particular enzyme (protein catalyst). Hence the energy is released in relatively small packages and is used by the organism in different ways, for example, to maintain optimum temperature, to perform work and to couple with other less favorable, but essential reactions, like the regeneration of ATP and reduced coenzymes, such as NADH. The energy diagram for a biological pathway between reactants and products will consist of many maxima and minima corresponding to the many steps, but the activation energies for all the steps will be much lower than the activation energy of the uncatalyzed reaction:

Class Questions
1. Sketch a reaction energy diagram for a single step reaction that is fast and highly exergonic.
2. Draw the transition state that corresponds to the following single step reactions.
(a) HO + Br-CH
2
-CH
3
HO-CH
2
CH
3
+ Br (S
N
2)
=
CH
3

HO
-
CH
2

Br
-
(b) HO + CH
3
CH(Br)CH
3
H
2
O + CH
2
=CHCH
3
+ Br (E2)
=
HO
-
H
CH
2
CH

Br
-
CH
3