General concept and application

1. Hammette Equation :-
(Quantitative treatment of the
effect of structure on reactivity)
This is general equation which relates
quantitatively structure to rate constant or
equilibrium constant.
Hammette set up an eqn ;
log(K/K₀)=ƍσ……(1)
Where K refers to rate constant or equilibrium
constant to the reaction of substituted phenyl
compound.(say Ionization of substituted benzoic
acid.)
…........cont.

2. ……..cont.
K₀ refers to the same reaction (say ionization
of benzoic acid). σ is substituent constant
which indicating relative electron
withdrawing or releasing group:-affect of
substitution on rate of reaction.
ƍ is reaction constant for given reaction
under given set of reaction. The value of ƍ
was set 1 for ionization of substituted and
unsubstituted
Benzoic acid in water at 25°C and σ values
were then calculated.
(………….cont…)

3. ……cont.
Thus,
log(K/K₀)=σ……….(2)
or, σ = log(KC6H4COOH/K₀C6H5COOH)
σ=Effect of substituent on rate of reaction.
Substituent have similar effect from reaction
to reaction.σ is different for meta and Para
position.
(………cont……)

4. ……cont.
Substituent Constant (σ):-
It is the number.
Since, σ is determined by calculating the
logarithm of ionization constant of substituted
benzoic acid to the ionization constant of
unsubstituted benzoic acid. σ value of H is
zero. σ value is measure of total polar effect
i.e. it represents the ability of substituent to
withdraw or release of electron by the
combination of I-effect and Resonance effect
of substituent. (…….cont.)

5. ……cont.
The σ value for substituent of meta position
differ from that for substituent at Para
position. σ value may be negative or positive
number.
A negative σ value for a group at particular
positions indicates its greater electron
donating ability to the reaction centre than
hydrogen whereas positive value for
substituent indicates its electron withdrawing
character. (cont………)

6. …………cont.
For Example:-
K C6H5COOH = 6.3 Х 10^-5
Km MeOC6H4COOH = 8.3 X 10^-5
σm = log (8.3X10^-5/6.3X10^-5)
= log8.3 – log 6.3
= 0.9191-0.7993
= +0.12
Hence, m-methoxybenzoic acid has greater
electron withdrawing ability than benzoic
acid. (cont……….)

7. ………………..cont.
Reaction Constant (ƍ) :-
It indicates relative need of reactions for
electron withdraw or release. This depends on
the reaction, nature of reaction centre and
condition ( pressure, temperature, solvent
catalyst etc). ƍ value may be positive or
negative. A negative value indicates a large
electron demand at the reaction centre. Since,
electron donating substituent accelerates the
rate of reaction.
(cont…………………..)

8. ………….cont.
A positive value is associated with developing
a negative charge in transition state. So, e-
withdrawing group accelerates the rate of
reaction.
Application (Uses of Hammette equation ) :-
1) Since, equation involve four measureable
quantities K , K₀ , ƍ & σ. If any three of them
are known the fourth can be calculated. (cont..

9. ……………cont.
2) To compare the acidity of acids
quantitatively :-
For e.g. p-nitro phenyl acetic acid (p-NO2
C6H5CH2COOH ) is more acidic than phenyl
acetic acid (C6H5CH2COOH) due to electron
withdrawing effect of p-nitro group. This can
be solved by Hammette equation.
- σ for nitro group = +0.78
- ƍ for ionization of C6H5CH2COOH = +0.49
(cont….)

10. (….cont.)
Log ( ) = σƍ
log = 0.78 X 0.49
or, = 10^0.3822
or, = 2.411
(cont…)
K p-nitro C6H4CH2COOH
K₀C6H5CH2COOH

11. (…...cont.)
It shows that the p-nitro phenyl acetic acid is
expected to be 2.4 times more acidic than
phenyl acetic acid.
3) To compare reactivity of two compounds
quantitatively by Hammette equation :-
For e.g. Reactivity of p-chloro phenyl methyl
chloride with that of Benzyl chloride in 50%
acetone at 60°C.
σ for Cl = +0.23
ƍ = -1.70 (cont…………)

12. (…………..cont.
)
log = σ X ƍ
or, log = 0.23 X - 1.70
or, = - 3.91
Thus, the rate of hydrolysis of p-chloro benzyl
chloride is slower than the Benzyl chloride .
(cont......)

13. (cont…….)
4) ƍ value & the reaction pathway :-
From the value of & sign of the reaction
constant, we can understand something about
the reaction mechanism. For e.g. the reaction
constant ƍ for the hydrolysis of Benzyl chloride
in 50% acetone & 60°C temperature is -1.70.
The negative value of ƍ indicates that the
transition state of rate determing step must
bear positive charge, the rate determing step
of Benzyl chloride into Benzyl cation and SN1
type of reaction involved ionization in rate
determing step . So, It follows SN1 path.