Linear Free Energy Relationships

Ionization of phenylacetic acids

 

Hammett Equation

s is measure of a substituent's electron-donating or electron-withdrawing effect.
+ s values are for electron-withdrawing groups; - are electron-donating.
s is dependent on inductive and resonance effects.

r values, reaction constant, measure how reaction affected by electron-withdrawing or electron-donating effects.
+ values of
r for reactions favored by electron-withdrawing groups and not by electron-donating groups. Reverse with - values of r.

Exercise: Predict if r > 0 or < 0

 

Table 1.   Ionization of phenylacetic acids (taken from Streitwieser and Heathcock, 1985)

R

pKam

sm

pKap

s p

H

4.31

0

4.31

0

CH3

  

-0.069

4.37

-0.170

CH3O

  

0.115

4.36

-0.268

F

  

0.337

4.25

0.062

Cl

4.14

0.373

4.19

0.227

Br

  

0.391

4.19

0.232

I

4.16

0.352

4.18

0.18

NO2

3.97

0.710

3.85

0.778

 

Using r to understand mechanisms

Possible pathways:

For each possible pathway, predict what the sign and magnitude (i.e., large or small) of r will be. Use your knowledge of what the actual product in this reaction is to decide which of the mechanisms can be eliminated on that basis. Is there any other data that you can use to decide on the correct mechanism?

A.  Proton transfer to carbon 1.

B.  Proton transfer to carbon 2.

C.  Bromide transfer to carbon 1.

D.  Bromide transfer to carbon 2.

 

E.  Concerted additions.