Numerical Expression of Linear Free-Energy Relationships

Numerical Expression of Linear Free-Energy Relationships 

Many important relationships between substituent groups and chemical properties have been developed. For example, in Section 1.2.5 (p. 53), we discussed the effect 

The linear correlation therefore indicates that the change in AG on introduction of a series of substituent groups is directly proportional to the change in the AG of ionization that is caused by the same series of substituents on benzoic acid. The correlations arising from such direct proportionality in free-energy changes are called linear free-energy relationships. 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) A// is constant and the A A terms are proportional for the series (2) AA is constant and the A// terms are proportional or (3) A// and AA are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. 

---