Concluding Remarks and Content of Chapters

There are virtually as many possible Lewis basicity scales as there are Lewis acids. This is a dramatic consequence of the Lewis definition of acids, which has considerably enlarged the number of chemical species showing an acid character and made the proton lose the status of reference acid. 

Mathematically, the aqueous Brbnsted basicity scale corresponds to a one-column data matrix. In fact, several columns are needed to take into account the influence of the medium but two media have been studied most, water and the gas phase. So the two most filled, and consequently most used, columns are the p/fBH+ nd GB scales. In the field of proton affinity, no column attains the degree of completeness and reliability of the gas-phase PA column. There is no need for spectroscopic scales of Bronsted basicity since the thermodynamic scales are satisfactory. 

The mathematics of the Lewis acid/base concept is that of a data matrix of m rows and n columns. Data are complexation constants, as logA or AG. Each row corresponds to a Lewis acidity scale towards a reference base B° (/ = 1 to m) and each column corresponds to a Lewis basicity scale towards a reference acid A°j (J = I to n). For a rigorous treatment, the data measured in different media cannot be mixed in the same data matrix. In the matrix measuring Lewis affinity, the data are complexation enthalpies. There are extrathermodynamic relationships (isoequilibrium relationships or enthalpy-entropy compensation law) which allow transformations between blocks of the affinity and basicity matrices. In the principal component analysis of Lewis basicity, this justifies, somewhat, the mixing of affinity columns and basicity columns in a unified basicity-affinity matrix. 

There are two main reasons for the paucity of data available for constructing basicity and affinity scales. First, the observation by Lewis himself in 1938 [30] that in studying acids and bases, we find that the relative strength depends not only upon the chosen solvent but also upon the particular base or acid used for reference very soon discouraged many chemists from measuring Lewis basicity (acidity) quantitatively, all the more so since statements similar to that of Lewis have become commonplace in the chemistry literature. 

Second, there are in practice not many systems in which a Lewis reference acid reacts with a series of diversified bases for which a series of reliable equilibrium constants can be measured easily by known physicochemical techniques over a large range of values (that is, from possibly very large to possibly very low equilibrium constants), and in the same conditions of temperature and medium. This is why chemists have turned to the determination of spectroscopic scales of Lewis basicity (affinity). 

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