Drago s equation

Enthalpy of specific interactions between the examined surface and the test solute may be correlated to acid-base properties of both species by using Drago s equation [23,52] or, in author s opinion better (and often used), through the following equation ... 

The greater complexity of Drago s equation in comparison with earlier correlations could be expected to allow a higher effectiveness, i.e. applicability to the interpretation of a greater number of different reaction types. In reality this has not proved to be the case. The explanation is that the effects of the various factors governing the different donor-acceptor interactions are so complex that even this two-term equation does not lead much closer than the simpler correlations to an understanding of the overall process. 

If the last term of Drago s equation is regarded as the heat of adduct formation between the given base and unsubstituted phenol (considered to be the reference), we can write... 

XPS is emerging as very precise method for evaluating acid-base interactions based on the works by Chehimi et al. There is very good correlation between XPS chemical shift and the change in exothermic enthalpy of acid-base interaction. Drago s equation is used for data interpretation ... 

From the above discussion of Drago s equation, the work of acid-base interaction for a pair of molecules is a function of the enthalpy of the interaction. 

The exothermic enthalpy of acid-base interaction (in kcal moF ) can be predicted from Drago s equation I13]. 

A graph similar to Figure 7 resulted with adsorption of tri-ethylamine onto the same iron oxide, with AHa< s=-13.1 Kcal/mole and Tm corresponding to 167 A2. Using Drago s values of Cg and Eg for triethylamine.il.09 and 0.99 respectively jin units of (Kcal/mole)V2>we can write equation (5) as ... 

Calculate the enthalpy of adduct formation predicted by Drago s E, C equation for the reactions of I2 with diethyl ether and diethyl sulfide. 

Drago s system emphasized the two factors involved in acid-base strength (electrostatic and covalent) in the two terms of his equation for enthalpy of reaction. Pearson s system put more obvious emphasis on the covalent factor. Pearson proposed the equation log K = + o- ag, with the inherent strength S modified by a soft-... 

Quantum chemical computations of H complexes heats formation in case of interaction of large organic molecules lead to high errors. A more perspective way is the use of well known relations of physical organic chemistry for this purpose. These equations allow to predict the heats of hydrogen-bonded or donor-acceptor complexes formation on the basis of donor (base) and acceptor (acid) empirical parameters. There are Drago and Weyland s equation [71]... 

Jensen [9] indicated that there is no evidence that Drago s parameters reflect the relative electrostatic and covalent contributions to the bonding in resulting adducts. They were not correlated with either a physical property (dipole moment, ionization potential) or with a quantum-mechanically calculated index. Drago s approach is a purely empirical method of calculating enthalpy of formation for molecular adducts. Fowkes applied the Lewis E C equation [19] and has attempted to determine E and C parameters for both polymers and surfaces. However, Jensen [9] indicated the potential problem connected... 

However, the sequence of C/E values is not in accordance with practical experience with the solvents. Drago s parameters and his equation also could not be used to describe Pearson s hard-soft concept. 

Drago s concept has the merit that two specific factors governing the solvent effect are written together in one common equation. As seen above, characterization of the solvent effect by means of this model succeeded well in certain systems, and less well in others. It appeared that replacement of the two-parameter approach by several parameters might lead to a more generally valid solution. For a joint description of non-specific and specific effects, Koppel and Palm [Ko 72] proposed the introduction of the following four-parameter equation ... 

Probably the most notable feature associated with the adsorption (or desorption) of any compound onto a solid snrface is the change in enthalpy that occurs during the process and is captured in Drago s eqnation (see Equation 3.2). 

Even if Drago s concept is an attempt to circumvent the quantum mechanical consideration of bond formation, the major importance of the above four parameters is their relationship with the HSAB principle. Actually, through the plot of Ea versus Ca for several liquids on a solid one can obtain indirectly the values of the chemical softness I/77 from the slope of C/E, as represented by the following equation ... 

Fowkes and Maruchi tested Drago s hypothesis applied to the interaction of liquids with a solid surface by measuring the contact angles of various acidic and basic liquids (which had been characterized by Drago in terms of their E and C parameters) on different acidic and basic surfaces. Fowkes calculated and for the liquid and solid and examined the difference between these two quantities, which according to the preceding equations is given by... 

R. S. Drago, B. B. Way land. A Double-Scale Equation for Correlating Enthalpies of Lewis Acid-Base Interactions. J. Am. Chem. Soc. 1965, 87, 3571-3577. 

Drago developed a universal polarity scale (the S scale) from more than three hundred spectral data (electronic transitions, F and N chemical shifts and RSE coupling constants) for 30 solutes in 31 non-protic solvents from cyclohexane to propylene carbonate. He used the equation... 

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