Gutmann equation

A similar approach was adopted by Schultz and co-workers [22] but using Equation (3.8) derived from the Gutmann Equation (3.1) to characterise the acid base characteristics of carbon fibres using IGC ... 

This method, based on the Gutmann equation, is also preferred by Panzer and Schreiber [23] who believe that the dominant weakness of the Drago approach is its failure to account for the amphoteric nature of the probe. 

Once the dissociative mechanism is established, it is possible to apply Gutmann s theoretical treatment (40) to the elucidation of the rate-determining step of the exchange reaction. For deuterium-tritium double labeling procedures, i.e., D O 100%, TgO 1%, it may be shown that the following normalized equations apply under initial exchange conditions ... 

Various criteria have been followed in an attempt to establi quantitative scales of acidity and basicity. In order to account for solvation and ionic dissociation phenomena Gutmarm introduced a parameter called donor number, DN, which correlates the behaviour of a donor sdvent towards a given solute with respect to the coordinating ability of a reference solvent towards the same sdute. The basicity of a solvent can be related to the enthalpy of its reaction with a reference acid. Gutmann s DN scale is built on the equation... 

It has been tried to overcome this drawback by the use of multi-parameter correlation equations. One approach involves the Gutmann donor number (DN) [81]. By this the absorption maximum (v ) observed for a dye in a certain liquid can be calculated from the absorption maximum of the dye in a reference medium (Vmax.o) according to [82-85]... 

Gutmann further proposed [20] that the enthalpy of a given acid-base interaction could be approximated by a two parameter equation of the form ... 

Values of B estimated using the data for Na+ ion given in table 4.6 are plotted against the Gutmann DN in fig. 4.16. A good linear correlation is found with a correlation coefficient of 0.921. The equation relating B to DN is... 

Fig. 4.16 Plot of the MSA parameter estimated in various solvents for the Na+ ion (equation (4.9.4)) against the Gutmann donor number DN.

DN values were computed using Gutmann s equation and the thermochemical data for binary polymer blends of a poly(styrene-co-vinylphenyl hexafluoro dimethyl carbinol) [55]. The copolymer contained 95% of styrene repeat units and its OH stretching frequency shifts were similar to those of HFIP [55]. For this reason the copolymer was assigned the Gutmann AN of HFIP [175]. 

Acceptor numbers (AN) have also been reported (175) for the solvents treated previously (again using the benzene AN number for toluene), which allows a multiparameter treatment according to Gutmann s donor-acceptor approach to solvent effects. In light of the near proportionality between AN and -K for non-HBD solvents shown in Equation 115o, this is roughly equivalent to a multiple-parameter correlation with DN and ir. The correlation equation with DN and AN is... 

Comparing Equations 133a,6 with Equations 134u,6, it is seen that the correlations with the solvatochromic parameters are somewhat better (but not convincingly so) than with Gutmann s parameters. It is therefore also useful to compare the J values calculated by the two multiparameter equations with the observed J value for pyridine (24), one of the out-of-Iine data points in Fig. 28. The results are J (Equation 1336) = 67.5 cps, J (Equation 1346) = 69.4 cps, 7(obs) = 67.0 cps, which seems to indicate that although the indicator is a nonprotonic Lewis acid, this property shows 18-type rather than DN-type behavior. 

As before, the solvatochromic parameters give somewhat better correlations (but not convincingly so) than Gutmann s parameters, so that a comparison of the results for pyridine is again appropriate. The results are 5 (Equation 1355) = 0.96 cps, 5(Equation 1365) = 1.34 cps, 6 (obs) = 0.94 cps. Again, although the indicator is a nonprotonic Lewis acid, the property shows /3-type behavior. 

The most important assumption of Gutmann s approach is that the order of base strengths established remains eonstant for all other aeids (solutes), the value of the enflialpy of formation of a given adduet is linearly related to flie donor number of flie base (solvent) through the equation [10.2.8] ... 

They found the frequency of this vibration in DMSO to be shifted by more than 150 cm and to be correlated to the Gutmann acceptor number (AN) for the solvents. Based on our analysis, the frequency shift reflects the acidity and, to a lesser extent, the polarity of the solvent, according to the following equation ... 

Gritzner examined the solvent effect on half-wave potentials and found those of relative to bis(biphenyl)chromium(l)/(0), designated Ein(BCr)K > to be related to the Gutmann donor number (DN) for the solvents, so he concluded that behaves as a Lewis acid against basic solvents. Based on the following equation, the behavior of EiQ(BCr)K is dictated largely by the basicity of the solvent but it is also dependent, however weakly, on its acidity ... 

However, the strength of Lewis acid-base interaction can be expressed in energy terms, such as the exothermic molar heat, —for the equilibrium (III) of adduct formation. The enthalpy term is preferred because entropy effects accompanying the formation of coordinative bonds are difficult to determine. Various models have been proposed for the theoretical estimation of the enthalpy term based on molecular properties of reactants and are reviewed in Ref 5. The most significant developments have been the hard and soft acid-base principle of Pearson [6], the E C equation of Drago and Wayland [7], the donor and acceptor numbers of Gutmann [8], and the perturbation theory of Hudson and Klopman [9]. 

Lewis [5] was the first to describe acids and bases in terms of their electron accepting and electron donating properties. Mulliken [6] further refined the understanding of the acid base interactions for which he was awarded the Nobel Prize for Chemistry. His quantum mechanical approach introduced the concept of two contributions, an electrostatic and a covalent, to the total acid-base interaction. Pearson [7] introduced the concept of hard and soft acids and bases, the HSAB principle, based on the relative contributions from the covalent (soft) interaction and the electrostatic (hard) interaction. In his mathematical treatment he defined the absolute hardness of any acid or base in terms of its ionisation potential and electron affinity. Pearson s is probably the most robust approach, but the approaches in most common use are those developed by Gutmann [8] and Drago [9], who separately developed equations and methods to quantify the acid or basic strength of compounds, from which their heats of interaction could be calculated. 

Gutmann then proposed that the heat of reaction between acids and bases (AH, ) could be calculated using Equation (3.1) ... 

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