Excess acidity method

Comparing Eqs. (8-95) and (8-97) shows that the quantity m X is a measure of solution acidity in excess of the ideal state this gives rise to the term excess acidity method for the X acidity function approach. We also have, from Eqs. (8-87) and (8-88),... 

Observed m values cluster about 1, but considerable variation is seen among structural types. For some systems, however. Ho + log Ch+ = —X in these cases the excess acidity method is equivalent to Bunnett and Olsen s method, in which the sum Ho + log Ch+ plays the acidity function role. 

A philosophical problem remains, however. The Bunnett-Olsen method, which assumes the linearity of activity coefficient ratios in one another, still uses H0, and H0 values are derived using the cancellation assumption The cancellation assumption is eliminated altogether in the excess acidity method (also called the Marziano-Cimino-Passerini and Cox-Yates methods, which is unfortunate since both are the same - the term excess acidity method is preferred). 

Equation (17) is the heart of the excess acidity method for the determination of unknown p bh+ values in strongly acidic media. Without going into detail (which is tedious) polynomial coefficients have been calculated that enable the calculation of X for 0-99.5 wt% H2SO4 and 0-80 wt% HCIO4. These are used with equation (18) and are given in Table 1. The form of equation (18) was... 

The actual using of the excess acidity method to obtain weak basicities and slope parameters is quite easy, and is now the method of choice. The following examples are chosen at random on the basis of not having been published before elsewhere, or of having been recalculated, and to illustrate the different possibilities and different acid systems. 

The measurement of pA bh+ and m values is sometimes complicated by the fact that the spectroscopic methods used (generally H and 13C NMR spectroscopy, and UV-vis) are subject to medium effects. Water and (say) 80 wt% H2SO4 are very different media, and it is not very surprising that spectral peaks for the same species in the two media can occur at different wavelengths or different chemical shifts. Several methods have been devised for handling this problem 24,99,100 the excess acidity method lends itself to dealing with medium effects quite well.101... 

Johnson and Stratton133 have compared pAbh+ values obtained using the Hammett acidity function method and the excess acidity method, and they consider that results obtained using the former may correspond more nearly to... 

By analogy with equation (12), the assumption made regarding the linearity of activity coefficient ratios is equation (45) (slope parameter j), and the resulting Bunnett-Olsen equations that apply to kinetic measurements are equations (46) and (47) for unprotonated and protonated substrates, respectively.156 These apply to the A1 and A-SE2 mechanisms for the A1 and A2 mechanisms they may require correction for partial substrate protonation as in equations (25) and (26) above. For A2 reactions an additional term such as the log water activity has to be added as in equation (33). These equations have been widely tested and work quite well.155-160 The difference between the Bunnett-Olsen and the excess acidity kinetic methods (discussed below) is that the Bunnett-Olsen method features an additive combination of the slope parameters e and , whereas the excess acidity method features a multiplicative one. There seems to be no theoretical justification for the former. Also the Bunnett-Olsen method still uses H0, whereas acidity functions are not needed for the excess acidity approach see above. 

The excess acidity method can also be used to obtain the protonation correction terms, if needed, in equations (51) and (54) dividing by Cs shows them to be log(l/(/+ 1)) and log(1/(1+ 1)), for the unprotonated and protonated cases, respectively, and log/values are available from equation (17). 

Excess acidity correlations have been used to show that some aromatic sulfonic acid desulfonations have an A-SE2 mechanism.188,189 This mechanism (alternative terminologies are Ad-E2 and A(E) +A(N))190 has also been found to apply to the hydration of acetylene itself,191 to ynamines192 and to many other alkynes,193-195 as well as to many different alkenes196-199 and vinyl ethers.200-203 The excess acidity method has been used to evaluate aA values for several alkene hydrations.204 205... 

Now a very useful feature of the excess acidity method comes into play likely nucleophiles or bases can be tested by subtracting their log activities or concentrations from the left-hand side of equations (59) and (60), and the species reacting with SH+ is uniquely identified when linearity of the result against X is achieved.145,161 For instance, subtraction of twice the water activity is required to attain linearity in ester hydrolysis processes such as equation (42), as shown in Fig. 11 for methyl benzoate41 and ethyl benzoate.210 The water activities given in Table 3 were used. The parameters of the lines in Fig. 11, obtained by curve-fitting, are methyl benzoate, slope 0.921 + 0.010, intercept... 

The excess acidity method has been used to show that some reactions do have pure A2 mechanisms, for instance the hydrolysis of some benzohydroxamic acids,126,211 the hydrolysis of sultams,212 and the oxidation of lactic acid in... 

Having seen that the excess acidity method works for second-order as well as for first-order acid-catalyzed processes, it is of interest to see whether it extends to reactions that are not acid catalyzed. The hydrolysis of acylimidazoles, equation (68), takes place in aqueous acids the substrate is protonated on the ring nitrogen in the pH range, and in acid media the reaction rate constants decrease steadily with increasing acidity.251,253... 

Apart from these typical acid-catalyzed reactions, the method is capable of dealing with bimolecular processes, and even reactions that are not acid-catalyzed. For any process that takes place in non-ideal aqueous acid media, it should be the first technique tried. Admixture of the aqueous acid with moderate amounts of inert organic solvent should not be a problem. The broad variety of reaction mechanisms given above should display the versatility and utility of the excess acidity method in physical organic chemistry. 

The excess acidity method has been applied to the acid-catalysed hydrolysis of isopropyl phenyl ether at different temperatures.152... 

Very recently (R. A. Cox et al., 1979), the variations of the enolisation rate coefficient as a function of sulphuric acid concentration (up to 60% w/w) were examined by means of the excess acidity method . According to this, the ratio / (7 = [YH+]/[Y]) between the concentrations of a protonated substrate YH+ and the corresponding free form Y in concentrated acid solutions can be expressed as (15), where [H+] is the acid concentration and X an empirical... 

Entropy of activation (continued) sign of, 256 Entropy unit, 242 Enzyme catalysis, 102 Enzyme-substrate complex, 102 Equilibrium, 60, 97, 99, 105, 125, 136 condition for, 205 displacement from, 62, 78 in transition state theory, 201, 205 Equilibrium assumption, 96 Equilibrium constant, 61. 138 complexation, 152 dissociation, 402 ionization, 402 kinetic determination of, 279 partition functions in, 204 pressure dependence of, 144 temperature dependence of, 143, 257 transition state, 207 Equivalence, kinetic, 123 Error analysis, 40 Error propagation, 40 Ester hydrolysis, 4 Euler s method, 106 Excess acidity method, 451 Exchange... 

R.A. Cox, Organic Reactions in Sulphuric Acid the Excess Acidity Method, Acc. Chem. Res., 1987, 20, 27. 

Estimate by Dickman and Bray s (excess acid) method. 

An alternative method of reconciling the various scales is the excess acidity method, developed by Marziano et al. (1973,1977) and confirmed and extended by Cox and Yates (1981, 1983 Cox, 1987, 2000). Cox defines X as the excess acidity over the stoichiometric acid concentration, writing... 

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