Bunnett-Olsen equations

Equation (12) is a linear free-energy relationship, since activity coefficients/can be represented as AG° values. The reason for defining the slope parameter as in equation (12) (subscript e for equilibrium) is that a little rearranging of equations (11) and (12) leads to the easy-to-use Bunnett-Olsen equation for equilibria, equation (13) 30... 

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. 

A modification of the Bunnett-Olsen equation concerned with solvent acidity in which log([SH+]/[S]) - log[H+] = m X -h p/ sH where [S] and [SH+] are the solvent and protonated solvent concentrations, and X is the activity function log[(7s7H+/ysH+)] for an arbitrary reference base. In practice, X = - (Ho + log[H+]), called the excess acidity (where Ho is the Hammett acidity function, m = 1- (f), and 4> represents the response of the S + H+ SH+ equilibrium to changes in the acid concentration). See Acidity Function Bunnett-Olsen Equation... 

VOLUME STRAIN BUNDLING PROTEIN BUNNETT-OLSEN EQUATIONS COX-YEATS EQUATION ACIDITY FUNCTION BURST KINETICS Buthionine sulfoximine,... 

ACIDITY FUNCTION BUNNETT-OLSEN EQUATIONS DECREE OF DISSOCIATION HAMMETT EQUATION HAMMOND PRINCIPLE/POSTULATE LEFFLER S ASSUMPTION REACTING BOND RULES HANES PLOT... 

Bunnett-Olsen equations The equations for the relation between lg([SH+]/[S]) + Ha and H0 + lg[H+] for base S in aqueous mineral acid solution, where H0 is Hammett s acidity function and H0 + lg[H+] represents the activity function lg(ys Yi i+)/yS + for the nitroaniline reference bases to build FU. 

Cox-Yates equation A modification of the Bunnett-Olsen equation of the form... 

We are now in the position to use measured activity coefficients to check the Bunnett-Olsen equation and to consider its meaning in more detail (Bonvicini et al., 1973 Levi et al., 1974). By rearranging eqn (12) we obtain (14). 

We have approached the problem of the relationship between protonation, solvation, and acidity functions. First we have discussed the present status of the determination of p and acidity functions for individual bases in terms of the Bunnett-Olsen equation. 

Taken from Reference 170. The values are averaged ones obtained by U V and N MR methods in H2S04 or HC104. Bunnett-Olsen s values, 0.4-0.6 in equation 29. This suggested that sulphoxides are not Hammett bases (J. F. Bunnett and F. P. Olsen, Can. J. Chem., 44, 1899 (1966))... 

Bunnett and Olsen equation 566 Butadienyl sulphones, reactions of 644, 652 Butadienyl sulphoxides reactions of 360 synthesis of 246, 279... 

A treatment partially based on the Bunnett-Olsen one is that of Bagno, Scorrano, and More OTerrall, which formulates medium effects (changes in acidity of solvent) on acid-base equilibria. An appropriate equilibrium is chosen as reference, and the acidity dependence of other reaetions compared with it, by use of the linear free energy equation... 

The second way, called the Bunnett-Olsen method,30 makes the less drastic assumption that log activity coefficient ratios such as those in equation (7) are linear functions of one another, rather than cancelling out. From the definition of H0 in equation (8) we can write equation (11), where Am refers to the primary aromatic amines used in the determination of Ho, and then any specific activity coefficient ratio, say for the weak base B, is assumed to be linear in this according to equation (12) ... 

Another acidity function was proposed by Bunnett and Olsen (equation 5)29-32 ... 

Another approach to the acidity function problem was proposed by Bunnett and Olsen,who derived the equation... 

The need for a special acidity function for each class of base in order to interpret acid-base equilibria in concentrated acids led to increasing disenchantment with this field. However, two empirical treatments have been reported in recent years which provide a means for returning the area to a sound basis. These equations have been proposed by Bunnett and Olsen (1966) and by Yates and McClelland... 

Bunnett and Olsen suppose that the variations of these ratios with sulphuric acid concentration are related by the equation... 

A plot of the left-hand side of Equation (9), containing only observable quantities, against Ho + lg[H ], where Hq is based on the nitroanilines, should therefore be a straight line of slope P and intercept pXgH Bunnett and Olsen showed that such plots are in fact almost always linear, confirming the assumption in (7) the values of P (corresponding to 1 — 0 in Bunnett and Olsen s notation) vary from 0.17 to 3.44, illustrating the... 

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