Proton coefficient comparison

P=f(Xp. pH). As described above, the magnitude of P is inexorably linked to the variations of x with pH and adsorption density. However, the response of x (and P) to T and pH varies among hydrous oxides. For example, Figure 9a shows the instantaneous (isotherm) proton coefficient (xp) "zones" determined for Cd ion adsorption onto (am)Fe20o O, a-A O and oc-TiC. The zones are defined by the calculated proton coefficients determined for a range of pH values and adsorption density. The "thickness" of each zone gives a qualitative comparison of the pH dependency of Xp at each adsorption... 

Figure 9. Comparison of a) net proton coefficient and b) log P pH and surface coverage "zones" for Cd(II) adsorption onto a-A O, (am)Fe20j.H20 and a-Tit. ...

Kresge et a/.498 have drawn attention to the fact that detritiation of [3H]-2,4,6-trihydroxy- and [3H]-2,4,6-trimethoxy-benzenes by concentrated aqueous perchloric acid gives correlations of log rate coefficient with — H0 with slopes of 0.80 and 1.14 respectively. Protonation to give the carbon conjugate acids is, however, governed by h0lA0 and h0l 9S, respectively, which suggests that the difference in kinetic acidity dependence is a property of the substrate and should not be interpreted as a major difference in mechanism. The kinetic difference can be eliminated by an appropriate comparison of kinetic and equilibrium acidity dependencies. In equation (230)... 

Fig. 14 Predicted variation in forward (/cB) and reverse (kM+) rate coefficients for proton transfer from an intramolecularly hydrogen-bonded acid (HA-) to bases (B) (solid line) and comparison with normal proton-transfer behaviour (dashed line)...

Figure 12. Water self-diffusion coefficient of Nafion 117 (EW =1100 g/equiv), as a function of the water volume fraction Xy and the water diffusion coefficient obtained from a Monte Carlo (MC) simulation (see text). The proton conductivity diffusion coefficient (mobility) is given for comparison. The corresponding data points are displayed in Figure 14.

For comparison purposes, the proton mobility. Do (for Nafion solvated with water), which is closely related to the self-diffusion coefficient of water, is also plotted. At low degrees of hydration, where only hydrated protons (e.g., H3O+) are mobile, it has a tendency to fall below the water diffusion coefficient (this effect is even more pronounced in other polymers), which may be due to the stiffening of the water structure within the regions that contain excess protons, as discussed in Section 3.1.1. . Interestingly, the proton mobility in Nafion solvated with methanol (Da(MeOH) in Figure 14a) is even lower than the methanol self-diffusion (Z ieon). This may... 

F eOH FH20, and Fmgoh) for different solvated acidic polymers are presented in a way that allows some interesting comparisons and the calculation or estimation of the elements of the transport matrix Ljj. In many publications, these transport parameters are reported as a function of the solvent content and are expressed as the number of solvent molecules (i.e., water) per sulfonic acid group. Because of the importance of percolation effects in all considered transport coefficients, we have converted these solvent contents to solvent volume fractions, except for proton conductivities, as shown in Figures 17 and 18. 

Upon comparison of eq 32 to 28, it is seen that the proton—water interaction is now taken into account. This interaction is usually not too significant, but it should be taken into account when there is a large gradient in the water (e.g., low humidity or high-current-density conditions). Upon comparison of eq 33 to 31, it is seen that the equations are basically identical where the concentration and diffusion coefficient of water have been substituted for the chemical potential and transport coefficient of water, respectively. Almost all of the models using the above equations make similar substitutions for these variables 15,24,61,62,128... 

The rate coefficient of a reactive process is a transport coefficient of interest in chemical physics. It has been shown from linear response theory that this coefficient can be obtained from the reactive flux correlation function of the system of interest. This quantity has been computed extensively in the literature for systems such as proton and electron transfer in solvents as well as clusters [29,32,33,56,71-76], where the use of the QCL formalism has allowed one to consider quantum phenomena such as the kinetic isotope effect in proton transfer [31], Here, we will consider the problem of formulating an expression for a reactive rate coefficient in the framework of the QCL theory. Results from a model calculation will be presented including a comparison to the approximate methods described in Sec. 4. 

It is well known that outside the pH range almost all predeterminations for unexcited molecules have been based on the Hammett indicator method (Hammett and Deyrup, 1932). Even in concentrated acid (or alkaline) solutions, where uncertainties in the value of b//bh become very serious, it is easy to measure the ratio of protonated to unprotonated indicator concentrations spectrophotometrically when the absorption peaks are sufficiently resolved. The difficulty arises in trying to extrapolate beyond the measurable [BH+]/[B] range to zero electrolyte concentration. Hammett and Deyrup assumed that the activity coefficient ratios of the type /b//bh+ were very similar for different indicators in the same acid solution. For the equilibrium (51) between two indicators A and B, a comparison of the concentration ratios [BH+]/[B] and [AH+]/[A] over an acidity range in which both could be measured would lead to a direct estimate of the difference in p-K-values using (52) and (53). Beginning with 4-nitroaniline, which is about half-... 

Px is the partition coefficient of a derivative and PH is that for the parent compound.) Also used were Hammett s o- constant, Taft s polar constant, steric parameter, Es. In a few examples (Equations 17, 21, 24, and 30), P values from oleyl alcohol/water have been used. In one instance (Equation 69) the chemical shift of a phenolic proton has been used for comparison with the a constant. Where possible, the experimentally measured partition coefficients for all members of the series have been used. In other instances only one member of a set has been measured. Values for the other members were obtained by taking advantage of the additivity principles of log P and tr. Details are given elsewhere (4, 7, and 8). For the new work of Table II, log P values for the parent compounds are given in the footnotes. 

A number of other proton transfer reactions from carbon which have been studied using this approach are shown in Table 8. The results should be treated with reserve as it has not yet been established fully that the derived Bronsted exponents correspond exactly with those determined in the conventional way. One problem concerns the assumption that the activity coefficient ratios cancel, but doubts have also been raised by one of the originators of the method that, unless solvent effects on the transition state are intermediate between those on the reactants and products, anomalous Bronsted exponents will be obtained [172(c)]. The Bronsted exponents determined for menthone and the other ketones in Table 8 are roughly those expected by comparison with the values obtained for ketones using the conventional procedure (Table 2). For nitroethane the two values j3 = 0.72 and 0.65 which are shown in Table 8 result from the use of different H functions determined with amine and carbon acid indicators, respectively. Both values are roughly similar to the values (0.50 [103], 0.65 [104]), obtained by varying the base catalyst in aqueous solution. The result for 2-methyl-3-phenylpropionitrile fits in well with the exponents determined for malononitriles by general base catalysis but differs from the value j3 0.71 shown for l,4-dicyano-2-butene in Table 8. This latter result is also different from the values j3 = 0.94 and 0.98 determined for l,4-dicyano-2-butene in aqueous solution with phenolate ions and amines, respectively. However, the different results for l,4-dicyano-2-butene are to be expected, since hydroxide ion is the base catalyst used in the acidity function procedure and this does not fit the Bronsted plot observed for phenolate ions and amines. The primary kinetic isotope effects [114] also show that there are differences between the hydroxide ion catalysed reaction (feH/feD = 3.5) and the reaction catalysed by phenolate ions (kH /kP = 1.4). The result for chloroform, (3 = 0.98 shown in Table 8, fits in satisfactorily with the most recent results for amine catalysed detritiation [171(a)] from which a value 3 = 1.15 0.07 was obtained. 

The bare proton has an exceedingly small diameter compared with other cations, and hence has a high polarising ability, and readily forms a bond with an atom possessing a lone pair of electrons. In aqueous solution the proton exists as the H30+ ion. The existence of the H30+ ion in the gas phase has been shown by mass spectrometry [4], and its existence in crystalline nitric acid has been shown by NMR [5], Its existence in aqueous acid solution may be inferred from a comparison of the thermodynamic properties of HC1 and LiCl [6]. The heat of hydration of HC1 is 136 kcal mole"1 greater than that of LiCl, showing that a strong chemical bond is formed between the proton and the solvent, whereas the molar heat capacity, molar volume and activity coefficients are similar,... 

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