Ho acidity function

Acidity function Ho proposed by L. P. Hammett for assessing the suength of very strong acids. 

For the bromination of benzoic acid, the rate increased more rapidly than [H+] at high mineral acid concentrations and apparently depended on the acidity function ho rather than [H+]. Neutral salts such as disodium hydrogen phosphate, lithium and sodium sulphates also increased the rate due either to a positive salt... 

In the recent past the potential of zeolites in the manufacture of fine chemicals has received considerable attention. High-Si zeolites can have Hammet s acidity function Ho of -12.8 which is close to those for superacids. MCM (Mobil Catalytic Materials) have opened up new vistas due to larger pore sizes. 

This linear plot works very well, giving p/STbh+ values as intercepts (and slopes < e) thus only one acidity function (Ho) is needed for the purpose of estimating weak basicities. In the Bunnett-Olsen method Ch+ is simply the acid molarity. The terms m from the Yates-McClelland method and (1 — e) from the Bunnett-Olsen method are, for all practical purposes, equivalent m = 1, e = 0 for primary nitroanilines m = 0.6, e = 0.4 for amides and so on. 

According to this, there is a linear relationship between the logarithm of the partition coefficients, log (cah+/ca)> the Hammett acid function Ho- Plattner et al. (1949) were able to confirm this relationship for a substantial number of methyl-substituted azulenes. However, the further analysis of these measurements with a view to obtaining pAg proved difficult since the partition coefficient Pa of the free azulene between the two phases, which enters into equation (12c), is unknown. For this reason, the authors took the for which Cah+ = Ca as a charac-... 

The acid-catalysed transannular cyclization of 8-10-membered y,5-unsaturated cyclic sulfides (59) or (60) yields c/x-fused bicyclic sulfonium salts (61) independently of the geometry of the double bond. The rate varies linearly with the acidity function -(Ho h with a slope of 1. The rate variations span a range of about 10 , the maximum rate difference being observed for the ( /Z)-thiacyclooct-4-ene pair. The data are consistent with the classical interpretation of the intramolecular reactivity in terms of internal strain of the substrate and/or of the transition state. ... 

Another problem is the very high concentrations of reactants present in the low-conversion region. The correct derivation of any rate expression such as Eqs. 2-20 and 2-22 requires the use of activities instead of concentrations. The use of concentrations instead of activities assumes a direct proportionality between concentration and activity. This assumption is usually valid at the dilute and moderate concentrations where kinetic studies on small molecules are typically performed. However, the assumption often fails at high concentrations and those are the reaction conditions for the typical step polymerization that proceeds with neat reactants. A related problem is that neither concentration nor activity may be the appropriate measure of the ability of the reaction system to donate a proton to the carboxyl group. The acidity function ho is often the more appropriate measure of acidity for nonaqueous systems or systems containing high acid concentrations [Ritchie, 1990]. Unfortunately, the appropriate ho values are not available for polymerization systems. 

The pH of an aqueous solution, where the concentration of the solute is not very high, is a good measure of the proton-donating/accepting ability of the solvent. But unfortunately this is no longer true in concentrated solutions because activity coefficients are no longer at unity. A measurement of solvent acidity is needed which works in concentrated solutions and applies to mixed solvents as well. This is established in the Hammett acidity function (Ho)10,11- This function is used for acidic solvents of high dielectric constants Hq is... 

A DIE of k 2o/k )2o = 3.2 has been found in the hydrolysis of a-benzoyloxystyrenes, 382, in concentrated perchloric acid solution450. The rate of hydrolysis was found to be linear with the acidity function, Ho- A small inverse deuterium KIE, A h /I d = 0.78, at the -carbon has been found in the oxidation of cinnamic and crotonic acids451 by quinolinium dichromate. The reaction involves electrophilic attack on the double bond and a carbonium-ion intermediate (p = —4.0). A small inverse D KIE (k /k ->) = 0.80, p = —4.0] has been also observed452 in the acid cleavage of substituted styrenes by quinolinium dichromate in DMF in the presence of acid452. 

The acid strength of a solid is defined as the ability of the surface to convert an adsorbed neutral base into its conjugate acid (2). If the reaction proceeds by means of proton transfer from the surface to the adsorbate, the acid strength is expressed by the Hammett acidity function Ho, Ho = pKa + log[B]/[BH + ], where [B] and [BH + ] are, respectively, the concentrations of the neutral base (basic indicator) and its conjugate acid, and pK.d is p BH +. If the reaction takes place by... 

Numbers in parentheses are values of the Hammett Acidity Function (Ho) calculated on the basis of the reported experimental preparative conditions and represent approximate acidity thresholds above which the particular species are stable in solution. 

In dilute aqueous solution, the acidity is measured using pH values. For concentrated acid solutions and non-aqueous acid solutions, pH values are no longer available. Hence, the Hammett acidity function Ho is used as a measure of the acidity of such media [130]. The proton donor ability of an acid in such media is measured by studying the equilibria of a series of indicator bases B (mostly nitroanilines), the UV/Vis absorption spectra of which are markedly different from those of their conjugate acids, so that the indicator concentration ratio I = [B]/[BH+] can be measured spectrophotometri-cally. The acidity function Ho is then given by Hq = p.Kbh+ + Ig f with the subscript zero indicating that the Hq function applies only to neutral bases B [130, 170], For dilute solutions, Ho corresponds exactly to pH in concentrated solutions, the two functions differ appreciably. 

Fig. 3. Hammett acidity function Ho of H3PO4 and those of other mineral adds [from Olah (i3) copyright 1973 John Wiley Sons Inc.].

This question was first studied systematically by L. P. Hammett and A. J. Deyrup. We referred, in Chapters Threfe and Four, to the difficulties encountered in measuring hydrogen ion activities in various solvents. When water is the solvent, we measure the activity of hydrated protons (hydronium ions) instead of the real proton activity and in other solvents too, it is the activity of the solvated protons which is determined. Accordingly, Hammett and Deyrup have proposed to express acidity in terms of an acidity function Ho which is measured with monoacidic indicator bases. 

Let us first consider the meaning of this term which otherwise might lead to considerable confusion. The acidity function Ho is defined by the following equation ... 

Hence only monoacidic indicator bases should be employed for the determination of the acidity function Ho. Confusion may result from the use of indicators belonging to other charge types. 

Several of the values for acidity function Ho measured by Hammett and Deyrup for water-sulfuric acid mixtures are recorded below. The acidity function of concentrated sulfuric acid is seen to be 10.6 and therefore this compound is (10.6 - - 7.0) = 17.6 units more acid than water (pH of water at 25° is 7.0). 

In these medium the acidity cannot be measured by pH. The Hammet-Deyrup acidity function , Ho (ref. 6), which shows the facility of protonation of a weak base by a superacid, allows to class the superacids (ref. 7) (Fig. 1). 

From the relation between the activity coeffijjient ratios and the acidity function (Ho), it is concluded that the transition state must be effectively a conjugate acid of the olefin which is not firmly bound- to any water molecule. Since the reactants are olefin and hydronium ion, such a transition state can be formed only by the isomerization from one unstable intermediate to another. The unimolecular isomerization of the r complex to the carbonium ion fits the requirements and constitutes the rate-determining step. Water molecules do not enter the transition state, thus the molecularity of the reaction is zero with respect to the solvent water. 

The rccison for the increased activity of protic acid-Lewis acid systems is ascribed to the enhancement of the protic acid acidity by the Lewis acid, (Table 2) 31). Whereas 100% HF has a value of —10.2, the acid system of HF +7% BF3 has an Ho value of —16.8, six orders of magnitude greater. The Hammett acidity function. Ho, is evaluated by the use of indicators, B, which are very weak bases and for which the acid ionization constants, Ka, of the conjugate acids, BH+, have been determined (usually spectrophotometrically), Eq. (9) ... 

The acidity function Ho gives information on the acid centers of a catalyst. It can be determined by means of a series of calibrated bases in the presence of special indicators, and in this way, comparison to sulfuric acid of known strength can be made. 

Indeed, following Hammett, the acidity of such solutions, as measured by its catalytic effects, can be described remarkably well by an acidity function Ho which takes the place of pH in concentrated solutions. 

Remembering (8.2.8), we then introduce the acidity function Ho by the definition ... 

The rate constant for the forward reaction k = ksKaho is proportional to ho and therefore — log k must change linearly with the acidity function Ho as is verified ex perimentally. 

Concentrations of HB and B are measurable by spectroscopy, and pK values of the acids HB" " are well known. Hammett acidity function. Ho, scales are useftil for comparing different acid media for acid strength. Typically, the Hammett acidity functions for the reaction mixtures to synthesize high-molecular-weight polyaniline are in the range —2 < Hq < 0.5. 

POLYMER-SUPPORTED SYNTHESIS Table 6.2 Values of Hammett acidity function (Ho) [108] ... 

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