Acidity constant, calculation

The acidity constants calculated from every point in the titration curve (Figure 2.2a and b) are microscopic acidity constants (Eqs. 2.5, 2.6). Each loss of a proton reduces the charge on the surface and thus affects the acidity of the neighboring... 

Figure 9.7. Titration of a suspension of a-FeOOH (goethite) in the absence of specifically adsoibable ions, (a) Acidimetric-alkalimetric titration in the presence of an inert electrolyte, (b) Charge calculated fix>m the titration curve (cluuge balance), (c) Microscopic acidity constants calculated from (a) and (b). Extrapolation to charge zero gives intrinsic and pA. (Data from Sigg and Stumm, 1981.)...

Obviously, to model these effects simultaneously becomes a very complex task. Hence, most calculation methods treat the effects which are not directly related to the molecular structure as constant. As an important consequence, prediction models are valid only for the system under investigation. A model for the prediction of the acidity constant pfQ in aqueous solutions cannot be applied to the prediction of pKj values in DMSO solutions. Nevertheless, relationships between different systems might also be quantified. Here, Kamlet s concept of solvatochro-mism, which allows the prediction of solvent-dependent properties with respect to both solute and solvent [1], comes to mind. 

The ionisation ratio (/ = [SH+]/[S]) can be calculated from a knowledge of the acidity function (hj.) followed by the substrate, and the acidity constant of the conjugate acid. Thus, when I p i ... 

If the substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid. The experiments of Berthelot and Jungfleiscli, and the thermodynamic deduction show, however, that the distribution law holds for each molecular state separately. Thus, if benzoic acid is shared between water and benzene, the partition coefficient is not constant for all concentrations, but diminishes with increasing concentration in the aqueous layer. This is a consequence of the existence of the acid in benzene chiefly as double molecules (C6H5COOH)2, and if the amount of unpolymerised acid is calculated by the law of mass action (see Chapter XIII.) it is found to be in a constant ratio to that in the aqueous layer, independently of the concentration (cf. Nernst, Theoretical Chemistry, 2nd Eng. trans., 486 Die Verteilnngssatz, W. Hertz, Ahrens h annulling, Stuttgart, 1909). 

As suggested by Roberts and Moreland many years ago (1953), the acidity constants of 4-substituted bicyclooctane-l-carboxylic acids provide a very suitable system for defining a field/induction parameter. In this rigid system the substituent X is held firmly in place and there is little possibility for mesomeric delocalization or polarization interactions between X and COOH (or COO-). Therefore, it can be assumed that X influences the deprotonation of COOH only through space (the field effect) and through intervening o-bonds. On this basis Taft (1956, p. 595) and Swain and Lupton (1968) were able to calculate values for o and crR. 

Interestingly, comparison of the values of pAHB and the acidity constants pKa in a series of the same family of compounds, such as carbonyl compounds, amines, pyridines and sulphoxides, shows that a good correlation exists between p/CHB and pgiving straight lines in each series of compounds with parallel slopes. This enables one to calculate the difference of the several pKa values at the same p/CHB value, and vice versa. Thus, at p= 0, p/CHB values of various functional groups were determined and are shown in Table 13. 

Because a proton transfer equilibrium is established as soon as a weak acid is dissolved in water, the concentrations of acid, hydronium ion, and conjugate base of the acid must always satisfy the acidity constant of the acid. We can calculate any of these quantities by setting up an equilibrium table like that in Toolbox 9.1. 

To calculate the pH and percentage deprotonation of a solution of a weak acid, set up an equilibrium table and determine the H30 concentration by using the acidity constant. 

The parent acids of common polyprotic acids other than sulfuric are weak and the acidity constants of successive deprotonation steps are normally widely different. As a result, except for sulfuric acid, we can treat a polyprotic acid or the salt of any anion derived from it as the only significant species in solution. This approximation leads to a major simplification to calculate the pH of a polyprotic acid, we just use Kal and take only the first deprotonation into account that is, we treat the acid as a monoprotic weak acid (see Toolbox 10.1). Subsequent deprotonations do take place, but provided Kal is less than about fCal/1000, they do not affect the pH significantly and can be ignored. 

The calculation of pH for very dilute solutions of a weak acid HA is similar to that for strong acids in Section 10.18. It is based on the fact that, apart from water, there are four species in solution—namely, HA, A, H,0 +, and OH. Because there are four unknowns, we need four equations to find their concentrations. Two relations that we can use are the autoprotolysis constant of water and the acidity constant of the acid HA ... 

Using the thermodynamic data available in Appendix 2A, calculate the acidity constant of HF(aq). 

Using only data given in Appendix 2B, calculate the acidity constant for HBrO. 

A strictly entropically controlled tendency for statistical ligand distribution was discussed 150) for ligand exchange when the sum of the Sb—X and Sb—Y bond energies remains constant. Calculations show that due to the electronic interaction in the entire molecule an energetic tendency also exists to form Lewis acids with mixed ligand spheres ... 

For a strong acid, the H, 0 concentration can be determined directly from the concentration of the acid. For a weak acid, the H, 0 1 concentration must be determined first from an equilibrium constant calculation (Sec. 20.3) then the pH is calculated. 

Values of Kadd for the addition of water (hydration) of alkenes to give the corresponding alcohols. These equilibrium constants were obtained directly by determining the relative concentrations of the alcohol and alkene at chemical equilibrium. The acidity constants pATaik for deprotonation of the carbocations by solvent are not reported in Table 1. However, these may be calculated from data in Table 1 using the relationship pA ik = pATR + logA dd (Scheme 7). 

Portmann and co-workers then studied the kinetic pathways in man for hydroxynalidixic acid, the active primary metabolite.(26) The rate constants for glucuronide formation, oxidation to the dicarboxylic acid and excretion of hydroxynalidixic acid were calculated. Essentially total absorption of hydroxynalidixic acid was found in every case. Good agreement between experimental and theoretical plasma levels, based on the first order rate approximations used for the model, was found. Again, the disappearance rate constant, kdoi was found to be very similar for each subject, although the individual excretion and metabolic rate constants varied widely. The disappearance rate constant, k was defined as the sum of the excretion rate constant, kg j and the metabolic rate constants to the glucuronide and dicarboxylic acid, kM-j and kgj, respectively. 

In these equations, HA symbolizes a weak acid and A symbolizes the anion of the weak acid. The calculations are beyond our scope. However, we can correlate the value of the equilibrium constant for a weak acid ionization, Ka, with the position of the titration curve. The weaker the acid, the smaller the IQ and the higher the level of the initial steady increase. Figure 5.2 shows a family of curves representing several acids at a concentration of 0.10 M titrated with a strong base. The curves for HC1 and acetic acid (represented as HAc) are shown, as well as two curves for two acids even weaker than acetic acid. (The IQ s are indicated.)... 

In Fig. C microscopic acidity constants of the reaction AlOHg =AIOH + H+ for y-AI203 are plotted as a function of AIOH. The data are for 0.1 M NaCICV This figure illustrates (within experimental precision) the conformity of the proton titration data to the constant capacitance model. Calculate the capacitance. 

Specific surface area 40 m2 g 1, acidity constants of FeOHg pK., (int) = 7.25, K 2 = 9.75, site density = 4.8 nrrr2, hematite cone = 10 mgle. Ionic strength 0.005. For the calculation the diffuse double layer model shall be used. 

Kluger and Lam, 1978. Comparison with the rate constant calculated for succinamic acid at 50° gives EM = 5 x 101. Correction for the better leaving group uses the ratio of rates for maleamic and maleanilic acids measured by Aldersley et al. (1974b) at 39°... 

Figure 6. Use of Method I, Equation 22, to calculate surface acidity constants with Ng - 12 sites nm" log Ka = -3.5 and log Ka2 = -8.1 or, in other terms, pHZpC = 5.8 and log Kd - -2.3. Capacitances were determined from the slopes according to Equation 22 acid branch, 0.77 F m base branch, 0.89 F m. Data are from Figure 5, Ti02 in 0.1 M KNO3 (32). ...

Table 1.5 represents acidity constants of organic compounds (AH) and their cation-radicals (AH+ ) calculated for their solutions in DMSO (a very polar solvent) at 25°C. 

Summarize the treatment of acids so far. A strong acid is virtually completely dissociated in aqueous solution, so the concentration is essentially identical to the concentration of the solution—for a 0.5 M solution of HCl, [H ] = 0.5 M. But because weak acids are only slightly dissociated, the concentrations of the ions in such acids must be calculated using the appropriate acid constant. 

Although these approaches seem to be similar, the former method has several limitations it should be recognized that intrinsic mobility (yu,A ) depends on the ionic strength of the buffer, as shown in Ref. 17. Also, the activity coefficients of the zwitterions could not be calculated via the De-bye-Hiickel equation, and other methods, such as melting point depression, should be used to obtain the activity coefficients of the zwitterions (31). On the other hand, the latter method is directly applicable to the zwitterions to obtain their acidity constants. 

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