Dissociation constant, thermodynamics

Partanen, J. I. Karki, M. H. Determination of the Thermodynamic Dissociation Constant of a Weak Acid by Potentiometric Acid-Base Titration, /. Chem. Educ. 1994,... 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

The protonation equilibria for nine hydroxamic acids in solutions have been studied pH-potentiometrically via a modified Irving and Rossotti technique. The dissociation constants (p/fa values) of hydroxamic acids and the thermodynamic functions (AG°, AH°, AS°, and 5) for the successive and overall protonation processes of hydroxamic acids have been derived at different temperatures in water and in three different mixtures of water and dioxane (the mole fractions of dioxane were 0.083, 0.174, and 0.33). Titrations were also carried out in water ionic strengths of (0.15, 0.20, and 0.25) mol dm NaNOg, and the resulting dissociation constants are reported. A detailed thermodynamic analysis of the effects of organic solvent (dioxane), temperature, and ionic strength on the protonation processes of hydroxamic acids is presented and discussed to determine the factors which control these processes. 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

The dissociation constants are thermodynamic constants, independent of ionic strength. Equation (8-33), which was derived from (8-30), is, therefore, identical in its form, and its salt effect, with Eq. (8-31). Therefore, salt effects cannot be used to distinguish between Eqs. (8-30) and (8-31). Another way to express this is that if kinetically equivalent forms can be written, it is not possible to determine, on the... 

Mass spectrometric studies yield principally three types of information useful to the radiation chemist the major primary ions one should be concerned with, their reactions with neutral molecules, and thermodynamic information which allows one to eliminate certain reactions on the basis of endothermicity. In addition, attempts at theoretical interpretations of mass spectral fragmentation patterns permit estimates of unimolecular dissociation constants for excited parent ions. 

FIG. 4 Thermodynamic equilibria for the interfacial distribution of a solute X which can be ionized n times, and X being its most acidic (or deprotonated) and its most basic (or protonated) forms, respectively. X and are the dissociation constants in the aqueous and organic phase, respectively, and P is the partition coefficient of the various species between the two phases. 

The binary complex ES is commonly referred to as the ES complex, the initial encounter complex, or the Michaelis complex. As described above, formation of the ES complex represents a thermodynamic equilibrium, and is hence quantifiable in terms of an equilibrium dissociation constant, Kd, or in the specific case of an enzyme-substrate complex, Ks, which is defined as the ratio of reactant and product concentrations, and also by the ratio of the rate constants kM and km (see Appendix 2) ... 

The equilibrium dissociation constant Ks has units of molarity and its value is inversely proportional to the affinity of the substrate for the enzyme (i.e., the lower the value of Ks, the higher the affinity). The value of Ks can be readily converted to a thermodynamic free energy value by the use of the familiar Gibbs free energy equation ... 

Consider the enzyme-catalyzed and noncatalyzed transformation of the ground state substrate to its transition state structure. We can view this in terms of a thermodynamic cycle, as depicted in Figure 2.4. In the absence of enzyme, the substrate is transformed to its transition state with rate constant /cM..M and equilibrium dissociation constant Ks. Alternatively, the substrate can combine with enzyme to form the ES complex with dissociation constant Ks. The ES complex is then transformed into ESt with rate constant kt , and dissociation constant The thermodynamic cycle is completed by the branch in which the free transition state molecule, 5 binds to the enzyme to form ESX, with dissociation constant KTX. Because the overall free energy associated with transition from S to ES" is independent of the path used to reach the final state, it can be shown that KTX/KS is equal to k, Jkail (Wolfenden,... 

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

As we described in Chapter 3, the binding of reversible inhibitors to enzymes is an equilibrium process that can be defined in terms of the common thermodynamic parameters of dissociation constant and free energy of binding. As with any binding reaction, the dissociation constant can only be measured accurately after equilibrium has been established fully measurements made prior to the full establishment of equilibrium will not reflect the true affinity of the complex. In Appendix 1 we review the basic principles and equations of biochemical kinetics. For reversible binding equilibrium the amount of complex formed over time is given by the equation... 

As stated earlier, the velocity terms are dependent on the concentration of substrate, relative to KM, used in the activity assay. Likewise in an activity assay the free fraction of enzyme is also in equilibrium with the ES complex, and potentially with an ESI complex, depending on the inhibition modality of the compound. To account for this, we must replace the thermodynamic dissociation constant Kt with the experimental value K-pp. Making this change, and substituting Equations (7.4) and (7.6) into Equation (7.7), we obtain (after canceling the common E T term in the numerator and denominator)... 

Roy, R. N. Gihhons, J. J. Padron, J. L. Moeller, J., Second-stage dissociation constants of piperazine-A,A -bis(2-ethanesulfonic acid) monosodium monohydrate and related thermodynamic functions in water from 5 to 55°C, Anal. Chem. 52, 2409-2412 (1980). 

Thus the magnitude of the constant called the thermodynamic or real dissociation constant,... 

Fig. 3.14 An extrapolation graph for determination of the thermodynamic dissociation constant of acetic acid using Eq. (3.3.14)...

Because the acid dissociation constants in solution are generally known, and also, often the solvation energies of the neutral AH have been determined by neutral gas-phase solution equilibria, equation 8 can be used to obtain the sum of the solvation energies AG°ol(A-) + AG°ol (H30+). When this approach is applied to a series of acids AH, values for the solvation energies AG°ol (A-), relative to the constant AG, (H30+), can be obtained. Such thermodynamic determinations of the... 

Regardless of the relative importance of polar and nonpolar interactions in stabilizing the cyclohexaamylose-DFP inclusion complex, the results derived for this system cannot, with any confidence, be extrapolated to the chiral analogs. DFP is peculiar in the sense that the dissociation constant of the cyclohexaamylose-DFP complex exceeds the dissociation constants of related cyclohexaamylose-substrate inclusion complexes by an order of magnitude. This is probably a direct result of the unfavorable entropy change associated with the formation of the DFP complex. Thus, worthwhile speculation about the attractive forces that lead to enantiomeric specificity must await the measurement of thermodynamic parameters for the chiral substrates. 

Among the possible analytical methods for alkalinity determination, Gran-type potentiometric titration [2] combined with a curve-fitting algorithm is considered a suitable method in seawaters because it does not require a priori knowledge of thermodynamic parameters such as activity coefficients and dissociation constants, which must be known when other analytical methods for alkalinity determination are applied [3-6],... 

All these reactions are thermodynamically favourable in the direction of proton transfer to hydroxide ion but the rate coefficients are somewhat below the diffusion-limited values. In broad terms, the typical effect of an intramolecular hydrogen bond on the rate coefficient for proton removal is to reduce the rate coefficient by a factor of up to ca 105 below the diffusion limit. Correspondingly the value of the dissociation constant of the acid is usually decreased by a somewhat smaller factor from that of a non-hydrogen-bonded acid. There are exceptions, however. 

CTC exhibits three acidic dissociation constants when titrated in aqueous solutions (18). Stephens et al. (19) identified the three acidic groups (Figure 4), and reported thermodynamic pKa values of 3.30, 7.44, and 9.27. Leeson et al. (20) assigned pKa values to the following acidic groups ... 

The thermodynamic EM for the hydrolysis of the salicylate derivative is therefore favoured by a factor presumably similar to that which favours the hydrogen-bonded form of the salicylate anion. In terms of the dissociation constant of the phenol group, which is some 3 pAT units less acidic than expected for a phenol with an ortAo-carboxylate group (Eberson, 1969), a factor of 103, which is of the right order of magnitude to explain the observed effect, could be involved. 

This procedure of lumping all non-idealities into a few adjustable parameters is unsatisfactory for many reasons. Thermodynamic rigor is lost if experimentally determined dissociation constants or vapor pressures are disregarded. Also the parameters determined in this way are accurate only over the range of variables fitted and usually the model cannot be used for extrapolation to other conditions. The attractive feature of these models in the past was their need for little input information and the simple equations could often be solved algebraically. 

VAN AKEN et al. 0) and EDWARDS et al. (2) made clear that two sets of fundamental parameters are useful in describing vapor-liquid equilibria of volatile weak electrolytes, (1) the dissociation constant(s) K of acids, bases and water, and (2) the Henry s constants H of undissociated volatile molecules. A thermodynamic model can be built incorporating the definitions of these parameters and appropriate equations for mass balance and electric neutrality. It is complete if deviations to ideality are taken into account. The basic framework developped by EDWARDS, NEWMAN and PRAUSNITZ (2) (table 1) was used by authors who worked on volatile electrolyte systems the difference among their models are in the choice of parameters and in the representation of deviations to ideality. 

Let us examine the following types of constants now.in use and their relationships to the thermodynamic constants K t) a) Apparent dissociation constants which are of practical use in ionic media (20)... 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

Brown and Melchiore (1966) have recently determined the temperature-dependence of complex formation of aromatic hydrocarbons with HCl and HRr in n-heptane solution. Dissociation constants and thermodynamic data were calculated. 

---