Thermodynamic dissociation constant

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. 

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)... 

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

Thermodynamic Dissociation Constants for Alkylated Succinic Acids in 50% Aqueous Ethanol... 

Observable constants, usually thermodynamic dissociation constants, for the association of a particular ligand with two or more sites on a larger molecular entity (e.g., a macromolecule). Macroscopic constants are composites of microscopic (i.e., intrinsic) constants. 

The negative sign indicates mobilization toward the anode. Hence, the thermodynamic dissociation constant for the weak acid is obtained from Eqs. (5) and (8) as follows ... 

Edwards, L. J. (1950), The hydrolysis of aspirin. A determination of the thermodynamic dissociation constant and a study of the reaction kinetics by ultraviolet spectrophotometry, Trans. Faraday Soc., 46,723-735. 

Table 6-5 gives thermodynamic dissociation constants and values of AG 0 and AH 0 for a number of acids of interest in biochemistry. Some of these values were used in obtaining the values of AGf° for the ions of Table 6-4. The data of Table 6-5 can also be used in evaluation of Gibbs energy changes for reactions of ionic forms not given in Table 6-4.

The protonation of amides (A) to yield the conjugated acids (AH+) in aqueous sulphuric acid takes place on the carbonyl oxygen158-161 and the ionization ratio (I = [AH+]/[A]) has been found to depend on the acidity of the solution as measured by the Ha acidity function25,162 163 where A ah+ is the thermodynamic dissociation constant of the conjugated acid (equations 33 and 34). 

In this formula K m is the dissociation constant expressed solely by the equilibrium concentrations, according to the classical Guldberg-Waage interpretation of the law of mass action. This value is identical with the true thermodynamical dissociation constant Km in highly diluted solutions only, for which the mean activity coefficient y+w very nearly equals unity. In all other solutions K m is not a true constant, but it depends on the actual concentration and on the presence of additional electrolytes therefore, it is called the apparent dissociation constant, in contradistinction of the true dissociation constant. For concentration expressed in terms of molarity, a similar equation is valid-... 

The relation between the function k and the true or thermodynamic dissociation constant K is obtained by combining equations (94) and (95) thus... 

Utilize the data referred to in Problem 1 to calculate the dissociation functions of acetic and a-crotonic acids at several concentrations by means of equation (10) compare the results with the thermodynamic dissociation constants obtained in Chap. V. 

If the usual value for Er u of the reference electrode is employed in this equation to derive pH s, the results are found to be inconsistent with other determinations that are thermodynamically exact. A possible way out of this difficulty is to find a value for such that its use in equation (2) gives pH values which are consistent with known thermodynamic dissociation constants. For this purpose use is made of equation (29) of Chap. IX, viz.,... 

V. Dissociation Constant Method.—All the methods described above give approximate values only of the so-called hydrolysis constantof the salt the most accurate method for obtaining the true hydrolysis constant is to make use of the thermodynamic dissociation constants of the weak acid or base, or both, and the ionic product of water. For this... 

In relating acid strength to catalytic activity, it has been customary to use the thermodynamic dissociation constant in water at 25°, and this practice has been defended by Dippy (92). However, it has been shown that the order of acid strength is not independent of the medium or the temperature (Everett, 93 Harned and Embree, 94). As pointed out by Everett and Wynne-Jones (95), the order for AF298 is not always the same as for the other thermodynamic functions. The parallelism between... 

The electrophoretic mobility of a neutral base B in a buffer at a given pH is correlated to its thermodynamic dissociation constant. Such correlations were used for determination of the pKd of HAA belonging to classes B and C of Table 2, by CZE-UVD (at 214 nm) of these compounds in buffers of pH from 3 to 9. The pKd values obtained by the CZE method are the same as those obtained from UW spectrophotometric measurements256. The pKd values derived from these experimental measurements are different from those appearing in Table 2, because the latter values are purely calculated ones (see note a in the table). 

Since the glass electrode provides a good approximation of h,o > the measured value of A" , differs from the thermodynamic value by the ratio of the two activity coefficients. The activity coefficient in the denominator of Equation 21 -27 does not change significantly as ionic strength increases because HA is a neutral species. The activity coefficient for A, on the other hand, decreases as the electrolyte concentration increases. This means that the observed hydrogen ion activity must be numerically larger than the thermodynamic dissociation constant. 

Whenever an organic acid contains two or more chemically identical (i.e., stereochemically equivalent) functional groups, statistical factors that originate in the entropy of formation of the acid and/or its conjugate base contribute to the variation of thermodynamic dissociation constants with the degree of dissociation of the acid. Such statistical effects are implicitly included in equations that are often used to describe acid-base equilibria in synthetic and natural polymers. Because those equations have frequently been applied to proton binding by humic substances, a brief discussion of statistical ef-... 

In the case where A and B are identical, K equals Kb and Kc equals Kd- It follows that Ki equals 2Ka and K2 equals 0.5/ff. Therefore, the thermodynamic dissociation constants differ from the intrinsic dissociation constants, with the ratio K /K2 equal to 4(Ka/Kc). Whether or not there are electrostatic interactions that affect Ki and K2 (discussed in the following sections), the statistical factor of 4 will always be present. A comparison of K1/K2 for a series of symmetrical dicarboxylic acids HOOC—(CH2) — COOH is given in Figure 1. As n increases, electrostatic effects should approach zero and KalKc should approach unity, leaving only a statistical factor of 4, as is evident in this figure. 

We must state, however, that the thermodynamic dissociation constants have a relatively small practical importance. It is true that they remain constant with changing ionic strength but to use them it is necessary to know the activity coefficients of the several components at different electrolyte concentrations. The simple Debye-Huckel equation for computing activity coefficients is valid only at very small ionic strengths. At larger ionic strengths it is preferable to determine empirically the stoichiometric dissociation constants for various types of electrolytes. 

Most dissociation constants recorded in the literature have been calculated on the basis of the old dissociation theory of Arrhenius. It is therefore of great practical interest to evaluate these data critically and to see how the thermodynamic dissociation constants may be calculated from them. Only the three most important methods for determining dissociation constants will be discussed. Sufficient information has been given... 

In order to calculate the thermodynamic dissociation constant from the paH and the known composition of the solution, the activity coefficients of the various components must be known. Unfortunately the simple Debye-HiJckel equation is valid only at small ionic strengths and in concentrated solutions, the values of the different factors (A, b, B) needed to calculate activity coefficients are unknown. Hence the calculation of these coefficients is at best an uncertain practice. 

Regardless of these difficulties, the fact remains that the thermodynamic dissociation constant is truly a constant, and that the quantity calculated on the basis of degree of dissociation does not yield a true cdnstant. 

The thermodynamic dissociation constants were calculated from the classical constants in a similar manner and independently of each other by D. A. MacInnes, M. S. Shebill and A. A. Noyes, and I. M. Koijhopp. ... 

By way of illustration we present the two following tables which include the thermodynamic dissociation constants of acetic acid and o-nitrobenzoic acid calculated from conductivity measurements by J. Kendall. The first column contains the acid concentration, the second contains the classical degree of dissociation a multiplied by 100, in the third is found the dissociation constant calculated by the classical method, the fourth gives ac (classical ion concentration), the fifth column shows the true ion concentration ac//x, the sixth contains the concentration of undissociated acid [cHA] = c — (aclf ), and in the last column is found Ka calculated by equation (15). 

Thermodynamic Dissociation Constants of Acetic Acid and o-Nitrobenzoic Acids Calculated from Conductivity... 

Table V. Thermodynamic Dissociation Constants of Carbonic Acid...

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