Acid dissociation constant relation

It is also common when building the knowledge base to find that the insertion of one piece of knowledge generates the need for further material. One step in a chemical analysis may require strongly acidic conditions, which are achieved by using a low pH. This implies that the ES needs to know about pH, which in turn demands an understanding of what is meant by the concentration of H+ ion. This may then require that the ES contains some information that relates to acid dissociation constants. 

To conduct meaningful mechanistic and kinetic studies in alcohol media reliable and simple measurement and control of the solution jjpH is essential. Potentiometric titration is the method of choice for obtaining acid dissociation constants or metal ion complex stability constants and in favorable cases the speciation of mixtures of metal-ion-containing complexes in solution can be proposed.20 Titrations in non-aqueous solvents are not nearly as widely reported as those in aqueous media, particularly in cases with metal ions21 and determination of pH in a non-aqueous solvent referenced to that solvent is complicated due to the lack of a way to relate the electrode EMF readings to absolute jjpH (see footnote and ref. 6) so non-aqueous solvents are generally inconvenient to use22 for detailed studies of reaction mechanisms where pH control is required. 

Metal-complex stability is also related to the basic strength of the ligand entity. For a series of 1 2 complexes of the bidentate naphthylazophenol ligand (5.64) with copper(II) ion, the acidic dissociation constants (pKa) are linearly related to the stability constants (log K1 2), the more acidic groups forming the less stable complexes. Thus where X = N02 in structure 5.64 then pKa = 8.1 and log K1 2 = 17.2, and where X = OCH3 then pKa = 8.5... 

In a similar investigation of the tautomeric tridentate ligand 2 -hydroxyphenylazo-2-naphthol (5.65 in Scheme 5.17), the first and second acidic dissociation constants (pKa) related to the two hydroxy groups in the parent structure (X = H) were found to be 11.0 and 13.75 respectively. On introduction of an electron-withdrawing substituent (X) the first dissociation constant decreased from 11.0 to 10.55 (X = Cl) or 7.67 (X = N02). The stability constants (log K1 1) of the derived 1 1 complexes were dependent on the metal ion introduced [46], being particularly high for nickel(n) at 19.6 and copper(II) at 23.3. 

By relating the concentrations of the different species in solution through the acid dissociation constants as a function of the total metal complex concentration [M], the observed rate constant (rf M / [M dt = 2kobs) can be obtained, and if the dioxo complex does not undergo observable oxygen exchange, it reduces to Eq. (22) (see also discussion for Re(V) and Tc(V)). 

These K values are often designated as Kp values (protonation constants) and are related to the commonly encountered acid dissociation constants, Ka, by the following relationship Kp = 1/Ka. From the Kp values, it can be seen that below pH values of 12.9 the ion is protonated to HS which lowers the concentration of ion in solution. The concentration of the ion is... 

The definition of pH is pH = —log[H+] (which will be modified to include activity later). Ka is the equilibrium constant for the dissociation of an acid HA + H20 H30+ + A-. Kb is the base hydrolysis constant for the reaction B + H20 BH+ + OH. When either Ka or Kb is large, the acid or base is said to be strong otherwise, the acid or base is weak. Common strong acids and bases are listed in Table 6-2, which you should memorize. The most common weak acids are carboxylic acids (RC02H), and the most common weak bases are amines (R3N ). Carboxylate anions (RC02) are weak bases, and ammonium ions (R3NH+) are weak acids. Metal cations also are weak acids. For a conjugate acid-base pair in water, Ka- Kb = Kw. For polyprotic acids, we denote the successive acid dissociation constants as Kal, K, K, , or just Aj, K2, A"3, . For polybasic species, we denote successive hydrolysis constants Kbi, Kb2, A"h3, . For a diprotic system, the relations between successive acid and base equilibrium constants are Afa Kb2 — Kw and K.a Kbl = A w. For a triprotic system the relations are A al KM = ATW, K.d2 Kb2 = ATW, and Ka2 Kb, = Kw. 

Condensation to monohydroxo-bridged complexes is often described by Eq. (28), for which the equilibrium constants Kd are related to those defined by Eq. (27) by Kd = Q2i/Qh, where is the first acid dissociation constant of the mononuclear aqua ion. 

The E1/2 for an electrode reaction of this type is pH dependent. As the pH increases, E1/2 shifts negatively due to decreasing availability of protons. A typical E1/2-pH plot is shown in Figure 3.29. The magnitude of negative shift per pH unit is related to the acid dissociation constants, Ka and Kaj, for the... 

As discussed in Section 3.10.3, in the gas phase the basicity of simple amines follows the order NMe3 > NHMe2 > NH2Me > NH3 because of the electron donating effect of the methyl (Me) groups. In solution, however, we can define a basicity constant as the equilibrium constant for the reaction shown in Equation 3.4. Note it is important to specify temperature, solvent (usually water) and solution ionic strength, 1 Basicity constants are related to the acid dissociation constants (/Q of the base s conjugate acid via the dissociation constant of water, K = 10 14 at 25 °C. Thus Kbx K = Kw. 

A final consideration in the calculation of log Kow is the role of ionization. The reality is that many molecules (especially drugs) contain one, and often more, ionizable functional groups. Methods to calculate log Kow assume that a molecule is uncharged. When a compound with strongly acidic or basic groups is placed in a test environment, it is unlikely to remain in the unionized form calculations may need to take account of this. The degree of ionization is related to the pH of the test system and the intrinsic acid dissociation constant (pKa) of the molecule (see Section IV). 

One can draw a useful analogy between acid-base and oxidation-reduction reactions. Both involve the transfer of a species from a source, the donor, to a sink, the acceptor. The source and sink nomenclature implies that the tendency of the proton (in the case of acids) or of the electron (for reducing agents) to undergo transfer is proportional to the fall in free energy. From the relation AG° = RTIn Ka. you can see that the acid dissociation constant is a measure of the fall in free energy of the proton when it is transferred from a donor HA to the solvent H2O, which represents the reference (zero) free energy level of the proton in aqueous solution. 

It is found that the rate of the nucleophilic attack of imidazole, k is related to its acid dissociation constant, pKi, by the relationship... 

Hence, equation (116) expresses the rate coefficient for proton transfer in terms of the equilibrium constant of the reaction using various parameters fa, WP, and X which relate to the detailed mechanism of the three step reaction (109). It often happens that the overall standard free energy (AG°) or equilibrium constant (K) for the reaction is not known, for example, where rate coefficients have been measured for reaction of a substrate HA of unknown p/fH a with a series of bases B with known pKB h In this case eqn. (116) can be modified to relate the experimental rate coefficient to the acid dissociation constant of the bases (XBH ) by including an unknown constant KHA, the acid dissociation constant of the substrate where K = KH a/Kq h. ... 

A couple of years ago, Kelly et al developed an implicit solvation model for aqueous solutions, related to those we discussed above in section HE. In a more recent work, they tested the model for the calculation of aqueous acid dissociation constants, i.e., the free energy change associated with the reaction... 

The temperature coefiicient of an acid dissociation constant is determined by the enthalpy change of the dissociation reaction, and is given by the thermodynamic relation... 

Green and co-workers 31, 32) have studied the effect of coordination on the acidity of the imino proton in pyridine-2-aldehyde-2-pyridyl-hydrazone and related compounds. The structures, names, and acid dissociation constants for these ligands are shown in Table II. 

That is, the acid dissociation constant and the base dissociation constant are related through the ionic product of water. 

Whether or not A and B represent identical ligands, the products KaKc and KbKa must be equal. The relationship between Ka and Kb or between Kc and Kd depends on whether or not A and B are identical. With complete generality, it can be shown that the thermodynamic acid dissociation constants (K and 2) are related to the microscopic constants by the following expressions ... 

In the context of drug-like substances, hydrophobicity is related to absorption, bioavailability, hydrophobic drug-receptor interactions, metabolism and toxicity. Closely related to log P is the octanol-water distribution coefficient (logDpn), accounting for partition of pH-dependent mixture of ionizable species. Ionization of any compound makes it more water soluble and then less lipophilic. The log D can be calculated from log Pand acid dissociation constant pJC, by the following expression [Cronin, Aptula et al, 2002b Livingstone, 2003] ... 

The other convention relates the basicity of an amine (R3N) to the acid dissociation constant of its conjugate acid (RsNH ) ... 

Fig. 1. The Relation Between the Logarithm of the Acid Dissociation Constant, pKi, in Series of Substituted Fatty Acids, and the Reciprocal of the Number of Carbon Atoms, d, between the Substituent and the Carboxyl Group.

Note it is important to specify temperature, solvent (usually water) and solution ionic strength, /. Basicity constants are related to the acid dissociation constants (KJ of the base s conjugate acid via the dissociation constant of water, = 10 at 25 °C. Thus K xK = K . 

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