Dissociation equilibrium constant definition

In addition, the equilibria on the left hand side of eqn (8.20) can sometimes be defined by the dissociation constants Kdissj (j = 1, 2,. .., m), that are very familiar from acid-base reactions (the acidity constants Kgj for polyprotic acids are in fact dissociation equilibrium constants). The relationships between all these constants are given by the sets of eqn (8.21). In certain cases, it is more convenient to use one type of equilibrium constants or another, and the choice is typically made based on the simplicity of the mathematical equations describing a system of interest. Definitions and uses of all equilibrium constants in determination of concentrations of all species present in a complex system are given in many monographs on coordination chemistry. ... 

Shuman and Michael [10] applied a rotating disk electrode to the measurement of copper complex dissociation rate constants in marine coastal waters. An operational definition for labile and non-labile metal complexes was established on kinetic criteria. Samples collected off the mid-Atlantic coast of USA showed varying degrees of copper chelation. It is suggested that the technique should be useful for metal toxicity studies because of its ability to measure both equilibrium concentrations and kinetic availability of soluble metal. 

The equilibrium constant and dissociation rate constant were determined simultaneously by non-linear least-squares fitting, unless the absorption signal was too low157 or no dependence of relaxation frequency on concentration was observed.159,161,162 The association rate constant was then calculated from the definition of the equilibrium constant. The equilibrium constants determined from the dynamics in this manner agree fairly well with equilibrium constants determined independently. 

This technique was employed to study the binding dynamics of Pyronine Y (31) and B (32) with /)-CD/ s The theoretical background for this particular system has been discussed with the description of the technique above. Separate analysis of the individual correlation curves obtained was difficult since the diffusion time for the complex could not be determined directly because, even at the highest concentration of CD employed, about 20% of the guest molecules were still free in solution. The curves were therefore analyzed using global analysis to obtain the dissociation rate constant for the 1 1 complex (Table 12). The association rate constant was then calculated from the definition of the equilibrium constant. 

One could go on with examples such as the use of a shirt rather than sand reduce the silt content of drinking water or the use of a net to separate fish from their native waters. Rather than that perhaps we should rely on the definition of a chemical equilibrium and its presence or absence. Chemical equilibria are dynamic with only the illusion of static state. Acetic acid dissociates in water to acetate-ion and hydrated hydrogen ion. At any instant, however, there is an acid molecule formed by recombination of acid anion and a proton cation while another acid molecule dissociates. The equilibrium constant is based on a dynamic process. Ordinary filtration is not an equilibrium process nor is it the case of crystals plucked from under a microscope into a waiting vial. 

With the assumptions, just given, division of (7a) and (7b) leads to a simple definition (8) of an apparent constant for the dissociation of TS-cat into TS and catalyst. Obviously, KTS is a woW-equilibrium constant, since... 

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. 

Common strong acids and bases are listed in Table 6-2, which you need to memorize. By definition, a strong acid or base is completely dissociated in aqueous solution. That is, the equilibrium constants for the following reactions are large. 

The equilibrium constant is called Ka, the acid dissociation constant. By definition, a weak acid is one that is only partially dissociated in water. This definition means that Ka is small for a weak acid. 

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. 

Typical values of pK[nt and pfor a humic acid are 2.67 and 4.46. The introduction of the electrostatic factor into the equilibrium constant is analogous to the coulombic term used in the definition of the intrinsic surface complexation constants. In addition another binding site (WAH) is recognised which is thought to behave as a weak acidic phenolic functional group. Although this site does not contribute to the titratable acidity and, therefore, no pK is needed for proton dissociation, it is involved in metal complexation reactions. The total number of the three monoprotic sites is estimated from titratable acidity and then paired to represent the humic substance as a discrete non-interacting mixture of three dipro-tic acids, which act as the metal complexation sites. The three sites are... 

Before discussing how acidity is measured, the definition of the equilibrium constant should be reviewed. Referring to Scheme 2.1, illustrating that an acid is in equilibrium with its dissociated ions, the degree of this dissociation as compared to the undissociated acid is measured according to its equilibrium constant (Kcgeneral chemistry coursework, we remember that Keq is the product of the ion concentrations divided by the concentration of the undissociated acid (Fig. 2.3). 

Because of the minus sign in this definition, the lower the pf, the larger the equilibrium constant, 2Ca, is and hence the stronger the acid. The pKa of the acid is the pH where it is exactly half dissociated. At pHs above the pfCa, the acid HA exists as A in water at pHs below the plCa, it exists as undissociated HA. 

Dissociation constants, which are chemical equilibrium constants for dissolution of acids, are defined in a manner similar to the definition of pH in the case of water. As discussed before, a weak acid such as H3PO4 goes through step-by-step ionization in water given by Eqs. 4.7-4.9. In each step, the dissociation constant is experimentally found to be... 

By assuming a definite formula for the polybromide attempts have been made to show that the relative proportions of the substance concerned in the reaction are in accord with the law of mass action. For example, with the polybromide KBr.nBrg of cone. 0, where the dissociation products are KBr of cone, and of cone. C2, the equilibrium condition is that KC=CiC, where K is the equilibrium constant. If the soln. are sat. with bromine, and the cone, of the free bromine in the soln. is constant, meaning that the cone, of the polybromide is proportional to the... 

The effect of tautomerism on the observed dissociation constant of an acid is to ihtroduce a complicating reaction whose equilibrium is established in addition to that of the dissociation. The measured equilibrium constant involves the sum of concentrations of tautomers in place of concentrations of definite compounds. Structural changes... 

The actual composition of the ternary compound is not known definitely, and has, therefore, been given in the simplest form, but even if different numbers of the reacting molecules were contained in it, the same principles and relations may be applied although the equations would be much more complicated. The relative velocities of the dissociation of the intermediate compound would determine which products are observed at any time, if the complete reaction has not been allowed to come to equilibrium. It is perhaps more usual to speak of the velocities of the various reactions than of the values of their equilibrium constants. 

The intensity decrease is clearly hyperbolic and therefore a mathematical binding analysis can be performed using the following quadratic equation obtained from the definition of the equilibrium constant (assuming all binding sites have the same dissociation constant Ka) ... 

In these equations, k or k2 refer to the rate or equilibrium constant for the unsubstituted molecule, p characterizes the sensitivity of the reaction to electronic substituent effects, and a is the relative electronic effect of the substituent. A substituent at the meta position has a different a value than that of the same substituent at the para position. By definition, p = 1.0 for the pi a of substituted benzoic acids and a is the substituent effect on this reaction. As an example, Figure 3.1 shows the relationship between Hammett a and the log of the acid dissociation constant (log Kf of metu-substituted phenols. The correlation coefficient of this relationship is 0.97. The data is presented in Table 3.1. 

Because of the minus sign in the definition (it s there too in the definition of pH) the lower the pfCj the larger the equilibrium constant and the stronger the acid. You may find the way we introduced pK more helpful as a concept for visualizing pK any acid is half dissociated in a solution whose pH matches the acid s pK. At a pH above the pK the acid exists largely as its conjugate base (A") but at a pH below the pK the acid largely exists as HA. 

The following entry defines the commonly used stability constants (stepwise, overall, conditional, association, dissociation, and pK) and relates the values to a rigorous thermodynamic definition of equilibrium constants. In addition, the article briefly outlines experimental techniques (potentiometric titration, spectroscopic methods involving ultraviolet/visible, infrared, Raman, fluorescence. and nuclear magnetic resonance spectroscopy), together with the numerical methods and computer programs that can be used to derive stability constants from such experimental data. 

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