Acid dissociation constant, definition

Letting Ka be the acid dissociation constant of the ligand, = c cJcu, which is combined with the definitions Xj = Ci — Ci and Eq. (4-38) to give... 

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. 

The most widely studied physical property of carbanions is their basicity, which of course is a direct measure of the acidity of the parent carbon acid. Carbon acidity measurements date back to the early part of the twentieth century and a myriad of techniques have been employed for the measurements. Although early measurements were only able to provide semiquantitative data, more recent ones have resulted in accurate acidity measurements across a vast range of effective acid dissociation constants, Ka values. This section will begin with a brief description of definitions and methodologies followed by representative data as well as applications of those data. 

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. 

A corresponding modification of equation (44) allows the expression for kjks of A-l reactions to include a correction for the transfer effect. Recalling the definition of K in equation (41) and noting that its reciprocal bears a formal resemblance to the definition of an acid dissociation constant (equation (12)), we may proceed from equation (44) by steps similar to those which led from equation (29) to (94), viz. ... 

Also, recall that the definition of the acid dissociation constant, Ka, is... 

Where Ka is the acid dissociation constant. (Note that the definition of Ka is based on the Bronsted definition.) Values of Ka can vary tremendously (IQis to 10-60). after all anything with at least one proton can be considered an acid under some circumstances with this definition. The common definition of a strong acid is an acid which dissociates completely in a 1 M solution. The common strong acids in aqueous solution, such as sulphuric, nitric and hydrochloric acids have Ka values (for the first dissociation in the case of sulfuric) of 10 to 10. Thus they all dissociate completely (first dissociation only for sulphuric) in aqueous solution, though they wiU have different strengths in some other solvents. Most common organic acids are weak in aqueous solution, having Ka values of lO-s to Note that... 

The Arrhenius Acid-Base Definition The Acid-Dissociation Constant (KJ Relative Strengths of Acids and Bases... 

Acids and bases are essential substances in home, industry, and the environment. In aqueous solution, water combines with the proton released from an acid to form the hydrated species represented by HgO laq). In the Arrhenius definition, acids contain H and yield HaO in water, bases contain OH and yield OH in water, and an acid-base reaction (neutralization) is the reaction of and OH to form HgO. Acid strength depends on [HaO" ] relative to [HA] in aqueous solution. Strong acids dissociate completely and weak acids slightly. The extent of dissociation is expressed by the acid-dissociation constant, K. Weak acids have values ranging from about 10 to 10 . Many acids and bases can be classified qualitatively as strong or weak based on their formulas. 

Because this equation has two unknowns, one of the unknowns must be expressed in terms of the other unknown. Using the definition of the acid dissociation constant (kTa)> we can define [HA] in terms of [A ], A a, and [H ]. 

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. 

By analogy to the definition of pH, we define pK as the negative logarithm of an equilibrium constant. For the acid dissociation constant in Equation 8-4 and the base hydrolysis constant in Equation 8-5, we can write... 

Because the species on either side of this equilibrium are the same, the equilibrium constant for this reaction is identically equal to 1, that is, the for the hydronium ion is exactly 1. Acids that are stronger than the hydronium ion (K > 1) will react completely with water to yield hydronium ion and the conjugate base therefore, they will be strong acids. This gives us a convenient definition of a strong acid as one with an acid dissociation constant greater than unity (in aqueous solution). All such acids will yield identical H30 concentrations in water, independent of their individual values—a phenomenon known as solvent leveling. 

Below are collected some acid-base constants, pK , the negative log of the acidity (dissociation) constant. See Chapter 5 for definitions and forms. First, the pK° values are given, followed by the conditional values at 25° and 0.1 M ionic strength, unless other conditions are stated. 

We start the kinetic analysis with Eq. 9.12, and substitute for RH using Eq. 9.13. Eq. 9.14 gives the kinetic expression for the mechanism of Eq. 9.11, assuming that the equilibrium between R and RH " is completely established. The kinetic expression contains [HsO ], as the definition of specific-acid catalysis implies. Hence, the reaction rate depends upon the pH. The expression also contains the acid dissociation constant (KaRHO of RH , which is an important factor that we will return to below. Note that k, [HsO""], and KaRH are constants during the reaction. Hence, we create a new rate constant, showing that the reaction appears... 

Arrhenius Acid-Base Definition Acid-Dissociation Constant (K,)... 

These are the definitions of the two characteristic dissociation constants normally expressed in terms of p K. When three dissociating groups are present in a molecule there are three piC values, ie, pfC, P 3- knowledge of these piC values is important in the separation or isolation of each amino acid by ion-exchange chromatography. 

Attempts have been made to deduce the structure of the predominant form of a potentially tautomeric compound from the shifts which occur in the ultraviolet spectrum of the compound in question on passing from neutral to basic or acidic solutions. The fact that no bathochromic shifts were observed for 2- and 4-hydroxy quinoline and 1-hydroxyisoquinoline under these conditions was taken as evidence that they existed in the oxo form [similar work on substituted quinol-4-ones led to no definite conclusions ]. A knowledge of the dissociation constants is essential to studies of this type, and the conclusions can, in any case, be only very tentative. A further dif-... 

The preparation of a buffer solution of a definite pH is a simple process once the acid (or base) of appropriate dissociation constant is found smhll variations in pH are obtained by variations in the ratios of the acid to the salt concentration. One example is given in Table 2.2. 

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