Theoretical background
The acid dissociation constant for an acid is a direct consequence of the underlyingDefinitions
According to Arrhenius's original molecular definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion (a proton): Chapter 6: Acid–Base and Donor–Acceptor Chemistry :Equilibrium constant
An acid dissociation constant is a particular example of anCumulative and stepwise constants
A cumulative equilibrium constant, denoted by is related to the product of stepwise constants, denoted by For a dibasic acid the relationship between stepwise and overall constants is as follows :Association and dissociation constants
When discussing the properties of acids it is usual to specify equilibrium constants as acid dissociation constants, denoted by ''K''a, with numerical values given the symbol p''K''a. : On the other hand, association constants are used for bases. : However, general purpose computer programs that are used to derive equilibrium constant values from experimental data use association constants for both acids and bases. Because stability constants for a metal-ligand complex are always specified as association constants, ligand protonation must also be specified as an association reaction. The definitions show that the value of an acid dissociation constant is the reciprocal of the value of the corresponding association constant. : : : Notes # For a given acid or base , the self-ionization constant of water. # The association constant for the formation of a supramolecular complex may be denoted as Ka; in such cases "a" stands for "association", not "acid". # For polyprotic acids, the numbering of stepwise association constants is the reverse of the numbering of the dissociation constants. For example, for phosphoric acid (details in #polyprotic acids, below) ::Temperature dependence
All equilibrium constants vary withDimensionality
In the equation : ''K''a appears to have dimensions of concentration. However, since , the equilibrium constant, , ''cannot'' have a physical dimension. This apparent paradox can be resolved in various ways. # Assume that the quotient of activity coefficients has a numerical value of 1, so that has the same numerical value as the thermodynamic equilibrium constant . # Express each concentration value as the ratio c/c0, where c0 is the concentration in a ypotheticalstandard state, with a numerical value of 1, by definition. # Express the concentrations on the mole fraction scale. Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number. The procedures, (1) and (2), give identical numerical values for an equilibrium constant. Furthermore, since a concentration is simply proportional to mole fraction and density : : and since the molar mass is a constant in dilute solutions, an equilibrium constant value determined using (3) will be simply proportional to the values obtained with (1) and (2). It is common practice inStrong acids and bases
An acid is classified as "strong" when the concentration of its undissociated species is too low to be measured. Any aqueous acid with a p''K''a value of less than 0 is almost completely deprotonated and is considered a ''strong acid''. Sec. 5.1c Strong and weak acids and bases All such acids transfer their protons to water and form the solvent cation species (H3O+ in aqueous solution) so that they all have essentially the same acidity, a phenomenon known as solvent leveling. Sec. 5.2 Solvent leveling They are said to be ''fully dissociated'' in aqueous solution because the amount of undissociated acid, in equilibrium with the dissociation products, is below theMonoprotic acids
After rearranging the expression defining ''K''a, and putting , one obtains : This is thePolyprotic acids
A polyprotic acid is a compound which may lose more than 1 proton. Stepwise dissociation constants are each defined for the loss of a single proton. The constant for dissociation of the first proton may be denoted as ''K''a1 and the constants for dissociation of successive protons as ''K''a2, etc. Phosphoric acid, , is an example of a polyprotic acid as it can lose three protons. : When the difference between successive p''K'' values is about four or more, as in this example, each species may be considered as an acid in its own right; In fact salts of may be crystallised from solution by adjustment of pH to about 5.5 and salts of may be crystallised from solution by adjustment of pH to about 10. The species distribution diagram shows that the concentrations of the two ions are maximum at pH 5.5 and 10. When the difference between successive p''K'' values is less than about four there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. The case of citric acid is shown at the right; solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5. According to Pauling's first rule, successive p''K'' values of a given acid increase . For oxyacids with more than one ionizable hydrogen on the same atom, the p''K''a values often increase by about 5 units for each proton removed, as in the example of phosphoric acid above. It can be seen in the table above that the second proton is removed from a negatively charged species. Since the proton carries a positive charge extra work is needed to remove it. That why p''K''a2 is greater than p''K''a1. p''K''a3 is greater than p''K''a2 because there is further charge separation. When an exception to Pauling's rule is found, it indicates that a major change in structure is also occurring. In the case of (aq), the vanadium is octahedral, 6-coordinate, whereas vanadic acid is tetrahedral, 4-coordinate. This means that four "particles" are released with the first dissociation, but only two "particles" are released with the other dissociations, resulting in a much greater entropy contribution to the standardIsoelectric point
For substances in solution, the isoelectric point (p''I'') is defined as the pH at which the sum, weighted by charge value, of concentrations of positively charged species is equal to the weighted sum of concentrations of negatively charged species. In the case that there is one species of each type, the isoelectric point can be obtained directly from the p''K'' values. Take the example of glycine, defined as AH. There are two dissociation equilibria to consider. :Bases and basicity
The equilibrium constant ''K''b for a base is usually defined as the ''association'' constant for protonation of the base, B, to form the conjugate acid, . :Basicity expressed as dissociation constant of conjugate acid
Because the relationship p''K''b = p''K''w − p''K''a holds only in aqueous solutions (though analogous relationships apply for other amphoteric solvents), subdisciplines of chemistry likeAmphoteric substances
An amphoteric substance is one that can act as an acid or as a base, depending on pH. Water (below) is amphoteric. Another example of an amphoteric molecule is theWater self-ionization
The water molecule may either gain or lose a proton. It is said to beAcidity in nonaqueous solutions
A solvent will be more likely to promote ionization of a dissolved acidic molecule in the following circumstances: # It is a protic solvent, capable of forming hydrogen bonds. # It has a high donor number, making it a strongMixed solvents
When a compound has limited solubility in water it is common practice (in the pharmaceutical industry, for example) to determine p''K''a values in a solvent mixture such as water/ dioxane or water/Factors that affect p''K''a values
Pauling's second rule is that the value of the first p''K''a for acids of the formula XO''m''(OH)''n'' depends primarily on the number of oxo groups ''m'', and is approximately independent of the number of hydroxy groups ''n'', and also of the central atom X. Approximate values of p''K''a are 8 for ''m'' = 0, 2 for ''m'' = 1, −3 for ''m'' = 2 and < −10 for ''m'' = 3. Alternatively, various numerical formulas have been proposed including p''K''a = 8 − 5''m'' (known as Bell's rule), p''K''a = 7 − 5''m'',Douglas B., McDaniel D.H. and Alexander J.J. ''Concepts and Models of Inorganic Chemistry'' (2nd ed. Wiley 1983) p.526 or p''K''a = 9 − 7''m''. The dependence on ''m'' correlates with the oxidation state of the central atom, X: the higher the oxidation state the stronger the oxyacid. For example, p''K''a for HClO is 7.2, for HClO2 is 2.0, for HClO3 is −1 and HClO4 is a strong acid (). The increased acidity on adding an oxo group is due to stabilization of the conjugate base by delocalization of its negative charge over an additional oxygen atom. This rule can help assign molecular structure: for example, phosphorous acid (H3PO3) has a p''K''a near 2, which suggested that the structure is HPO(OH)2, as later confirmed byThermodynamics
An equilibrium constant is related to the standard Gibbs energy change for the reaction, so for an acid dissociation constant : . ''R'' is the gas constant and ''T'' is theExperimental determination
The experimental determination of p''K''a values is commonly performed by means of titrations, in a medium of high ionic strength and at constant temperature. A typical procedure would be as follows. A solution of the compound in the medium is acidified with a strong acid to the point where the compound is fully protonated. The solution is then titrated with a strong base until all the protons have been removed. At each point in the titration pH is measured using a glass electrode and a pH meter. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method ofMicro-constants
For some molecules, dissociation (or association) can occur at more than one nonequivalent site, and the observed macroscopic equilibrium constant or macroconstant is a combination of microconstants involving distinct species. When one reactant forms two products in parallel, the macroconstant is a sum of two microconstants, This is true for example for the deprotonation of theApplications and significance
A knowledge of p''K''a values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist inValues for common substances
There are multiple techniques to determine the p''K''a of a chemical, leading to some discrepancies between different sources. Well measured values are typically within 0.1 units of each other. Data presented here were taken at 25 °C in water. Chapter 8 More values can be found in theSee also
*Notes
References
Further reading
* (Previous edition published as ) * * (Non-aqueous solvents) * (translation editor: Mary R. Masson) * * Chapter 4: Solvent Effects on the Position of Homogeneous Chemical Equilibria. *External links