“Acid dissociation constant”的意思、由来-开放百科全书

An acid dissociation constant, K_a, (also known as acidity constant, or acid-ionization constant) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid–base reactions.^[1]

The chemical species HA, A⁻, and H⁺ are said to be in equilibrium when their concentrations (written above in square brackets) do not change with the passing of time, because both forward and backward reactions are occurring at the same very fast rate.^[2]

where HA is a generic acid that dissociates into A⁻, the conjugate base of the acid and a hydrogen ion, H⁺. It is implicit in this definition that the quotient of activity coefficients, Γ,

is a constant that can be ignored in a given set of experimental conditions.^[3]

For many practical purposes it is more convenient to discuss the logarithmic constant, pK_a

The more positive the value of pK_a, the smaller the extent of dissociation at any given pH (see Henderson–Hasselbalch equation)—that is, the weaker the acid. A weak acid has a pK_a value in the approximate range −2 to 12 in water.

For a buffer solution consisting of a weak acid and its conjugate base, pK_a can be expressed as:

The pK_a for a weak monoprotic acid is conveniently determined by potentiometric titration with a strong base to the equivalence point (neutralization point) and taking the pH value measured at one-half this volume (the so-called midpoint of the titration) as being equal to pK_a. That is because at this half equivalence point, the number of moles of strong base added is one-half the number of moles of weak acid originally present, while the concentrations of the conjugate base and the remaining weak acid are the same; the term in parenthesis is thus equal to unity.

Acids with a pK_a value of less than about −2 are said to be strong acids. In water, the dissociation of a strong acid in dilute solutions is effectively (but not exactly) complete such that the final concentration of the undissociated acid [HA]_final is extremely low. Consider a strong monoprotic acid, such as HCl (K_a = 1x10⁷). Because of their 1:1 ratio, the final concentration of the conjugate base, [Cl^-]_final, is taken to be equal to the concentration of the hydronium ion [H₃O⁺], which can be directly measured by a pH meter. For strong monoprotic acids like HCl, [A^-]_final and [H₃O⁺] are both very nearly equal to the initial concentration of [HA]_initial placed into solution (before dissociation occurs). Unfortunately, with conventional acid-base titration methods it is difficult to measure the pH of a strong acid solution and, hence, to determine the [H₃O⁺] or [A^-]_final, with a sufficient number of significant figures (most pH meters cannot resolve past three decimal places, or one-one thousandth of a pH unit) to accurately and precisely compute the extremely low values encountered for [HA]_final ([HA]_final = [HA]_initial - [H₃O⁺]), which can be as low as 10^-9 mol per liter for some strong acids. Furthermore, if exactly 100% dissociation is assumed, [HA]_final is exactly zero and the fraction within parenthesis in the equation above becomes undefined. Because the second expression on the right-hand side of the above equation is therefore indeterminable by conventional titration methods, the entire equation is not generally as useful a means of experimentally measuring pK_a for strong acids as it is for weak acids.

However, pK_a and/or K_a values for strong acids can be estimated by theoretical means, such as computing gas phase dissociation constants and using Gibbs free energies of solvation for the molecular anions.^[5] It is also possible to use spectroscopy in some cases to determine the ratio of the concentrations of the conjugate base produced and the undissociated acid. For example, the Raman spectra of dilute nitric acid (HNO₃) solutions contain signals of the nitrate ion (NO₃^-, the conjugate base) and as the solutions become more concentrated signals of undissociated nitric acid molecules also emerge.^[6]

Theoretical background

The acid dissociation constant for an acid is a direct consequence of the underlying thermodynamics of the dissociation reaction; the pK_a value is directly proportional to the standard Gibbs free energy change for the reaction. The value of the pK_a changes with temperature and can be understood qualitatively based on Le Châtelier's principle: when the reaction is endothermic, K_a increases and pK_a decreases with increasing temperature; the opposite is true for exothermic reactions.

The value of pK_a also depends on molecular structure of the acid in many ways. For example, Pauling proposed two rules: one for successive pK_a of polyprotic acids (see Polyprotic acids below), and one to estimate the pK_a of oxyacids based on the number of =O and −OH groups (see Factors that affect pK_a values below). Other structural factors that influence the magnitude of the acid dissociation constant include inductive effects, mesomeric effects, and hydrogen bonding. Hammett type equations have frequently been applied to the estimation of pK_a.^[7]^[8]

The quantitative behaviour of acids and bases in solution can be understood only if their pK_a values are known. In particular, the pH of a solution can be predicted when the analytical concentration and pK_a values of all acids and bases are known; conversely, it is possible to calculate the equilibrium concentration of the acids and bases in solution when the pH is known. These calculations find application in many different areas of chemistry, biology, medicine, and geology. For example, many compounds used for medication are weak acids or bases, and a knowledge of the pK_a values, together with the water–octanol partition coefficient, can be used for estimating the extent to which the compound enters the blood stream. Acid dissociation constants are also essential in aquatic chemistry and chemical oceanography, where the acidity of water plays a fundamental role. In living organisms, acid–base homeostasis and enzyme kinetics are dependent on the pK_a values of the many acids and bases present in the cell and in the body. In chemistry, a knowledge of pK_a values is necessary for the preparation of buffer solutions and is also a prerequisite for a quantitative understanding of the interaction between acids or bases and metal ions to form complexes. Experimentally, pK_a values can be determined by potentiometric (pH) titration, but for values of pK_a less than about 2 or more than about 11, spectrophotometric or NMR measurements may be required due to practical difficulties with pH measurements.

Definitions

According to Arrhenius's original definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion H⁺ (a proton):^[9]

The equilibrium constant for this dissociation reaction is known as a dissociation constant. The liberated proton combines with a water molecule to give a hydronium (or oxonium) ion H₃O⁺ (naked protons do not exist in solution), and so Arrhenius later proposed that the dissociation should be written as an acid–base reaction:

The acid loses a proton, leaving a conjugate base; the proton is transferred to the base, creating a conjugate acid. For aqueous solutions of an acid HA, the base is water; the conjugate base is A⁻ and the conjugate acid is the hydronium ion. The Brønsted–Lowry definition applies to other solvents, such as dimethyl sulfoxide: the solvent S acts as a base, accepting a proton and forming the conjugate acid SH⁺.

In solution chemistry, it is common to use H⁺ as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution H⁺ denotes a solvated hydronium ion rather than a proton.^[13]^[14]

The designation of an acid or base as "conjugate" depends on the context. The conjugate acid BH⁺ of a base B dissociates according to

The hydroxide ion OH⁻, a well known base, is here acting as the conjugate base of the acid water. Acids and bases are thus regarded simply as donors and acceptors of protons respectively.

A broader definition of acid dissociation includes hydrolysis, in which protons are produced by the splitting of water molecules. For example, boric acid (B(OH)₃) produces H₃O⁺ as if it were a proton donor,^[15] but it has been confirmed by Raman spectroscopy that this is due to the hydrolysis equilibrium:^[15]

Similarly, metal ion hydrolysis causes ions such as [Al(H₂O)₆]³⁺ to behave as weak acids:^[16]

According to Lewis's original definition, an acid is a substance that accepts an electron pair to form a coordinate covalent bond.^[17]

Equilibrium constant

An acid dissociation constant is a particular example of an equilibrium constant. For the specific equilibrium between a monoprotic acid, HA and its conjugate base A⁻, in water,

the thermodynamic equilibrium constant, {{tmath|K^\\ominus}} can be defined by^[18]

where {A} is the activity of the chemical species A, etc. {{tmath|K^\\ominus}} is dimensionless since activity is dimensionless. Activities of the products of dissociation are placed in the numerator, activities of the reactants are placed in the denominator. See activity coefficient for a derivation of this expression.

Since activity is the product of concentration and activity coefficient (γ) the definition could also be written as

where [HA] represents the concentration of HA and Γ is a quotient of activity coefficients.

To avoid the complications involved in using activities, dissociation constants are determined, where possible, in a medium of high ionic strength, that is, under conditions in which Γ can be assumed to be always constant.^[18] For example, the medium might be a solution of 0.1 molar (M) sodium nitrate or 3 M potassium perchlorate. Furthermore, in all but the most concentrated solutions it can be assumed that the concentration of water, [H₂O], is constant, approximately 55 M. On dividing {{tmath|K^\\ominus}} by the constant terms and writing [H⁺] for the concentration of the hydronium ion the expression

is obtained. This is the definition in common use.^[19] pK_a is defined as −log₁₀(K_a).

Note, however, that all published dissociation constant values refer to the specific ionic medium used in their determination and that different values are obtained with different conditions, as shown for acetic acid in the illustration above. When published constants refer to an ionic strength other than the one required for a particular application, they may be adjusted by means of specific ion theory (SIT) and other theories.^[20]

Using the equation as shown K_a has dimensions of concentration, but the exact definition uses chemical activities, which can be dimensionless. Therefore, K_a, as defined properly, is also dimensionless. But as defined here it is correct to quote a value with a dimension as, for example, "K_a = 300 M".

Monoprotic acids

After rearranging the expression defining K_a, and putting {{nowrap|pH {{=}} −log₁₀[H⁺]}}, one obtains^[21]

This is the Henderson–Hasselbalch equation, from which the following conclusions can be drawn.

In water, measurable pK_a values range from about −2 for a strong acid to about 12 for a very weak acid (or strong base).

A buffer solution of a desired pH can be prepared as a mixture of a weak acid and its conjugate base. In practice the mixture can be created by dissolving the acid in water, and adding the requisite amount of strong acid or base. When the pK_a and analytical concentration of the acid are known, the extent of dissociation and pH of a solution of a monoprotic acid can be easily calculated using an ICE table.

Strong acids and bases

An acid is classified as "strong" when the concentration of its undissociated species is too low to be measured, as the equilibrium is shifted very far to the right (in the forward direction) because of a very large K_a. Any acid with a pK_a value of less than −2 is more than 99.9% dissociated at low pH. This is known as solvent leveling since all such acids are "fully dissociated", regardless of their pK_a values. Hydrochloric acid, HCl, which has a pK_a value, estimated from thermodynamic quantities, of −9.3 in water is an example of a strong acid^†.^[22] It is said to be fully dissociated in aqueous solution because the amount of undissociated acid, in equilibrium with the dissociation products, is below the detection limit.

Likewise, any base with a pK_a value larger than about 12 is more than 99% dissociated in solution, even in strongly alkaline conditions, and is classified as a strong base.^[11]

^†In dilute solution nitric acid (pK_a = −1.4^[23]) behaves as a strong acid. When the ratio of water molecules to acid molecules in a solution of an acid is too small to fully solvate the dissociation products, dissociation is not complete, for example, with extremely concentrated solutions of sulphuric acid and hydrochloric acid.

Polyprotic acids

Polyprotic acids are acids that can lose more than one 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, H₃PO₄, is an example of a polyprotic acid as it can lose three protons.

When the difference between successive pK values is about four or more, as in this example, each species may be considered as an acid in its own right;^[25] In fact salts of {{chem|H|2|PO|4|−}} may be crystallised from solution by adjustment of pH to about 5.5 and salts of {{chem|HPO|4|2−}} 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 pK 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 pK values of a given acid increase (pK_a2 > pK_a1).^[26] For oxyacids with more than one ionizable hydrogen on the same atom, the pK_a values often increase by about 5 units for each proton removed,^[27]^[28] as in the example of phosphoric acid above.

it can be seen 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 is the cause of the trend noted above. Phosphoric acid values (above) illustrate this rule, as do the values for vanadic acid, H₃VO₄. When an exception to the rule is found it indicates that a major change in structure is occurring. In the case of VO₂⁺ (aq), the vanadium is octahedral, 6-coordinate, whereas vanadic acid is tetrahedral, 4-coordinate. This is the basis for an explanation of why pK_a1 > pK_a2 for vanadium(V) oxoacids.

Isoelectric point

For substances in solution the isoelectric point (pI) 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 pK values. Take the example of glycine, defined as AH. There are two dissociation equilibria to consider.

At the isoelectric point the concentration of the positively charged species, AH₂⁺, is equal to the concentration of the negatively charged species, A⁻, so

pI values for amino acids are listed at Proteinogenic amino acid#Chemical properties. When more than two charged species are in equilibrium with each other a full speciation calculation may be needed.

Water self-ionization

Water possesses both acidic and basic properties and is said to be amphiprotic. The ionization equilibrium can be written

where in aqueous solution H⁺ or H⁺(aq) denotes a solvated proton. Often this is written as the hydronium ion H₃O⁺, but this formula is not exact because in fact there is solvation by more than one water molecule and species such as H₅O₂⁺, H₇O₃⁺ and H₉O₄⁺ are also present.^[29]

When, as is usually the case, the concentration of water can be assumed to be constant, this expression may be replaced by

The self-ionization constant of water, K_w, is thus just a special case of an acid dissociation constant. A logarithmic form analogous to pK_a may also be defined

From this equation, pK_w = 14 at 24.87 °C. At that temperature both hydrogen and hydroxide ions have a concentration of 10⁻⁷ M.

Protonation constants

The dissociation of a monoprotic acid can also be described as the protonation of the conjugate base of the acid

This leads to the definition of an association (protonation) constant, denoted here as K_association, as

The definitions show that the values of the two constants are reciprocals of each other and

The situation is a little more complicated with polybasic acids. For example, with phosphoric acid

Amphoteric substances

An amphoteric substance is one that can act as an acid or as a base, depending on pH. Water (above) is amphoteric. Another example of an amphoteric molecule is the bicarbonate ion {{chem|HCO|3|−}} that is the conjugate base of the carbonic acid molecule H₂CO₃ in the equilibrium

but also the conjugate acid of the carbonate ion {{chem|CO|3|2−}} in (the reverse of) the equilibrium

Carbonic acid equilibria are important for acid–base homeostasis in the human body.

An amino acid is also amphoteric with the added complication that the neutral molecule is subject to an internal acid–base equilibrium in which the basic amino group attracts and binds the proton from the acidic carboxyl group, forming a zwitterion.

At pH less than about 5 both the carboxylate group and the amino group are protonated. As pH increases the acid dissociates according to

Thus the zwitterion, {{chem|NH|3|+|CHRCO|2|−}}, is amphoteric because it may either be protonated or deprotonated.

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, HB⁺.

K_b is related to K_a for the conjugate acid. In water, the concentration of the hydroxide ion, [OH⁻], is related to the concentration of the hydrogen ion by K_w = [H⁺][OH⁻], therefore

When K_a, K_b and K_w are determined under the same conditions of temperature and ionic strength, it follows, taking cologarithms, that pK_b = pK_w − pK_a. In aqueous solutions at 25 °C, pK_w is 13.9965,^[31] so

with sufficient accuracy for most practical purposes. In effect there is no need to define pK_b separately from pK_a, but it is done here as often only pK_b values can be found in the older literature.

For metal hydroxides K_b can also be defined as the dissociation constant for loss of a hydroxide ion: {{nowrap|B(OH) {{eqm}} B⁺ + OH⁻}} or {{nowrap|B(OH)₂ {{eqm}} B(OH)⁺ + OH⁻}}.^[32] This is the reciprocal of a stability constant for formation of the complex.

Because the relationship pK_b = pK_w − pK_a holds only in aqueous solutions (though analogous relationships apply for other solvents), subdisciplines of chemistry like organic chemistry that usually deal with nonaqueous solutions generally do not use pK_b as a measure of basicity. Instead, the pK_a of the conjugate acid, denoted by pK_aH, is quoted when basicity needs to be quantified. A higher value for pK_aH corresponds to a stronger base. For example, the values pK_aH(C₅H₅N) = 5.25 and pK_aH((CH₃CH₂)₃N) = 10.75 indicate that triethylamine is a stronger base than pyridine.

Temperature dependence

All equilibrium constants vary with temperature according to the van 't Hoff equation^[33]

R is the gas constant and T is the absolute temperature . Thus, for exothermic reactions, (the standard enthalpy change, {{tmath|\\Delta H^\\ominus}}, is negative) K decreases with temperature, but for endothermic reactions ({{tmath|\\Delta H^\\ominus}} is positive) K increases with temperature.

The standard enthalpy change for a reaction is itself a function of temperature, according to Kirchhoff's law of thermochemistry:

where ΔC_p is the heat capacity change at constant pressure. In practice {{tmath|\\Delta H^\\ominus}} may be taken to be constant over a small temperature range.

Acidity in nonaqueous solutions

A solvent will be more likely to promote ionization of a dissolved acidic molecule in the following circumstances:^[34]

pK_a values of organic compounds are often obtained using the aprotic solvents dimethyl sulfoxide (DMSO)^[34] and acetonitrile (ACN).^[35]

DMSO is widely used as an alternative to water because it has a lower dielectric constant than water, and is less polar and so dissolves non-polar, hydrophobic substances more easily. It has a measurable pK_a range of about 1 to 30. Acetonitrile is less basic than DMSO, and, so, in general, acids are weaker and bases are stronger in this solvent. Some pK_a values at 25 °C for acetonitrile (ACN)^[36]^[37]^[38] and dimethyl sulfoxide (DMSO)^[39] are shown in the following tables. Values for water are included for comparison.

Ionization of acids is less in an acidic solvent than in water. For example, hydrogen chloride is a weak acid when dissolved in acetic acid. This is because acetic acid is a much weaker base than water.

Compare this reaction with what happens when acetic acid is dissolved in the more acidic solvent pure sulfuric acid^[40]

The unlikely geminal diol species {{chem|CH|3|C(OH)|2|+}} is stable in these environments. For aqueous solutions the pH scale is the most convenient acidity function.^[41] Other acidity functions have been proposed for non-aqueous media, the most notable being the Hammett acidity function, H₀, for superacid media and its modified version H₋ for superbasic media.^[42]

In aprotic solvents, oligomers, such as the well-known acetic acid dimer, may be formed by hydrogen bonding. An acid may also form hydrogen bonds to its conjugate base. This process, known as homoconjugation, has the effect of enhancing the acidity of acids, lowering their effective pK_a values, by stabilizing the conjugate base. Homoconjugation enhances the proton-donating power of toluenesulfonic acid in acetonitrile solution by a factor of nearly 800.^[43]

In aqueous solutions, homoconjugation does not occur, because water forms stronger hydrogen bonds to the conjugate base than does the acid.

Mixed solvents

When a compound has limited solubility in water it is common practice (in the pharmaceutical industry, for example) to determine pK_a values in a solvent mixture such as water/dioxane or water/methanol, in which the compound is more soluble.^[45] In the example shown at the right, the pK_a value rises steeply with increasing percentage of dioxane as the dielectric constant of the mixture is decreasing.

A pK_a value obtained in a mixed solvent cannot be used directly for aqueous solutions. The reason for this is that when the solvent is in its standard state its activity is defined as one. For example, the standard state of water:dioxane mixture with 9:1 mixing ratio is precisely that solvent mixture, with no added solutes. To obtain the pK_a value for use with aqueous solutions it has to be extrapolated to zero co-solvent concentration from values obtained from various co-solvent mixtures.

These facts are obscured by the omission of the solvent from the expression that is normally used to define pK_a, but pK_a values obtained in a given mixed solvent can be compared to each other, giving relative acid strengths. The same is true of pK_a values obtained in a particular non-aqueous solvent such a DMSO.

As of 2008, a universal, solvent-independent, scale for acid dissociation constants has not been developed, since there is no known way to compare the standard states of two different solvents.

Factors that affect pK_a values

Pauling's second rule is that the value of the first pK_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 pK_a are 8 for m = 0, 2 for m = 1, −3 for m = 2 and < −10 for m = 3.^[26] Alternatively, various numerical formulas have been proposed including pK_a = 8 − 5m (known as Bell's rule),^[27]^[46] pK_a = 7 − 5m,^[28]^[47] or pK_a = 9 − 7m.^[27] 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, pK_a for HClO is 7.2, for HClO₂ is 2.0, for HClO₃ is −1 and HClO₄ is a strong acid ({{nowrap|pK_a ≪ 0}}).^[11] 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.^[46] This rule can help assign molecular structure: for example phosphorous acid (H₃PO₃) has a pK_a near 2 suggested that the structure is HPO(OH)₂, as later confirmed by NMR spectroscopy, and not P(OH)₃ which would be expected to have a pK_a near 8.^[47]

With organic acids inductive effects and mesomeric effects affect the pK_a values. A simple example is provided by the effect of replacing the hydrogen atoms in acetic acid by the more electronegative chlorine atom. The electron-withdrawing effect of the substituent makes ionisation easier, so successive pK_a values decrease in the series 4.7, 2.8, 1.4, and 0.7 when 0, 1, 2, or 3 chlorine atoms are present.^[48] The Hammett equation, provides a general expression for the effect of substituents.^[49]

Alcohols do not normally behave as acids in water, but the presence of a double bond adjacent to the OH group can substantially decrease the pK_a by the mechanism of keto–enol tautomerism. Ascorbic acid is an example of this effect. The diketone 2,4-pentanedione (acetylacetone) is also a weak acid because of the keto–enol equilibrium. In aromatic compounds, such as phenol, which have an OH substituent, conjugation with the aromatic ring as a whole greatly increases the stability of the deprotonated form.

Structural effects can also be important. The difference between fumaric acid and maleic acid is a classic example. Fumaric acid is (E)-1,4-but-2-enedioic acid, a trans isomer, whereas maleic acid is the corresponding cis isomer, i.e. (Z)-1,4-but-2-enedioic acid (see cis-trans isomerism). Fumaric acid has pK_a values of approximately 3.0 and 4.5. By contrast, maleic acid has pK_a values of approximately 1.5 and 6.5. The reason for this large difference is that when one proton is removed from the cis isomer (maleic acid) a strong intramolecular hydrogen bond is formed with the nearby remaining carboxyl group. This favors the formation of the maleate H⁺, and it opposes the removal of the second proton from that species. In the trans isomer, the two carboxyl groups are always far apart, so hydrogen bonding is not observed.^[53]

Effects of the solvent and solvation should be mentioned also in this section. It turns out, these influences are more subtle than that of a dielectric medium mentioned above. For example, the expected (by electronic effects of methyl substituents) and observed in gas phase order of basicity of methylamines, Me₃N > Me₂NH > MeNH₂ > NH₃, is changed by water to Me₂NH > MeNH₂ > Me₃N > NH₃. Neutral methylamine molecules are hydrogen-bonded to water molecules mainly through one acceptor, N–HOH, interaction and only occasionally just one more donor bond, NH–OH₂. Hence, methylamines are stabilized to about the same extent by hydration, regardless of the number of methyl groups. In stark contrast, corresponding methylammonium cations always utilize all the available protons for donor NH–OH₂ bonding. Relative stabilization of methylammonium ions thus decreases with the number of methyl groups explaining the order of water basicity of methylamines.^[8]

Thermodynamics

An equilibrium constant is related to the standard Gibbs energy change for the reaction, so for an acid dissociation constant

The standard enthalpy change can be determined by calorimetry or by using the van 't Hoff equation, though the calorimetric method is preferable. When both the standard enthalpy change and acid dissociation constant have been determined, the standard entropy change is easily calculated from the equation above. In the following table, the entropy terms are calculated from the experimental values of pK_a and ΔH{{sup|⊖}}. The data were critically selected and refer to 25 °C and zero ionic strength, in water.^[56]

The first point to note is that, when pK_a is positive, the standard free energy change for the dissociation reaction is also positive. Second, some reactions are exothermic and some are endothermic, but, when ΔH{{sup|⊖}} is negative TΔS{{sup|⊖}} is the dominant factor, which determines that ΔG{{sup|⊖}} is positive. Last, the entropy contribution is always unfavourable ({{nowrap|ΔS{{sup|⊖}} < 0}}) in these reactions. Ions in aqueous solution tend to orient the surrounding water molecules, which orders the solution and decreases the entropy. The contribution of an ion to the entropy is the partial molar entropy which is often negative, especially for small or highly charged ions.^[57] The ionization of a neutral acid involves formation of two ions so that the entropy decreases ({{nowrap|ΔS{{sup|⊖}} < 0}}). On the second ionization of the same acid, there are now three ions and the anion has a charge, so the entropy again decreases.

Note that the standard free energy change for the reaction is for the changes from the reactants in their standard states to the products in their standard states. The free energy change at equilibrium is zero since the chemical potentials of reactants and products are equal at equilibrium.

Experimental determination

The experimental determination of pK_a values is commonly performed by means of titrations, in a medium of high ionic strength and at constant temperature.^[58] 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 of least squares.^[59]

The total volume of added strong base should be small compared to the initial volume of titrand solution in order to keep the ionic strength nearly constant. This will ensure that pK_a remains invariant during the titration.

A calculated titration curve for oxalic acid is shown at the right. Oxalic acid has pK_a values of 1.27 and 4.27. Therefore, the buffer regions will be centered at about pH 1.3 and pH 4.3. The buffer regions carry the information necessary to get the pK_a values as the concentrations of acid and conjugate base change along a buffer region.

Between the two buffer regions there is an end-point, or equivalence point, at about pH 3. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount: pK_a2 − pK_a1 is about three in this example. (If the difference in pK values were about two or less, the end-point would not be noticeable.) The second end-point begins at about pH 6.3 and is sharp. This indicates that all the protons have been removed. When this is so, the solution is not buffered and the pH rises steeply on addition of a small amount of strong base. However, the pH does not continue to rise indefinitely. A new buffer region begins at about pH 11 (pK_w − 3), which is where self-ionization of water becomes important.

It is very difficult to measure pH values of less than two in aqueous solution with a glass electrode, because the Nernst equation breaks down at such low pH values. To determine pK values of less than about 2 or more than about 11 spectrophotometric^[60]

or NMR^[19]^[62] measurements may be used instead of, or combined with, pH measurements.

When the glass electrode cannot be employed, as with non-aqueous solutions, spectrophotometric methods are frequently used.^[37] These may involve absorbance or fluorescence measurements. In both cases the measured quantity is assumed to be proportional to the sum of contributions from each photo-active species; with absorbance measurements the Beer-Lambert law is assumed to apply.

Isothermal titration calorimetry (ITC) may be used to determine both a pK value and the corresponding standard enthalpy for acid dissociation.^[63] Software to perform the calculations is supplied by the instrument manufacturers for simple systems.

Aqueous solutions with normal water cannot be used for ¹H NMR measurements but heavy water, D₂O, must be used instead. ¹³C NMR data, however, can be used with normal water and ¹H NMR spectra can be used with non-aqueous media. The quantities measured with NMR are time-averaged chemical shifts, as proton exchange is fast on the NMR time-scale. Other chemical shifts, such as those of ³¹P can be measured.

Micro-constants

A base such as spermine has a few different sites where protonation can occur. In this example the first proton can go on the terminal –NH₂ group, or either of the internal –NH– groups. The pK_a values for dissociation of spermine protonated at one or other of the sites are examples of micro-constants. They cannot be determined directly by means of pH, absorbance, fluorescence or NMR measurements. Nevertheless, the site of protonation is very important for biological function, so mathematical methods have been developed for the determination of micro-constants.^[64]

Applications and significance

A knowledge of pK_a values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist in biochemistry; for example, the pK_a values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins.^[65] Protein pK_a values cannot always be measured directly, but may be calculated using theoretical methods. Buffer solutions are used extensively to provide solutions at or near the physiological pH for the study of biochemical reactions;^[66] the design of these solutions depends on a knowledge of the pK_a values of their components. Important buffer solutions include MOPS, which provides a solution with pH 7.2, and tricine, which is used in gel electrophoresis.^[67]^[68] Buffering is an essential part of acid base physiology including acid–base homeostasis,^[69] and is key to understanding disorders such as acid–base imbalance.^[70]^[71]^[72] The isoelectric point of a given molecule is a function of its pK values, so different molecules have different isoelectric points. This permits a technique called isoelectric focusing,^[73] which is used for separation of proteins by 2-D gel polyacrylamide gel electrophoresis.

Buffer solutions also play a key role in analytical chemistry. They are used whenever there is a need to fix the pH of a solution at a particular value. Compared with an aqueous solution, the pH of a buffer solution is relatively insensitive to the addition of a small amount of strong acid or strong base. The buffer capacity^[74] of a simple buffer solution is largest when pH = pK_a. In acid–base extraction, the efficiency of extraction of a compound into an organic phase, such as an ether, can be optimised by adjusting the pH of the aqueous phase using an appropriate buffer. At the optimum pH, the concentration of the electrically neutral species is maximised; such a species is more soluble in organic solvents having a low dielectric constant than it is in water. This technique is used for the purification of weak acids and bases.^[75]

A pH indicator is a weak acid or weak base that changes colour in the transition pH range, which is approximately pK_a ± 1. The design of a universal indicator requires a mixture of indicators whose adjacent pK_a values differ by about two, so that their transition pH ranges just overlap.

In pharmacology, ionization of a compound alters its physical behaviour and macro properties such as solubility and lipophilicity, log p). For example, ionization of any compound will increase the solubility in water, but decrease the lipophilicity. This is exploited in drug development to increase the concentration of a compound in the blood by adjusting the pK_a of an ionizable group.^[76]

Knowledge of pK_a values is important for the understanding of coordination complexes, which are formed by the interaction of a metal ion, M^m+, acting as a Lewis acid, with a ligand, L, acting as a Lewis base. However, the ligand may also undergo protonation reactions, so the formation of a complex in aqueous solution could be represented symbolically by the reaction

To determine the equilibrium constant for this reaction, in which the ligand loses a proton, the pK_a of the protonated ligand must be known. In practice, the ligand may be polyprotic; for example EDTA⁴⁻ can accept four protons; in that case, all pK_a values must be known. In addition, the metal ion is subject to hydrolysis, that is, it behaves as a weak acid, so the pK values for the hydrolysis reactions must also be known.^[77]

Assessing the hazard associated with an acid or base may require a knowledge of pK_a values.^[78] For example, hydrogen cyanide is a very toxic gas, because the cyanide ion inhibits the iron-containing enzyme cytochrome c oxidase. Hydrogen cyanide is a weak acid in aqueous solution with a pK_a of about 9. In strongly alkaline solutions, above pH 11, say, it follows that sodium cyanide is "fully dissociated" so the hazard due to the hydrogen cyanide gas is much reduced. An acidic solution, on the other hand, is very hazardous because all the cyanide is in its acid form. Ingestion of cyanide by mouth is potentially fatal, independently of pH, because of the reaction with cytochrome c oxidase.

In environmental science acid–base equilibria are important for lakes^[79] and rivers;^[80]^[81] for example, humic acids are important components of natural waters. Another example occurs in chemical oceanography:^[82] in order to quantify the solubility of iron(III) in seawater at various salinities, the pK_a values for the formation of the iron(III) hydrolysis products Fe(OH)²⁺, {{chem|Fe(OH)|2|+}} and Fe(OH)₃ were determined, along with the solubility product of iron hydroxide.^[83]

Values for common substances

There are multiple techniques to determine the pK_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.^[11]^[84] More values can be found in thermodynamics, above. A table of pK_a of carbon acids, measured in DMSO, can be found on the page on carbanions.

See also

Notes

1. ^The hydrogen ion does not exist as such in solution. It combines with a solvent molecule; when the solvent is water an hydronium ion is formed: H⁺ + H₂O → H₃O⁺. This reaction is quantitative and hence can be ignored in the context of chemical equilibrium
2. ^{{cite book| last1 = Whitten| first1 = Kenneth W.| last2 = Gailey| first2 = Kenneth D.| last3 = Davis| first3 = Raymond E.| date = 1992| title = General Chemistry| edition = 4th| page = 660| publisher = Saunders College Publishing| isbn = 0-03-072373-6}}
3. ^{{cite book| last1 = Petrucci| first1 = Ralph H.| last2 = Harwood| first2 = William S.| last3 = Herring| first3 = F. Geoffrey| date = 2002| title = General Chemistry| edition = 8th| pages = 667-8| publisher = Prentice Hall| isbn = 0-13-014329-4}}
4. ^pK_a is sometimes referred to as an acid dissociation constant, but this is incorrect, strictly speaking, as the constant is K_a whereas pK_a is the cologarithm of the dissociation constant value. Also, it is usual in chemistry to write K_a as a simple ratio of concentrations which appears to have units of concentration. More correctly, each thermodynamic activity factor should be replaced by c/c₀, where c₀ is the solute standard state 1 mol/L, so that K_a = [H⁺][A^-]/[HA]c₀ which is a pure number whose logarithm can be defined.
5. ^{{cite web |url=https://pubs.acs.org/doi/ipdf/10.1021/acs.jpca.6b02253 |title=Acidity of Strong Acids in Water and Dimethyl Sulfoxide}}
6. ^ {{cite web |url=https://link.springer.com/article/10.1134%2FS0036024417070196 |title=Dissociation constant of nitric acid}}
7. ^{{cite book| last1 = Perrin| first1 = DD| last2 = Dempsey| first2 = B| last3 = Serjeant| first3 = EP| name-list-format = vanc| title = pK_a Prediction for Organic Acids and Bases| publisher = Chapman & Hall| year = 1981| location = London| isbn = 978-0-412-22190-3| doi = 10.1007/978-94-009-5883-8| chapter = Chapter 3: Methods of pK_a Prediction| pages = 21–26| department = (secondary)}}
8. ^¹{{cite encyclopedia| last = Fraczkiewicz| first = R| name-list-format = vanc| title = In Silico Prediction of Ionization| encyclopedia = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering [Online]| editor-last = Reedijk| editor-first = J| volume = vol. 5| publisher = Elsevier| location = Amsterdam, The Netherlands| year = 2013| doi = 10.1016/B978-0-12-409547-2.02610-X| department = (secondary)}}
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12. ^{{Housecroft3rd}} Chapter 6: Acids, Bases and Ions in Aqueous Solution
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84. ^{{cite book| title = Lange's Handbook of Chemistry| last = Speight| first = J.G.| year = 2005| publisher = McGraw–Hill| edition = 18th| isbn = 0-07-143220-5}} Chapter 8

References

Theoretical background

Definitions

Equilibrium constant

Monoprotic acids

Strong acids and bases

Polyprotic acids

Isoelectric point

Water self-ionization

Protonation constants

Amphoteric substances

Bases and basicity

Temperature dependence

Acidity in nonaqueous solutions

Mixed solvents

Factors that affect pK_a values

Thermodynamics

Experimental determination

Micro-constants

Applications and significance

Values for common substances

See also

Notes

References

Further reading

External links

Theoretical background

Definitions

Equilibrium constant

Monoprotic acids

Strong acids and bases

Polyprotic acids

Isoelectric point

Water self-ionization

Protonation constants

Amphoteric substances

Bases and basicity

Temperature dependence

Acidity in nonaqueous solutions

Mixed solvents

Factors that affect pKa values

Thermodynamics

Experimental determination

Micro-constants

Applications and significance

Values for common substances

See also

Notes

References

Further reading

External links

Factors that affect pK_a values