Acid dissociation constant

In chemistry and biochemistry, the acid dissociation constant, the acidity constant, or the acid-ionization constant (K_a) is a specific type of equilibrium constant that indicates the extent of dissociation of hydronium ions from an acid. The equilibrium is that of a proton transfer from an acid, HA, to water, H₂O. The term for the concentration of water, [H₂O], is omitted from the general equilibrium constant expression because the concentration of water is so large (55.5M) in relation to the other concentrations in the expression that it remains essentially unchanged throughout dissociation.

HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq)

$K_{a}={\frac {[{\mbox{H}}_{3}{\mbox{O}}^{+}][{\mbox{A}}^{-}]}{[{\mbox{HA}}]}}$

The equilibrium is often written in terms of "H⁺(aq)", which reflects the Brønsted-Lowry Theory of acids.

HA(aq) ⇌ H⁺(aq) + A⁻(aq)

Because this constant differs for each acid and varies over many degrees of magnitude, the acidity constant is often represented by the additive inverse of its common logarithm, represented by the symbol pK_a (using the same mathematical relationship as [H⁺] is to pH).

pK_a = −log₁₀ K_a

In general, a larger value of K_a (or a smaller value of pK_a) indicates a stronger acid, since the extent of dissociation is larger at the same concentration.

Using the acid dissociation constants, the concentration of acid, its conjugate base, protons and hydroxide can be easily determined. If an acid is partly neutralized, the K_a can also be used to find the pH of the resulting buffer solution. This same information is summarized in the Henderson-Hasselbalch equation.

Basicity constant of the conjugate base

By analogy, one can define the basicity constant K_b and the pK_b of the conjugate base A⁻:

$K_{b}={\frac {[{\mbox{HA}}][{\mbox{OH}}^{-}]}{[{\mbox{A}}^{-}]}}$

pK_b = −log₁₀ K_b

This is the dissociation constant for the equilibrium

A⁻(aq) + H₂O(l) ⇌ HA(aq) + OH⁻(aq)

Analogously to K_a, an increasing value of K_b indicates a stronger base, since the number of protons accepted is larger at an identical concentration.

Relationship between acidity and basicity constants

There exists a relationship between the value of K_a for an acid HA and the value of K_b for its conjugate base A⁻. Since adding the ionization reaction for HA and the ionization reaction of A⁻ always gives the reaction for the self-ionization of water, the product of the acidity and basicity constants gives the dissociation constant of water (K_w), which is 1.0 × 10⁻¹⁴ at 25°C. In other words,

As the product of K_a and K_b remains constant, it follows that stronger acids have weaker conjugate bases, while weaker acids have stronger conjugate bases.

Factors that determine the relative strengths of acids and bases

Being an equilibrium constant, the acid dissociation constant K_a is determined by the difference in free energies ΔG° between the reactants and products, specifically, between the protonated (AH) and deprotonated (A⁻) states. Molecular interactions that favor the deprotonated (A⁻) state over the protonated (AH) state will increase K_a (because the ratio [A⁻]/[AH] increases) or, equivalently, decrease pK_a. Conversely, molecular interactions that favor the protonated (AH) state over the deprotonated (A⁻) state will decrease K_a (because the ratio A⁻]/[AH] is lower) or, equivalently, increase pK_a.

For example, suppose that the protonated (AH) form donates a hydrogen bond AH$\cdots$X to another atom X, which the deprotonated form cannot do (since it has no hydrogen left). The protonated form is favored by having a hydrogen bond, so the pK_a increases (the K_a decreases). The magnitude of the pK_a shift can even be determined from the change in ΔG° using the equation $K_{a}=e^{-{\frac {\Delta G^{\circ }}{RT}}}$.

Other molecular interactions can also shift the pK_a. Adding an electron-withdrawing chemical group (such as oxygen, a halide, a cyano group or even a phenyl ring) to the molecule near the titrating hydrogen will favor the deprotonated state (by stabilizing the electron left behind when the proton dissociates) and thus decrease pK_a (increase K_a). For example, successive oxidation of hypochlorous acid leads to ever-increasing K_a: HClO < HClO₂ < HClO₃ < HClO₄. The difference in values of K_a between hypochlorous acid HClO and perchloric acid HClO₄ is approximately 11 orders of magnitude (pK_a shift of ~11). Electrostatic interactions can affect the equilibrium as well. The presence of surrounding negative charges would disfavor the formation of a negatively charged, de-protonated species and thus increase pK_a. In particular, the ionization of one group on a molecule can affect the pK_a of another.

Fumaric and maleic acid are classic examples of pK_a shifts. Both molecules have the same composition, being two carboxylic acid groups separated by two double-bonded carbon atoms; fumaric acid is the trans isomer, whereas maleic acid is the cis isomer. By symmetry, one might imagine that the two carboxylic acids had the same pK_a, which is typically ~4 for carboxylic acids. This is almost true for fumaric acid, which has pK_a's of roughly 3.5 and 4.5. By contrast, maleic acid has pK_a's of roughly 1.5 and 6.5. When one of its carboxylic acids de-protonates, the other can form a strong hydrogen bond to it; overall, the effect is to favor the deprotonated state of the hydrogen-bond-accepting group (lowering its pK_a from ~4 to 1.5) and to favor the protonated state of the hydrogen-bond-donating group (raising its pK_a from ~4 to 6.5).

Importance of pK_a values

The pK_a value(s) of a compound influence many characteristics of the compound such as its reactivity, solubility and spectral properties (colour). In biochemistry 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.

See Methods for calculating protein pKa values

pK_a of some common substances

Measurements are at 25ºC in water, except for those with a pKa below -1.76:

• - 25.00: Fluoroantimonic acid
• - 15.00: Magic acid
• - 10.00: Fluorosulfuric acid
• - 10.00: Hydroiodic acid
• - 9.00: Hydrobromic acid
• - 8.00: Hydrochloric acid
• - 7.00: Perchloric acid
• - 3.00, 1.99: Sulfuric acid
• - 2.00: Nitric acid
• - 1.76: Hydronium ion
• 3.15: Hydrofluoric acid
• 3.60: Carbonic acid
• 3.75: Formic acid
• 4.04: Ascorbic acid (Vitamin C)
• 4.19: Succinic acid
• 4.20: Benzoic acid
• 4.63: Aniline*
• 4.74: Acetic acid
• 4.76: Dihydrogencitrate ion (Citrate)
• 5.21: Pyridine*
• 6.40: Monohydrogencitrate ion (Citrate)
• 6.99: Ethylenediamine*
• 7.00: Hydrogen sulfide, Imidazole* (as an acid)
• 7.50: Hypochlorous acid
• 9.25: Ammonia*
• 9.33: Benzylamine*
• 9.81: Trimethylamine*
• 9.99: Phenol
• 10.08: Ethylenediamine*
• 10.66: Methylamine*
• 10.73: Dimethylamine*
• 10.81: Ethylamine*
• 11.01: Triethylamine*
• 11.09: Diethylamine*
• 11.65: Hydrogen peroxide
• 12.50: Guanidine*
• 12.67: Monohydrogenphosphate ion (Phosphate)
• 14.58: Imidazole (as a base)
• - 19.00 (pKb) Sodium amide
• 37.00: Lithium diisopropylamide (LDA)
• 45.00: Propane
• 50.00: Ethane

* Listed values for ammonia and amines are the pK_a values for the corresponding ammonium ions.

Further reading

• Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight. 3rd ed. New York: W. H. Freeman and Company, 2005

See also

• Hammett equation
• QSAR

External links

• Free online pKa calculations using ChemAxon's Marvin and Calculator Plugins - requires Java
• Bordwell pKa Table in DMSO
• Harvard University: Evans Group pKa Table
• Shodor.org Acid-Base Chemistry
• Factors that Affect the Relative Strengths of Acids and Bases
• Purdue Chemistry
• "Acidity constant" definition (from the IUPAC "Gold Book")
• Distribution diagrams of acids and bases (generation from p$K_{a}$ values with free spreadsheet)
• pKa calculation software, first principle method based on Quantum Mechanics and Poisson-Boltzmann solvation model
• SPARC Physical/Chemical property calculator