Acid dissociation constant

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The acid dissociation constant (K_a), also known as the acidity constant or the acid-ionization constant, is a specific equilibrium constant for the reaction of an acid with its conjugate base in aqueous solution ^[1].

Contents 1 Definition 2 Usage 3 The base dissociation constant 4 Factors that determine the relative strengths of acids and bases 5 Importance of pKa values 6 Acidity in nonaqueous solutions 7 pKa of some common substances 8 Further reading 9 See also 10 References 11 External links

[edit] Definition

When an acid dissolves in water, it partly dissociates forming hydronium ions and the conjugate base.

HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq)

For a normal equilibrium constant, the concentration of water would be included in its definition. This is not the case for the acid dissociation constant because the reaction takes place in aqueous solution, so the change in the concentration of water will be negligable. This means that the acid dissociation constant is defined as:

The value of K_a varies over many degrees of magnitude and so it is common to take the logarithm to base ten of the value. This new constant, pK_a makes acids easier to compare as it varies over a much smaller range.

[edit] Usage

The pK_a of an acid is often used to compare the strength of two acids. Stronger acids are acids that are more dissociated, and so they have a higher K_a. Because of this, the pK_a of an acid decreases with strength in a similar way to the pH scale.

K_a can also be used to predict values for the pH of a solution of known concentration. Using the approximation that, in dilute aqueous solutions:

By assuming that only a negligable amount of the acid dissociates, and that the concentation of A⁻ is equal to that of H⁺, it is possible to rearrange these equations to give

A similar technique, whereby the pH of a buffer solution can be predicted is known as the Henderson-Hasselbalch equation.

[edit] The base dissociation constant

The base dissociation constant is the basic equivalent of the acid dissociation constant. It can be defined in a similar way, using the equation for the dissociation of a base in aqueous solution.

B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq)

Using similar reasoning to before:

In the same way as K_a, the higher the value of K_b, the stronger the base.

There is a relationship between K_a and K_b. If you combine the equations for the dissociation of an acid with those of the dissociation of its conjugate base, you always get the reaction for the self-ionization of water. This implies for an acid-base conjugate pair, , where K_w is the dissociation constant of water ().

This in turn implies that stronger acids have weaker conjugate bases, and also vice versa.

[edit] 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 AHX 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 .

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).

[edit] 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

[edit] Acidity in nonaqueous solutions

The acidity of compounds changes when the solvent is not water. In general, aprotic solvents are less effective than water for stabilising ions, with the result that compounds tend to ionize less in nonaqueous media. For example, the pK_a of acetic acid in acetonitrile is 22, i.e. acetic acid is approximately 17 orders of magnitude less ionized than in water. Stated differently, in acetonitrile solution, the acetate anion is a strong base.

Acidity scales have been developed for many compounds in nonaqueous solvents, but especially for dimethylsulfoxide and acetonitrile.^[2] Such scales help chemists to select bases to effect particular deprotonations.

In nonaqueous solution, ions tend to associate, which complicates the interpretation of pK_a's. In particular, the process of homoconjugation describes the reaction between the conjugate base and its parent acid. Homoconjugation describes the following equilibrium:

HA + A^- → HA₂^-

Typically HA₂^- would have the structure A---H---A, i.e. the conjugate base binds to the parent acid via a hydrogen bond.

In acetonitrile solution, para-toluenesulfonic acid has a pK_a of 8.7, which indicates that only a minuscule percentage of this acid is ionized. The corresponding homoconjugation constant, pK^f, is -2.9, which indicates that the toluenesulfonate anion, once formed, strongly tends to form a hydrogen bond with the parent acid. Homoconjugation has the effect of enhancing the acidity of acids, lowering their effective pK_a’s, by stabilizing the conjugate base. Due to homoconjugation, the proton-donating power of toluenesulfonic acid in acetonitrile solution is enhanced by almost 1000 fold.^[3]

[edit] 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)
• 15.76: Hydroxide ion
• - 19.00 (pKb) Sodium amide
• 37.00: Lithium diisopropylamide (LDA)
• 45.00: Propane
• 50.00: Ethane

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

[edit] Further reading

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

[edit] See also

• Hammett equation
• QSAR

[edit] References

1. ^ http://www.avogadro.co.uk/definitions/acidka.htm
2. ^ March, J. “Advanced Organic Chemistry” 4th Ed. J. Wiley and Sons, 1992: New York. ISBN 0-471-60180-2.
3. ^ Coetzee, J. F. and Padmanabhan, G. R., "Proton Acceptor Power and Homoconjugation of Mono- and Diamines", Journal of the American Chemical Society, 1965, volume 87, pp 5005-5010.DOI:10.1021/ja00950a006.

[edit] 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 pK_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
• List of Aqueous-Equilibrium Constants