Factors That Affect PKa Values
Pauling's second rule states that the value of the first pKa for acids of the formula XOm(OH) n is approximately independent of n and X and is approximately 8 for m = 0, 2 for m = 1, −3 for m = 2 and < −10 for m = 3. This correlates with the oxidation state of the central atom, X: the higher the oxidation state the stronger the oxyacid. For example, pKa for HClO is 7.2, for HClO2 is 2.0, for HClO3 is −1 and HClO4 is a strong acid.
With organic acids inductive effects and mesomeric effects affect the pKa 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 pKa values decrease in the series 4.7, 2.8, 1.4 and 0.7 when 0,1, 2 or 3 chlorine atoms are present. The Hammett equation, provides a general expression for the effect of substituents.
- log Ka = log Ka0 + ρσ.
Ka is the dissociation constant of a substituted compound, Ka0 is the dissociation constant when the substituent is hydrogen, ρ is a property of the unsubstituted compound and σ has a particular value for each substituent. A plot of log Ka against σ is a straight line with intercept log Ka0 and slope ρ. This is an example of a linear free energy relationship as log Ka is proportional to the standard fee energy change. Hammett originally formulated the relationship with data from benzoic acid with different substiuents in the ortho- and para- positions: some numerical values are in Hammett equation. This and other studies allowed substituents to be ordered according to their electron-withdrawing or electron-releasing power, and to distinguish between inductive and mesomeric effects.
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 pKa 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 pKa values of approximately 3.0 and 4.5. By contrast, maleic acid has pKa 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.
Proton sponge, 1,8-bis(dimethylamino)naphthalene, has a pKa value of 12.1. It is one of the strongest amine bases known. The high basicity is attributed to the relief of strain upon protonation and strong internal hydrogen bonding.
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 mailnly 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.
Read more about this topic: Acid Dissociation Constant
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