Organic Chemistry Text Book (CHEM 3401 and 3402)

The relative acidities of different acids are commonly measured and cited as pKa values, relative to a standard solvent base, often water. These numbers reflect the equilibrium acidities of the acids. An astounding range of acidities is displayed by even rather simple compounds. The table on the right lists some elemental hydrides from groups 4 through 7 of the periodic table. The pK_a's determined (or in some cases estimated) for these compounds are shown beneath the formulas. Approximate values for higher members of group 4 and 5 hydrides (e.g. silane and phosphine) have not been reported. Note that these logarithmic numbers encompass nearly sixty powers of ten. This is a greater span than that encompassed by distance measurements starting from the radius of a hydrogen atom and extending to the diameter of the known universe.

Why do these relatively simple compounds differ in acid strength so markedly? Two factors may be discerned:
    • First, the compounds in the top row clearly show the importance of electronegativity. All the heavier elements have greater electronegativities than hydrogen, with carbon being the least different. The ionic character of these covalent bonds is such that hydrogen carries a partial positive charge, and the heavier atom a corresponding negative charge. The greatest charge separation is in H-F, where the electronegativity difference is nearly 2. Removal of a proton is facilitated by this charge separation. The covalent bond energies do not correlate inversely with acid strength, as one might have expected, since the two strongest acids have the strongest bonds (H-O 111 kcal/mol & H-F 135 kcal/mol). Finally, the heavy atoms in the top row have similar sizes, the covalent radii being 0.75 ±0.02 Å. The importance of this fact will become apparent in the following discussion.
    • Second, the compounds in the columns representing periodic groups 6 and 7 show an increase in acidity moving from the top to the bottom. This is opposite to the electronegativity change, and is best attributed to an increase in heavy atom size. When an acid transfers a proton to a base, the remaining residue (the conjugate base) must carry a negative charge. Ignoring solvent stabilization (solvation), the stability of ions is a function of charge density. A small ion has a higher charge density than a larger ion of the same charge, making the smaller ion less stable. From the covalent radius of oxygen compared with sulfur, and fluorine compared with chlorine, it can be estimated that the charge density on the larger atom is half that of the smaller. The resulting stabilization of the conjugate base more than compensates for the decrease in electronegativity in moving down the column; so H₂S is a stronger acid than H₂O, and HCl a stronger acid than HF. Since sulfur and chlorine are nearly the same size (covalent radii being 1.02 ±0.02 Å), electronegativity explains the difference in acidity between H₂S and HCl.

If the heavy atom of an acid carries a formal charge, its acidity will be changed substantially. This is demonstrated by the examples on the right. Ammonium and hydronium ions carry a positive charge, and the acidity of the species is increased by over fifteen powers of ten relative to uncharged ammonia and water. By contrast, hydrogen sulfide and hydrogen selenide are dibasic acids (they have two acidic protons). Once the first proton has been lost, the acidity of the negatively charged conjugate base is reduced over a million fold. This is true for most other dibasic acids such as H₂SO₄ and H₂CO₃.

Accurate acidity measurements in the pK_a range from 1 to 14 can usually be made in water solution. However, acids stronger than the hydronium ion (H₃O⁽⁺⁾) and bases stronger than hydroxide ion (OH^(–)) react immediately with this solvent, and the resulting "leveling effect" prevents direct measurement of their pK_a's. One way of circumventing this difficulty is to examine the acidity of very strong ( pK_a < 0) and very weak ( pK_a > 15) acids in different (non-aqueous) solvents, and to extrapolate these measurements to water. For example, solvents such as acetic acid, acetonitrile and nitromethane are often used for studying very strong acids. Very weakly acidic solvents such as DMSO, acetonitrile, toluene, amines and ammonia are used to study the acidities of very weak acids. The errors introduced in extreme cases, such as methane, are often large; but the overall range of acid strengths observed in this manner cannot be questioned. 
It must be recognized that pK_a values for the same compound measured in different solvents will generally be different. The two most common solvents in which such measurements have been made are water and DMSO. The following table presents data for a few representative compounds, with the pK_a difference noted in the right hand column. Since anion solvation by water is superior to that provided by DMSO, the pK_a values from the latter solvent tend to be higher. However, a decrease in charge density, as with sulfur, or internal delocalization of negative charge, as in the last four compounds, lessens this difference.