Lesson 9 · 25 min

Hard and soft acids and bases

Aluminium occurs as oxides, mercury as sulfides; Fe³⁺ likes F⁻ best and Hg²⁺ likes I⁻. The ladder of halide stability constants and the absolute hardness computed from ionisation energies turn “hard likes hard, soft likes soft” into numbers you can check.

In this lesson

Sort common Lewis acids and bases into hard, soft and borderline, and say what the sorting rests on
Use the “ladder” of halide stability constants to judge whether a metal ion is hard or soft
Compute an ion’s absolute hardness η = (I − A)/2 from successive ionisation energies, and say what it does and does not explain
Use “hard likes hard, soft likes soft” to explain which ores metals form, why heavy metals are toxic and how antidotes are chosen

Aluminium, magnesium and calcium occur as oxides, silicates, carbonates and fluorides — bauxite, dolomite, fluorite; lead, zinc, mercury and silver come almost entirely as sulfides — galena PbS, sphalerite ZnS, cinnabar HgS, argentite Ag₂S. Goldschmidt (1923) divided the elements accordingly into “rock-loving” and “sulfur-loving”. Why do some metal ions prefer oxygen and fluorine, others sulfur and iodine? Pearson’s (1963) terse answer: hard likes hard, soft likes soft.

Predict first

In water, which halide binds Hg²⁺ most strongly (largest first stability constant)?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

F⁻: the smallest, most concentrated charge Cl⁻ Br⁻ I⁻

Hard and soft

Hard acids are small, highly charged and have electron clouds that are hard to deform: H⁺, Li⁺, Na⁺, Mg²⁺, Ca²⁺, Al³⁺, Fe³⁺. Soft acids are large, of low charge and easily polarised — mostly heavy-metal ions with full or nearly full d shells: Cu⁺, Ag⁺, Au⁺, Hg²⁺, Cd²⁺, Pd²⁺, Pt²⁺. Bases likewise: F⁻, OH⁻, H₂O and O²⁻ are hard bases; I⁻, S²⁻, CN⁻, CO and phosphines are soft bases. Those in between are borderline: Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺ and Pb²⁺, and Br⁻ and pyridine.

Hard–hard binding is mostly electrostatic — the more concentrated the charge, the stronger; soft–soft binding is mostly covalent, the overlap of large, deformable electron clouds. Before Pearson, Ahrland, Chatt and Davies (1958) had noticed the two opposite orders of halide stability constants and divided metals into class (a) and class (b) — hard and soft, as they were later called.

\eta = \frac{I - A}{2}, \qquad \eta(\text{M}^{n+}) = \frac{I_{n+1} - I_n}{2}

The absolute hardness of Parr and Pearson (1983): half the difference between the energy to remove an electron and the energy released on adding one. For a cation Mⁿ⁺ the electron affinity A is the ionisation energy of M⁽ⁿ⁻¹⁾⁺, Iₙ.

$I$: ionisation energy
$A$: electron affinity
$I_n$: nth ionisation energy

Stability constants from NIST 46 · absolute hardness computed from NIST ionisation energies

Hard and soft acids: the halide ladder

lg K₁ from F⁻ to I⁻

Absolute hardness against the preference for chloride over fluoride

hard
borderline
soft

Fe³⁺: η = (I4 − I3) / 2 = (54.91 − 30.65) / 2 = 12.13 eV

lg K₁: F⁻ 6.04 · Cl⁻ 1.48 (halide complexes not listed are too weak to record)

Pearson class: hard

Left: the lines of hard acids fall from F⁻ to I⁻, those of soft acids rise, and borderline Pb²⁺ is almost flat. Right: every ion with η above 12 eV prefers F⁻ and every ion below 8 eV prefers Cl⁻ — but the middle is untidy: Cd²⁺ is softer than Zn²⁺ although their η are almost equal.

Worked example

The hardness of silver and aluminium ions

Silver’s first and second ionisation energies are 7.58 and 21.48 eV; aluminium’s third and fourth are 28.45 and 119.99 eV. Find the absolute hardness of Ag⁺ and Al³⁺.

Pearson’s classification (common examples)
Kind	Hard	Borderline	Soft
Acids	H⁺, Li⁺, Na⁺, Mg²⁺, Ca²⁺, Al³⁺, Fe³⁺, BF₃	Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Pb²⁺	Cu⁺, Ag⁺, Au⁺, Hg²⁺, Cd²⁺, Pd²⁺, Pt²⁺
Bases	F⁻, OH⁻, H₂O, O²⁻, NH₃, RCOO⁻	Br⁻, NO₂⁻, pyridine	I⁻, S²⁻, RS⁻, CN⁻, CO, PR₃

Concept check

In mercury, cadmium or lead poisoning, which group of the body’s proteins do these metals mainly bind, inactivating enzymes?

carboxylate (—COO⁻) the thiol of cysteine (—SH) phosphate hydroxyl (—OH)

Try the calculation

Sodium’s first and second ionisation energies are 5.139 and 47.286 eV. What is the absolute hardness of Na⁺ (eV)?

Key takeaways

Hard acids and bases are small, charge-dense and hard to polarise, and bind electrostatically; soft ones are large and polarisable, and bind covalently: hard likes hard, soft likes soft.
The halide ladder is the most direct test: lg K₁ of hard acids falls from F⁻ to I⁻ (Fe³⁺ 6.0 → 1.5), that of soft acids rises (Hg²⁺ 1.6 → 13.4).
Absolute hardness η = (I − A)/2 follows from ionisation energies: Al³⁺ 45.8 eV, Ag⁺ 7.0 eV; it separates the ends but cannot order the middle.

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Data and references

R. G. Pearson, “Hard and soft acids and bases”, J. Am. Chem. Soc. 85, 3533–3539 (1963).
S. Ahrland, J. Chatt & N. R. Davies, “The relative affinities of ligand atoms for acceptor molecules and ions”, Q. Rev. Chem. Soc. 12, 265–276 (1958).
R. G. Parr & R. G. Pearson, “Absolute hardness: companion parameter to absolute electronegativity”, J. Am. Chem. Soc. 105, 7512–7516 (1983).
NIST Critical Stability Constants (SRD 46), as carried in the MINTEQA2 v4 database distributed with PHREEQC (USGS); NIST Atomic Spectra Database, ionisation energies (2024).
V. M. Goldschmidt, Geochemische Verteilungsgesetze der Elemente (1923–1938).