Chemistry 2e · Equilibria of Other Reaction Classes

Lewis Acids and Bases

8 min read

Formation constant K_f = 1.1 × 10¹³ for [ Cu(NH₃)₄]²⁺ is a standard textbook value at 25 °C; tabulated values vary slightly among reference sources.

On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

The Arrhenius definition (acids release H⁺; bases release OH⁻) and the Brønsted–Lowry definition (acids donate H⁺; bases accept H⁺) both require a proton. The Lewis definition is broader and more fundamental: a is any species that can accept an electron pair, and a is any species that can donate an electron pair. The donated pair forms a with the acceptor, producing a combined species called an .

Because it focuses on electron pairs rather than protons, Lewis theory covers proton reactions and thousands of reactions that involve no H⁺ at all: boron trifluoride binding fluoride, carbon dioxide reacting with hydroxide, and transition-metal ions surrounding themselves with ligands. Nearly every general chemistry reaction can be viewed as a Lewis acid–base reaction in disguise.

Why this matters

Lewis acid–base thinking is the working language of coordination chemistry, catalysis, and much of biochemistry. The iron in hemoglobin binds oxygen because Fe²⁺ (a Lewis acid) accepts electron pairs from ligands; chlorophyll's magnesium and vitamin B₁₂'s cobalt sit inside cages for the same reason. Industrial catalysts such as AlCl₃ and TiCl₄ function as Lewis acids, and the cyanide ion's toxicity comes from its power as a Lewis base that binds the Fe³⁺ of cytochrome oxidase. Water treatment plants use Al³⁺ or Fe³⁺ (Lewis acids) to coagulate suspended particles. Understanding who donates and who accepts electron pairs lets you predict adduct formation, complex stability, and even drug–metal interactions.

The college version

Core Concepts

The electron-pair definition

A Lewis base has a lone pair (or π electrons) it can share: NH₃, H₂O, OH⁻, F⁻, Cl⁻, CN⁻, and halide ions are all bases. A Lewis acid has an empty orbital able to receive that pair: H⁺ (empty 1s), BF₃ and AlCl₃ (electron-deficient central atoms with empty p orbitals), CO₂ and SO₃ (polarized π systems), and nearly all metal cations such as Fe³⁺, Cu²⁺, and Zn²⁺.

In the reaction

$BF 3 + NH 3 \to F 3 B - NH 3$

NH₃ donates its nitrogen lone pair into boron's empty orbital. BF₃ is the Lewis acid (acceptor), NH₃ is the Lewis base (donor), and the product is the adduct.

Coordinate covalent bonds: the same bond, different origin

A coordinate covalent bond is a covalent bond whose electron pair came from one atom. Once formed, it is indistinguishable from any other covalent bond — the "coordinate" label only describes the pair's origin. Counting electrons confirms the electron bookkeeping: nitrogen in NH₃ has 5 valence electrons, uses 3 in N–H bonds, and keeps 1 lone pair (an octet with one pair to spare). Boron in BF₃ has 3 valence electrons in 3 B–F bonds — only 6 electrons total, an incomplete octet, so it happily accepts a fourth pair to reach 8.

Lewis theory is the most general acid–base model

Every Arrhenius acid is a Brønsted–Lowry acid, and every Brønsted–Lowry acid is a Lewis acid (H⁺ accepts a pair). But the Lewis definition includes reactions with no proton at all:

$CO 2 + OH - \to HCO 3 -$

$SO 3 + O 2- \to SO 4 2-$

In both, the oxide-bearing species donates an electron pair to the electron-poor central atom. This generality is why the Lewis model is used in organic chemistry (curved arrows are electron-pair donation) and in describing metal–ligand bonding.

Complex ions: Lewis acid–base equilibrium in action

A transition-metal cation surrounded by Lewis-base ligands is a . Each ligand donates a lone pair, and the equilibrium is quantified by a formation constant K_f:

$Cu 2+ (aq) + 4 NH 3 (aq) ⇌ [Cu (NH 3) 4] 2+ (aq)$

with K_f = 1.1 × 10¹³ at 25 °C. Large K_f values mean the complex is strongly favored — which is why ammonia can pull Cu²⁺ out of solid precipitates, and why chelating agents used in heavy-metal poisoning therapy work.

How It Works / Step-by-Step Process

Identify lone pairs (or π electrons) available for donation — these mark potential Lewis bases.
Identify empty orbitals or electron-poor atoms that can accept a pair — these mark potential Lewis acids.
Draw the dative bond from donor to acceptor and count electrons on each atom to confirm octets.
Classify each reactant as acid or base; write the adduct or complex ion.
For complex formation, use K_f to judge whether the complex forms significantly at given concentrations.

Common Confusions

Common Confusion	Correct Understanding
"BF₃ can't be an acid — it has no hydrogen."	Lewis acidity needs only an empty orbital, not H⁺. BF₃ is a classic Lewis acid and not a Brønsted acid at all.
"A Lewis base must carry a negative charge."	Neutral molecules with lone pairs (NH₃, H₂O, CO) are superb Lewis bases.
"A coordinate covalent bond is a different kind of bond."	Only the pair's origin differs; the finished bond is identical to any covalent bond.
"H⁺ transfer and electron-pair donation are competing theories."	They are nested: every Brønsted acid–base reaction is also a Lewis reaction (H⁺ is the acceptor).
"Transition-metal complexes violate the octet rule, so they are impossible."	Metals commonly exceed an octet using d orbitals; the octet rule is a light-element guideline, not a law.
"The bigger the cation charge, the weaker the complex."	Higher charge density generally strengthens Lewis acidity (Fe³⁺ binds CN⁻ more strongly than Fe²⁺).

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of electron pairs as LEGO connectors. A Lewis base is a LEGO brick with a stud (a pair it can share); a Lewis acid is a brick with an open socket (an empty spot). When the stud clicks into the socket, the two bricks become one piece. The most important reactions in chemistry are just bricks snapping together.

Worked examples

Classify the acid and base in each reaction:

(a) BF₃ + F^- → BF₄^-. Boron has only 6 valence electrons (3 bonds), so it accepts the fluoride lone pair: BF₃ is the Lewis acid, F⁻ the Lewis base.

(b) AlCl₃ + Cl^- → AlCl₄^-. Aluminum, like boron, is electron-deficient (6 electrons); it accepts Cl⁻'s pair. AlCl₃ acid, Cl⁻ base. This reaction explains why AlCl₃ dissolves in concentrated HCl.

(c) CO₂ + OH^- → HCO₃^-. The hydroxide oxygen donates its lone pair to the carbon of CO₂ (a Lewis acid). This is how CO₂ is absorbed in basic solutions and how it reacts in the body's bicarbonate buffer.

(d) Fe³⁺ + 6CN^- → [Fe(CN)₆]^3-. Fe³⁺ accepts six cyanide lone pairs into its empty d orbitals; Fe³⁺ is the acid, CN⁻ the base.

The formation of [ Cu(NH₃)₄]²⁺ has K_f = 1.1 × 10¹³. Convert this to a standard free-energy change to see the driving force:

$Δ G ° = -RT ln K f$

Substitute R = 8.314 J mol^-1K^-1, T = 298.15 K, and K_f = 1.1 × 10¹³:

$Δ G ° = -(8.314 J mol -1 K -1)(298.15 K) ln (1.1 \times 1013)$

Since ln(1.1 × 10¹³) = 30.03,

$Δ G ° = -(8.314)(298.15)(30.03) J mol -1 = -7.44 \times 104 J mol -1 = -74.4 kJ mol -1$

The units check out: J mol⁻¹ K⁻¹ × K = J mol⁻¹. A ΔG^° near −74 kJ/mol tells us the complex forms essentially completely under standard conditions — the reason deep-blue [ Cu(NH₃)₄]²⁺ appears as soon as ammonia is added to a copper(II) solution.

Key takeaways

Lewis acid = electron-pair acceptor; Lewis base = electron-pair donor.
Lewis theory includes all Brønsted–Lowry and Arrhenius acid–base reactions, plus many with no H⁺ involved.
The bond formed by a donated pair is a coordinate covalent bond; it is identical to a normal covalent bond once formed.
Electron-deficient species (BF₃, AlCl₃, carbocations) and metal cations are classic Lewis acids.
Neutral molecules with lone pairs (NH₃, H₂O) are Lewis bases — a base need not carry a negative charge.
Metal ions + ligands = complex ions; the formation constant K_f measures complex stability.
Bigger K_f → stronger driving force; related to free energy by ΔG^°= -RTlnK_f (Chapter 16).
Lewis acid–base reactions are equilibria: they can be shifted by concentration changes, just like any other equilibrium.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

In Ag⁺ + 2NH₃ ⇌ [Ag(NH₃)₂]⁺, which species is the Lewis acid and which the Lewis base?
Show answer
Ag⁺ is the Lewis acid (electron-pair acceptor); NH₃ is the Lewis base (donor). This is the complexation that dissolves AgCl in ammonia.
Why is every Brønsted–Lowry acid also a Lewis acid, but not every Lewis acid a Brønsted acid?
Show answer
Brønsted acids donate H⁺, and H⁺ itself is an electron-pair acceptor, so the proton transfer is a Lewis reaction. But Lewis acids like BF₃ or CO₂ accept pairs without donating H⁺.
How many electrons surround boron in BF₃ before and after it accepts F⁻?
Show answer
Before: 6 (three B–F bonds). After: 8 (four bonds), a complete octet in the BF₄⁻ adduct.
What does a very large K_f (e.g., 10¹³) imply about the equilibrium position?
Show answer
Products are strongly favored; the complex forms almost completely, which is why ligands can pull metal ions out of precipitates.
Name two biological metal complexes that rely on Lewis acid–base bonding.
Show answer
Hemoglobin (Fe²⁺ binding O₂), chlorophyll (Mg²⁺ in a porphyrin ring), and vitamin B₁₂ (Co³⁺) are standard examples.

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Study toolsKey vocabulary

Key vocabulary

Lewis acid: Any species that accepts an electron pair
Lewis base: Any species that donates an electron pair
coordinate covalent bond: Covalent bond whose shared pair came from one atom
adduct: Product of a Lewis acid–base combination
ligand: Lewis base bonded to a metal center in a complex
complex ion: Metal cation surrounded by bonded ligands
formation constant (Kf): Equilibrium constant for complex-ion formation

Sources & references

openstax.org — Chemistry 2e

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