15.2 Lewis Acids and Bases

Lewis Acids and Bases

The Brønsted-Lowry model defines acids and bases by proton transfer, but that only covers part of the picture. The Lewis model broadens the definition: acids and bases interact through electron pair sharing, not just proton exchange. This lets you explain reactions that don't involve any protons at all, like why $\text{BF}_3$ reacts with $\text{NH}_3$ even though neither one is donating or accepting an $\text{H}^+$.

These interactions produce adducts and complex ions, and the equilibrium constants that describe their formation (called formation constants) tell you how stable the products are.

Lewis Acids vs. Bases

A Lewis acid is an electron pair acceptor. It has either an incomplete octet or an empty orbital that can receive electrons. Common examples include $\text{BF}_3$, $\text{AlCl}_3$, and metal cations like $\text{Ag}^+$.

A Lewis base is an electron pair donor. It has at least one lone pair available to share. Examples include $\text{NH}_3$, $\text{H}_2\text{O}$, and $\text{OH}^-$.

When a Lewis base donates a lone pair to a Lewis acid, they form a coordinate covalent bond, a bond where both electrons come from the same atom. The product of this reaction is called an adduct (for neutral species) or a complex ion (when a metal cation is involved).

The octet rule helps you predict these interactions. Atoms that lack a full octet (like boron in $\text{BF}_3$, which has only 6 electrons around it) are strong Lewis acids because accepting an electron pair completes their octet.

Formation of Adducts and Complex Ions

Adduct formation happens when a Lewis acid and base combine into a single new species. For example:

$\text{BF}_3 + \text{NH}_3 \rightarrow \text{F}_3\text{B–NH}_3$

Here, the nitrogen on $\text{NH}_3$ donates its lone pair to the boron on $\text{BF}_3$, which had an empty orbital. The result is one new coordinate covalent bond holding the adduct together.

Complex ion formation is the same idea, but with a metal cation acting as the Lewis acid and molecules or ions called ligands acting as Lewis bases. For example:

$\text{Ag}^+ + 2\text{NH}_3 \rightarrow [\text{Ag}(\text{NH}_3)_2]^+$

The $\text{Ag}^+$ ion accepts electron pairs from two $\text{NH}_3$ molecules. The brackets and charge notation are standard for writing complex ions. Other examples you might see include $[\text{Cu}(\text{NH}_3)_4]^{2+}$ and $[\text{Fe}(\text{CN})_6]^{3-}$.

Lewis structures are used to show the coordinate covalent bonds in these products. The key visual difference from a regular covalent bond is that both electrons in the bond originated from the Lewis base.

Equilibrium in Lewis Acid-Base Systems

The formation of adducts and complex ions is an equilibrium process. The equilibrium constant for this reaction is called the formation constant ($K_f$). A large $K_f$ means the product is very stable and the reaction strongly favors the complex; a small $K_f$ means the complex forms only to a limited extent.

For the $\text{BF}_3$/$\text{NH}_3$ system, the expression looks like this:

K_f = \frac{[\text{F}_3\text{B–NH}_3}]}{[\text{BF}_3][\text{NH}_3]}

Calculating Equilibrium Concentrations

You can find equilibrium concentrations using the same ICE table method from earlier equilibrium units:

1. Write the balanced equation and set up an ICE table with the given initial concentrations.
2. Define the change in terms of $x$. If the reaction proceeds forward by $x$, reactant concentrations decrease by $x$ and product concentration increases by $x$ (adjusted for stoichiometric coefficients).
3. Write equilibrium expressions by substituting $([\text{initial}] \pm x)$ terms into the $K_f$ expression.
4. Solve for $x$, then plug it back in to find each equilibrium concentration.

Factors Affecting $K_f$

• Strength of the Lewis acid and base: Stronger acids (more electron-deficient) and stronger bases (better electron donors) produce more stable complexes and larger $K_f$ values.
• Steric factors: Bulky groups around the acid or base can physically block the electron pair donation, reducing $K_f$.
• Solvent effects: The polarity and donor/acceptor properties of the solvent can compete with or stabilize the Lewis acid-base interaction.

Bonding and Geometry in Lewis Acid-Base Interactions

The coordinate covalent bond formed in a Lewis acid-base reaction behaves just like any other covalent bond once it's formed. You can use VSEPR theory to predict the geometry of the resulting adduct or complex ion based on the number of electron pairs around the central atom.

For instance, $\text{BF}_3$ is trigonal planar (3 bonding regions), but after it accepts a lone pair from $\text{NH}_3$, the adduct $\text{F}_3\text{B–NH}_3$ has four bonding regions around boron, making it tetrahedral. Predicting these geometry changes matters because shape affects the physical and chemical properties of the product.