03 Acids, Bases, and Curved-Arrow Notation

Two ways to define acids and bases

Acid–base chemistry can be described by tracking either proton transfer or electron-pair transfer. These perspectives overlap, but each highlights a different part of a reaction.

Proton transfer and conjugate pairs

In the Brønsted model, a Brønsted acid donates a proton, while a Brønsted base accepts one. When an acid loses a proton, it becomes its conjugate base; when a base gains a proton, it becomes its conjugate acid. Each conjugate acid–base pair differs by one proton.

For example, acetic acid transfers a proton to hydroxide:

Acetic acid is the acid and becomes acetate, its conjugate base. Hydroxide is the base and becomes water, its conjugate acid.

The Lewis model focuses on electrons: a Lewis base donates an electron pair, and a Lewis acid accepts one. This broader definition includes proton-transfer reactions, but it also applies when no proton moves. For example, ammonia donates a lone pair to electron-deficient boron in boron trifluoride, forming a nitrogen–boron bond:

Takeaway: Brønsted definitions track proton transfer; Lewis definitions track electron-pair transfer.

Following electrons with curved arrows

Curved-arrow notation shows the movement of electrons during a reaction. The tail starts at the electron pair—often a lone pair or a bond—and the head points to where the electrons move. The arrow does not represent an atom moving by itself.

For the reaction of acetic acid with hydroxide, draw two arrows:

1. Start at a lone pair on the hydroxide oxygen and point to the acidic hydrogen.

2. Start at the acid’s O–H bond and point to the oxygen that loses the hydrogen. The bond electrons stay with oxygen as acetate forms.

For the ammonia and boron trifluoride reaction, draw an arrow from the nitrogen lone pair to boron. A full-headed curved arrow represents two electrons. A fishhook arrow represents one electron and is used for radical processes.

Takeaway: Begin every curved arrow where the electrons are and point it toward their destination.

Using pKa to compare acid strength

Acid strength describes how readily an acid donates a proton. The acid-dissociation constant $K_\mathrm{a}$ measures this tendency, and its logarithmic form is:

A lower $\mathrm{p}K_\mathrm{a}$ means a stronger acid; a higher $\mathrm{p}K_\mathrm{a}$ means a weaker acid. The stronger an acid is, the weaker its conjugate base tends to be. Comparisons should use pKa values measured or estimated under consistent solvent and reaction conditions, because values depend on those conditions.

Takeaway: Lower pKa means a stronger acid, while higher pKa means a weaker acid.

Predicting reaction direction

For a proton-transfer reaction, write the reactant-side acid as $\mathrm{HA}$ and the product-side acid as $\mathrm{HB}$:

The approximate equilibrium constant is:

Equilibrium favors the side with the weaker acid—the acid with the higher pKa—and the weaker base. Therefore:

• If the product-side acid has a much higher pKa than the reactant-side acid, products are favored.

• If it has a much lower pKa, reactants are favored.

• If the pKa values are similar, neither side is overwhelmingly favored.

For acetic acid reacting with hydroxide, $\mathrm{p}K_\mathrm{a}$ of acetic acid is about $4.8$, while $\mathrm{p}K_\mathrm{a}$ of water is about $15.7$. The difference is about $11$, giving $K$ of roughly $10^{11}$. Acetate and water are therefore strongly favored. This is an estimate for predicting reaction direction; actual equilibrium also depends on conditions and solvent.

A reliable prediction sequence is:

1. Identify the acid and base, then write the proton-transfer products.

2. Draw arrows from the base’s electron pair to the proton and from the acid bond to the atom that loses the proton.

3. Identify the acid on each side.

4. Compare their pKa values; equilibrium favors the side with the higher-pKa acid.

Takeaway: Compare the acids on both sides: the side with the weaker acid and weaker base is generally favored.