2.8 Acid and Base Strength

Acid and Base Strength

Acid and base strength determines how readily a molecule donates or accepts a proton. In organic chemistry, predicting which way a proton transfer will go is essential for understanding nearly every reaction mechanism you'll encounter. The tools for making these predictions come down to the pKa scale and a handful of structural factors that stabilize (or destabilize) conjugate bases.

Acid and Base Strength

Acid strength comparison using pKa

The pKa is the standard measure of acid strength. It's defined as the negative logarithm of the acid dissociation constant ($K_a$):

$pK_a = -\log(K_a)$

A lower pKa means a stronger acid. That's because a lower pKa corresponds to a larger $K_a$, which means the equilibrium favors dissociation. For reference, HCl has a pKa of about $-7$ (very strong acid), while acetic acid sits at $4.76$ (weak acid). The scale spans a huge range, so even a difference of a few pKa units represents a large difference in acid strength.

Four main structural factors determine how strong an acid is, and they all work by affecting how well the conjugate base handles its negative charge:

• Electronegativity of the atom bonded to the acidic hydrogen. More electronegative atoms stabilize the negative charge on the conjugate base better. For example, $HF$ (pKa ≈ 3.2) is a stronger acid than $H_2O$ (pKa = 15.7) partly because fluorine is more electronegative than oxygen.
• Atom size. Larger atoms spread the negative charge over a bigger volume, stabilizing the conjugate base. This is why $HI$ (pKa ≈ $-10$) is a stronger acid than $HF$ (pKa ≈ 3.2), even though fluorine is more electronegative. Going down a column of the periodic table, size dominates over electronegativity.
• Resonance stabilization of the conjugate base. If the negative charge can be delocalized across multiple atoms, the conjugate base is more stable. Carboxylic acids (pKa ≈ 4–5) are much more acidic than alcohols (pKa ≈ 16) because the carboxylate anion delocalizes its charge over two equivalent oxygen atoms.
• Inductive effects from nearby electron-withdrawing groups. Groups like $-NO_2$, $-CF_3$, or halogens pull electron density away from the conjugate base through sigma bonds, stabilizing the negative charge. For instance, trichloroacetic acid ($Cl_3CCOOH$, pKa ≈ 0.65) is far more acidic than acetic acid (pKa ≈ 4.76).

Inverse relationship of acid-base strength

Every acid-base reaction produces a conjugate pair. When an acid donates a proton, what's left behind is its conjugate base:

$\text{HA} + H_2O \rightleftharpoons A^- + H_3O^+$

The key relationship: stronger acids produce weaker conjugate bases, and weaker acids produce stronger conjugate bases. This makes intuitive sense. If an acid gives up its proton very easily (strong acid), the conjugate base has little tendency to grab that proton back (weak base).

• HCl is a strong acid, so $Cl^-$ is a very weak base (essentially no tendency to accept a proton in water).
• Acetic acid ($CH_3COOH$) is a weak acid, so acetate ($CH_3COO^-$) is a moderately strong conjugate base.

This inverse relationship is what lets you predict the direction of proton-transfer reactions. Equilibrium always favors the side with the weaker acid and the weaker base. So if you compare pKa values of the acid on each side, the proton ends up on the side with the higher pKa.

In aqueous solution at 25°C, the pKa of an acid and the pKb of its conjugate base are related by:

$pK_a + pK_b = 14$

Calculation of water's pKa

Water can act as both an acid and a base. Its autoionization equilibrium is:

$H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-$

The equilibrium constant for this process is the ion-product constant, $K_w$:

$K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14} \text{ (at 25°C)}$

In pure water, $[H_3O^+] = [OH^-]$, so:

$[H_3O^+] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \text{ M}$

To get water's pKa, you need its $K_a$. When water acts as the acid ($H_2O \rightleftharpoons H^+ + OH^-$), the true $K_a$ equals $K_w / [H_2O]$. Since the concentration of pure water is about 55.5 M:

$K_a = \frac{1.0 \times 10^{-14}}{55.5} = 1.8 \times 10^{-16}$

$pK_a = -\log(1.8 \times 10^{-16}) \approx 15.7$

You'll see water's pKa listed as 15.7 in most organic chemistry textbooks. The value of 14 (from $pK_w$) is sometimes used in general chemistry contexts, but 15.7 is the more accurate number because it accounts for water's molar concentration.

Acid-Base Theories and Concepts

Two definitions of acids and bases come up repeatedly in organic chemistry:

• Brønsted-Lowry theory defines acids as proton donors and bases as proton acceptors. This is the framework you'll use most often when analyzing proton-transfer reactions.
• Lewis theory is broader. It defines acids as electron-pair acceptors and bases as electron-pair donors. This definition covers reactions where no proton transfer occurs, like when $BF_3$ accepts an electron pair from $NH_3$. Lewis acid-base chemistry becomes especially important in later units when you study electrophiles and nucleophiles.

Two additional concepts worth knowing:

• Leveling effect. A solvent limits how strong an acid can appear to be. In water, any acid stronger than $H_3O^+$ (pKa ≈ $-1.7$) is fully dissociated, so all strong acids like HCl, $HBr$, and $HNO_3$ appear equally strong in water. To distinguish their strengths, you'd need a less basic solvent.
• Buffer solutions. A mixture of a weak acid and its conjugate base resists pH changes when small amounts of acid or base are added. Buffers work best when the pH is close to the pKa of the weak acid. This concept connects directly to the Henderson-Hasselbalch equation you may see in problem sets.