2.9 Predicting Acid–Base Reactions from pKa Values

Acid-Base Reactions and pKa Values

Acid-base reactions in organic chemistry come down to one question: which way does the proton move? The pKa value of an acid tells you how easily it gives up a proton, and by comparing pKa values, you can predict whether a reaction will actually happen and which side equilibrium favors.

Predicting Acid-Base Reactions

Under the Brønsted-Lowry definition, acids are proton donors and bases are proton acceptors. In any proton-transfer reaction, the proton moves from the stronger acid to the stronger base.

Here's how to predict the direction of an acid-base reaction:

1. Identify the acid and base on each side of the equation.
2. Look up (or estimate) the pKa of the acid on the left and the pKa of the conjugate acid that forms on the right.
3. The proton transfers from the species with the lower pKa (stronger acid) to the base whose conjugate acid has the higher pKa (stronger base).
4. Equilibrium favors the side with the weaker acid and weaker base.

For example, if formic acid (pKa 3.75) reacts with ammonia (conjugate acid pKa 9.25), the proton transfers from formic acid to ammonia because formic acid is the stronger acid. The products, formate ion and ammonium ion, are the weaker acid-base pair, so equilibrium favors the product side.

A useful rule of thumb: when the $\Delta pKa$ (difference between the two pKa values) is greater than about 3, the reaction essentially goes to completion. When the $\Delta pKa$ is small, you'll get a significant amount of both reactants and products at equilibrium.

Comparison of Acid-Base Strengths

Comparing acids is straightforward: the acid with the lower pKa is the stronger acid. HBr (pKa ≈ −9) is a far stronger acid than HF (pKa 3.2), for instance.

Comparing bases requires an extra step. You compare the pKa values of their conjugate acids. A stronger base has a conjugate acid with a higher pKa. For example, hydroxide (conjugate acid water, pKa 15.7) is a stronger base than methylamine (conjugate acid $CH_3NH_3^+$, pKa 10.6).

The leveling effect limits what acids and bases can exist in a given solvent. In water, any acid stronger than $H_3O^+$ (pKa −1.7) will fully protonate water, so all strong acids appear equally strong. Similarly, any base stronger than $OH^-$ will fully deprotonate water. This is why you need non-aqueous solvents to distinguish between the strengths of very strong acids or very strong bases.

Calculating Ka from pKa

The acid dissociation constant ($K_a$) quantifies how much an acid dissociates in solution. A larger $K_a$ means more dissociation and a stronger acid. The pKa scale converts these often unwieldy numbers into something easier to compare.

The two key relationships:

$pK_a = -\log_{10}(K_a)$

$K_a = 10^{-pK_a}$

For benzoic acid with a pKa of 4.19: $K_a = 10^{-4.19} = 6.5 \times 10^{-5}$

To find the equilibrium constant for an acid-base reaction, use the $\Delta pKa$:

$K_{eq} = 10^{\Delta pK_a}$

where $\Delta pK_a = pK_a(\text{product acid}) - pK_a(\text{reactant acid})$

Watch the sign carefully here. If acetic acid (pKa 4.76) donates a proton to ammonia (conjugate acid $NH_4^+$, pKa 9.25), then:

$K_{eq} = 10^{(9.25 - 4.76)} = 10^{4.49} \approx 3.1 \times 10^{4}$

A $K_{eq}$ much greater than 1 tells you the reaction strongly favors products. A $K_{eq}$ much less than 1 means reactants are favored.

pH, Buffers, and the Henderson-Hasselbalch Equation

pH measures how acidic or basic a solution is. In organic chemistry, you'll most often use pH in the context of buffer solutions and predicting protonation states of functional groups.

A buffer is a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid). Buffers resist changes in pH when small amounts of acid or base are added, because the equilibrium shifts to absorb the added protons or hydroxide ions.

The Henderson-Hasselbalch equation connects pH, pKa, and the ratio of conjugate base to acid:

$pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$

This equation is useful in two directions. You can calculate the pH of a buffer if you know the concentrations, or you can figure out the ratio of $[A^-]$ to $[HA]$ needed to hit a target pH. One thing worth remembering: when $[A^-] = [HA]$, the log term equals zero, so $pH = pK_a$. That's the point where the buffer works best.