Weak Acids, Weak Bases, and pKa

The pKa concept is the quantitative backbone of drug design: pharmaceutical chemists routinely tune a candidate molecule's pKa to control its ionization state at physiological pH (7.4) versus stomach pH (~1.5–3.5), because only the neutral (un-ionized) form of most small-molecule drugs crosses lipid membranes efficiently — a principle formalized in the pH-partition hypothesis and central to predicting oral bioavailability. Aspirin (acetylsalicylic acid, pKa ≈ 3.5) is absorbed efficiently in the acidic stomach where it remains largely neutral, while morphine's tertiary amine (pKa ≈ 8) is protonated and charged at physiological pH, affecting its distribution and blood-brain-barrier penetration. In enzymology, catalytic residues are chosen by evolution precisely because their pKa values can be tuned by the local protein environment to sit near the operating pH of the reaction. The catalytic triad of chymotrypsin (Ser195–His57–Asp102) works because the local electrostatic environment lowers the effective pKa of the serine hydroxyl (via the histidine acting as a general base) enough for it to act as a nucleophile at physiological pH — a mechanism whose full kinetic analysis depends on exactly the equilibrium framework built here. Aspartate and glutamate side chains (free pKa ≈ 3.9 and 4.1) are sometimes shifted upward by 3–4 units when buried in a hydrophobic active site, allowing them to act as general acids at neutral pH where they would otherwise be fully deprotonated in bulk solution — this is the essence of pKa perturbation in enzyme catalysis. Hemoglobin's Bohr effect — the pH-dependence of oxygen binding that lets red blood cells release more O₂ in metabolically active, CO₂-rich (and hence more acidic) tissue — arises because specific histidine residues (notably His146 of the β-chain) change pKa upon the protein's conformational shift between oxy and deoxy states, altering how many protons the protein binds as it changes shape. Buffer systems throughout physiology — bicarbonate/carbonic acid in blood plasma (pKa ≈ 6.1, effective near pH 7.4 because of the open CO₂ reservoir), phosphate in cytoplasm (pKa₂ = 7.21), and histidine imidazole groups in proteins (pKa ≈ 6.0) — are all selected because their pKa values sit usefully close to the pH ranges they must stabilize, a direct, load-bearing application of everything derived above, and the immediate conceptual bridge to The Henderson-Hasselbalch Equation and quantitative Titration Curves.

Ask the tutor: How does burying a histidine side chain in a hydrophobic active-site pocket shift its pKa, and why does that shift matter for catalysis?

Consider dropping acetic acid, CH₃COOH, into water. Some molecules give up a proton to a nearby water molecule; most do not. The reaction

reaches equilibrium almost instantly — proton transfers are among the fastest reactions known, occurring on picosecond-to-nanosecond timescales because they require no bond-making to heavy atoms, only the shuttling of a proton along a hydrogen-bonded network. What distinguishes a weak acid from a strong one is not the speed of the reaction but its position at equilibrium. Strong acids like HCl transfer essentially all their protons to water; weak acids like acetic acid transfer only a small, well-defined fraction, leaving the bulk of the acid in its protonated (neutral) form. The equilibrium constant for this reaction, written with water's concentration folded into the constant (since [H₂O] ≈ 55.5 M is essentially unchanged by the reaction — a compositional invariant, not a "coincidence"), is called the acid dissociation constant Ka:

Here [H⁺] is shorthand for [H₃O⁺], the hydronium ion. A large Ka means the equilibrium lies far to the right — lots of dissociation, a "stronger" weak acid. A small Ka means the equilibrium favors the intact HA — a "weaker" weak acid still. Because Ka values for biological acids span more than twelve orders of magnitude (from Ka ≈ 10⁻² for phosphoric acid's first proton to Ka ≈ 10⁻¹³ for some very weakly acidic protons), chemists compress this range logarithmically, exactly as is done for [H⁺] itself:

This is the same logarithmic trick that turns [H⁺] into pH, and it is why pKa values conveniently fall in the 0–14 range that overlaps directly with physiological pH. A low pKa (e.g., 2) means a large Ka — a comparatively strong (readily dissociating) acid. A high pKa (e.g., 10) means a tiny Ka — a very weak acid that mostly stays protonated even in neutral water. Every acid HA is paired with a conjugate base A⁻: the species that remains after the proton leaves. Conversely, every base B (like ammonia, NH₃) has a conjugate acid BH⁺ (ammonium, NH₄⁺). A conjugate acid-base pair always differs by exactly one proton and share the same equilibrium — writing the base reaction

with equilibrium constant Kb, one finds Ka(for BH⁺) and Kb(for B) are linked through water's autoionization constant Kw:

This means every base's strength can be re-expressed as the pKa of its conjugate acid — biochemists almost universally do this, so that ammonia's basicity is reported as "pKa(NH₄⁺) = 9.25" rather than as a separate Kb. This single-scale convention is what lets a table of pKa values describe both acids and bases with one consistent number.

The next figure shows why pKa is the "tipping point" pH: it is precisely the pH at which [HA] = [A⁻], so that the log term in the ionization ratio vanishes.

The central equilibrium expression for any monoprotic weak acid HA is

where: $[\text{H}^+]$ is the equilibrium hydrogen-ion (hydronium) concentration in mol/L, $[\text{A}^-]$ and $[\text{HA}]$ are the equilibrium concentrations of conjugate base and undissociated acid, and $K_a$ has units of concentration (mol/L), though it is conventionally treated as dimensionless once referenced to the standard 1 M state.

Reading: Ka is just the equilibrium constant of a proton-transfer reaction, no more mysterious than the equilibrium constant for any other reversible reaction. It tells you the ratio of products to reactant concentrations that the system settles into, not how fast it gets there. The logarithmic form:

Reading: This is a purely notational compression, identical in spirit to pH = −log₁₀[H⁺]. A one-unit change in pKa corresponds to a tenfold change in Ka. Rearranging the Ka expression gives the ionization ratio directly as a function of pH — the seed of the Henderson–Hasselbalch relation developed elsewhere:

Reading: When pH = pKa, the exponent is zero, so $[\text{A}^-]/[\text{HA}] = 1$ — equal concentrations. When pH exceeds pKa by one unit, A⁻ outnumbers HA tenfold; when pH is one unit below pKa, HA outnumbers A⁻ tenfold. This single relation is the mechanistic seed of both Titration Curves and The Henderson-Hasselbalch Equation, though their full development belongs elsewhere. The thermodynamic origin of pKa, connecting equilibrium to free energy:

where: $R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$, $T$ is absolute temperature (K), and $\Delta G^{\circ}$ is the standard free-energy change for the dissociation reaction HA → H⁺ + A⁻ in dilute aqueous solution.

Reading: pKa is not an arbitrary empirical number — it is a disguised free energy. A high pKa (weak acid) corresponds to a large positive ΔG° (dissociation is thermodynamically unfavorable); a low pKa (strong acid) corresponds to a small or negative ΔG° (dissociation is favorable). At 25°C (298 K), each pKa unit corresponds to 2.303RT ≈ 5.7 kJ/mol of standard free energy.

Example 1 — Foundational: fractional ionization of acetic acid at gastric-adjacent pH. Acetic acid has pKa = 4.76. Find the ratio [A⁻]/[HA] and the percent ionized at pH 3.20 (a mildly acidic environment, distinctly asymmetric from pKa — not the trivial pH = pKa case). Using $[\text{A}^-]/[\text{HA}] = 10^{\,\text{pH}-\text{pKa}}$:

Evaluate: $10^{-1.56} = 10^{-2}\times10^{0.44} = 0.01 \times 2.754 = 0.0275$. So at pH 3.20, only about 2.75 A⁻ ions exist for every 100 HA molecules. Converting to percent ionized: if $x = [\text{A}^-]/([\text{HA}]+[\text{A}^-])$, then from the ratio $r = 0.0275 = [\text{A}^-]/[\text{HA}]$,

So acetic acid is only 2.68% ionized at pH 3.20 — it is overwhelmingly present as neutral CH₃COOH. This illustrates the general principle: when pH is well below pKa, a weak acid stays predominantly protonated. Limiting case check: at pH = pKa = 4.76 exactly, the ratio becomes $10^0 = 1$, giving exactly 50% ionization — the defining tipping point, consistent with the derivation above.

Example 2 — Applied: the second dissociation of phosphoric acid in cytoplasmic buffering. Inorganic phosphate is one of the cell's dominant buffers, and its physiologically important equilibrium is the second dissociation,

Find the ratio $[\text{HPO}_4^{2-}]/[\text{H}_2\text{PO}_4^-]$ at intracellular pH 7.05 (a physiologically realistic, slightly acidic-of-neutral value, chosen deliberately off pKa2 and off pH 7.00 to avoid masking errors with round numbers).

Evaluate: $10^{-0.16} = 10^{-1}\times10^{0.84} = 0.1\times6.918 = 0.6918$. So at pH 7.05, there are about 0.692 mol of HPO₄²⁻ for every mole of H₂PO₄⁻ — the two forms are present in comparable amounts (roughly 41% HPO₄²⁻, 59% H₂PO₄⁻), which is exactly why phosphate is such an effective physiological buffer: its pKa2 sits close to intracellular pH, so both the proton-donating and proton-accepting forms are abundant simultaneously and can respond to acid or base loads in either direction. Compute the percent as HPO₄²⁻ explicitly: with $r = 0.6918$,

So 40.9% of phosphate is in the HPO₄²⁻ form at pH 7.05, and 59.1% is H₂PO₄⁻ — confirming the near-even split expected when pH is close to pKa.

Example 3 — Exam/competition level: multiprotic amino acid, finding the pH at which a specific microspecies dominates. Histidine has three ionizable groups: the α-carboxyl (pKa₁ = 1.82), the imidazole side chain (pKa₂ = 6.00), and the α-amino group (pKa₃ = 9.17). At what pH is the ratio of the fully protonated cationic species (COOH, imidazolium⁺, NH₃⁺; net charge +2) to the next species (COO⁻, imidazolium⁺, NH₃⁺; net charge +1) equal to exactly 3:1, and which ionization event does this correspond to? The transition between the +2 species and the +1 species is governed entirely by loss of the α-carboxyl proton, since that is the only group differentiating the two species (both retain protonated imidazole and protonated amino group). This is governed by pKa₁ = 1.82:

We want the protonated (+2) form to exceed the deprotonated (+1) form by 3:1, i.e., $[\text{+1}]/[\text{+2}] = 1/3$:

Take $\log_{10}$ of both sides:

So at pH 1.34, the fully protonated (+2) form of histidine outnumbers the (+1) form three to one — a pH found in the stomach, where free histidine (from protein digestion) would indeed exist predominantly in its doubly protonated cationic form. Notice this calculation used only pKa₁, correctly ignoring pKa₂ and pKa₃ since at pH 1.34 those groups are essentially fully protonated regardless (pH is more than four units below both), so their ionization states do not change appreciably across this narrow pH window — a check worth stating explicitly: at pH 1.34, $\text{pH}-\text{pKa}_2 = 1.34-6.00 = -4.66$, so $[\text{imidazole free base}]/[\text{imidazolium}] = 10^{-4.66} \approx 2.2\times10^{-5}$, confirming imidazole is >99.998% protonated and can be treated as a spectator group in this calculation.

Ka and pKa as we use them today are inseparable from the broader Brønsted–Lowry framework for acids and bases, developed independently and almost simultaneously in 1923 by Johannes Nicolaus Brønsted in Denmark and Thomas Martin Lowry in England. Before their work, acids and bases were understood mainly through the more restrictive Arrhenius definition (acids produce H⁺ in water; bases produce OH⁻), which could not naturally accommodate species like ammonia or the amino acid side chains central to biochemistry. Brønsted's insight — that an acid is simply a proton donor and a base is a proton acceptor, defined always in relation to a conjugate partner — is exactly the conceptual scaffold used throughout this article: every HA has its A⁻, every B has its BH⁺, and "acid" or "base" is a role a molecule plays relative to a specific proton-transfer partner, not an immutable label. Brønsted, a physical chemist working at the University of Copenhagen, was deeply interested in reaction kinetics and catalysis, and his acid-base theory grew out of his attempts to systematize how general acid and general base catalysis worked in organic reactions — a concern that turns out to be exactly the concern of enzymologists studying how histidine, aspartate, and lysine side chains catalyze biological reactions today. The logarithmic pKa notation itself traces to Søren Sørensen's 1909 introduction of pH at the Carlsberg Laboratory, extended naturally by later chemists to dissociation constants once Brønsted's generalized framework made "acid strength" a quantity worth tabulating systematically across both classical mineral acids and the growing catalogue of biologically relevant weak acids and bases.