Defining pKa and the Acidity Constant

A single number on a bathroom-cabinet label — say, aspirin's pKa of 3.5 — silently encodes an entire equilibrium. It tells you how strongly a molecule clings to a proton. It predicts how the molecule behaves in your stomach (pH ≈ 1.5) versus your bloodstream (pH ≈ 7.4). It also determines whether the molecule crosses a lipid membrane as a neutral species, or gets trapped as a charged one. Chemists could report acid strength as a raw equilibrium constant, $K_a$ . But these numbers span more than sixty orders of magnitude. They range from $10^{10}$ for the ferociously acidic $\text{HSbF}_6$ superacids to $10^{-50}$ for methane. No chart, no intuition, and no mental arithmetic survives numbers like that. The logarithmic transform to pKa compresses this absurd range into a manageable scale. That scale is additive and humanly-readable. It works in exactly the way decibels tame sound intensity, or the Richter scale tames earthquake energy. This matters because essentially every question in organic reactivity reduces to comparing pKa values. Which proton comes off first, which nucleophile is protonated, whether a reaction runs forward or backward, why phenol is acidic but ethanol is not — all of it comes down to pKa. It is the single most-consulted number in a synthetic chemist's mental toolkit. It is more load-bearing than melting points, and more predictive than "electronegativity intuition" alone. Understanding what pKa is, mechanistically and thermodynamically, matters more than merely knowing "lower pKa means more acidic." That deeper understanding separates students who can look up a number from students who can reason about a molecule they have never seen before. The big picture is that pKa is nothing but a disguised free energy. Every acid–base reaction is an equilibrium. It is governed by the Conjugate Acid-Base Pairs and Reaction Direction framework: an acid HA hands a proton to some base. This generates the conjugate base A⁻ and the conjugate acid of the base. The equilibrium constant for that proton transfer, $K_a$ , is a direct report of $\Delta G^\circ$ for ionization in water. Taking $-\log_{10}$ of $K_a$ does two things at once. First, it converts a multiplicative quantity — equilibrium constants multiply when reactions add — into an additive one. Second, it converts a free energy, measured in kJ/mol, into a small, mostly positive, easily memorized integer-ish number. Free energy in kJ/mol is an awkward unit for quick mental comparison. This article builds pKa from first principles. It covers the equilibrium expression itself, and the mechanistic meaning of "acid dissociation" as a proton-transfer reaction with curved arrows. It also covers the thermodynamic identity connecting $K_a$ to $\Delta G^\circ$ . Finally, it explains the operational meaning of the pKa number for any molecule you might encounter. It sets up, but does not yet fully develop, two ideas that follow directly. One is using pKa differences to predict which side of an equilibrium is favored. The other is the deeper structural reason acids differ in strength — the stability of the conjugate base.

Key takeaways

$K_a$ is the equilibrium constant for the reaction $\text{HA} + \text{H}_2\text{O} \rightleftharpoons \text{A}^- + \text{H}_3\text{O}^+$ , written with water's concentration folded into the constant.
$\text{pK}_a = -\log_{10}K_a$ ; this logarithmic transform converts a 60-order-of-magnitude range into numbers roughly between $-10$ and $+50$ .
Lower (more negative) pKa = stronger acid = more readily donates a proton = larger $K_a$ = more negative $\Delta G^\circ_{\text{ionization}}$ .
pKa is a disguised free energy: $\Delta G^\circ = -RT\ln K_a = 2.303\,RT\cdot \text{pK}_a$ , so each pKa unit is worth about 5.7 kJ/mol at 25 °C.
pKa is a property of a specific ionizable proton in a specific solvent (almost always water, by convention) at a specific temperature — not a property of "the whole molecule" in the abstract.
The pKa scale runs continuously across strong acids (pKa < 0), weak acids (0–20), and "non-acids" (pKa 20–50) — there is no hard boundary, only a smooth gradient of proton affinity.
Key idea: pKa is just $-\log K_a$ , and $K_a$ is just the equilibrium constant for donating a proton to water — so a pKa number is nothing more than a compact, logarithmic report of how favorable that one proton-transfer equilibrium is.

The core insight

pKa converts the equilibrium constant for "acid gives its proton to water" into a small, additive, easily compared number; every mechanistic and structural argument about acid strength is ultimately an argument about the sign and magnitude of $\Delta G^\circ$ for that one proton transfer.

Where this lives today

pKa is not a historical curiosity confined to titration curves; it is a live, daily-use quantity across chemistry, biology, and industry. In medicinal chemistry, pKa prediction (both experimental and computational, via software using Hammett-type substituent parameters) is a first-pass filter in drug design: a candidate molecule's ionization state at gut pH (≈1.5–2), plasma pH (7.4), and inside a cell's acidic lysosome (≈4.5–5) is dictated entirely by the interplay of its pKa values with local pH through the Henderson–Hasselbalch relation used in Example 2 — determining oral bioavailability, blood–brain barrier penetration, and renal excretion. In enzyme biochemistry, active-site residues (histidine's imidazole, pKa ≈ 6, is the classic example) are catalytically useful precisely because their pKa sits close to physiological pH, letting the same residue act as either acid or base catalyst depending on the microenvironment — a principle exploited by serine proteases, RNase A, and countless other enzymes whose catalytic mechanisms are taught by first establishing the relevant side-chain pKa. In materials and analytical chemistry, pKa determines buffer selection (a buffer works best within about one pH unit of its pKa, a direct consequence of the Henderson–Hasselbalch ratio staying between roughly 1:10 and 10:1 in that window), ion-exchange chromatography retention, and the design of pH-responsive polymers and hydrogels used in controlled drug release, where a polymer's ionizable side chains are tuned to swell or collapse across a physiologically relevant pH range. In synthetic organic chemistry, pKa tables (Bordwell's DMSO-based tables in particular) are the primary tool chemists use before ever running a reaction, to predict which base will successfully deprotonate a given substrate, which proton in a polyfunctional molecule will be removed first, and whether a proposed mechanism's proposed intermediate is thermodynamically plausible at all — a direct foreshadowing of using pKa differences to Predicting Equilibrium Position from pKa and of the deeper structural question of Stability of the Conjugate Base as the Master Principle, both of which build immediately on the definitions established here.

Ask the tutor: If two acids differ in pKa by exactly 4 units, what is the exact ratio of their Ka values, and what free energy difference (in kJ/mol at 298 K) does that correspond to?

The physical picture

Start from the reaction itself, because pKa is meaningless detached from a specific chemical equation. Acid dissociation is a proton-transfer reaction, and like every proton transfer it is a Lewis acid–base reaction in disguise: a lone pair on a Brønsted base attacks the acidic hydrogen, and the H–A bond electrons flow onto the departing atom A. Water, acting as the base, uses a lone pair on oxygen to attack the proton of HA; simultaneously, the electron pair of the H–A σ-bond collapses onto A, generating the conjugate base A⁻ and the hydronium ion H₃O⁺. This is a single concerted step for essentially every simple Brønsted acid: no intermediate, no leaving group chemistry, just electron pair in, electron pair out. The equilibrium constant for this reaction is written in the ordinary way, as products over reactants, each raised to its stoichiometric coefficient, but with one deliberate convention: water is the solvent, present in enormous and essentially constant excess (55.5 M in dilute aqueous solution), so its concentration is absorbed into the constant rather than written explicitly. This is exactly analogous to how the constant $K_w = 10^{-14}$ for water's autoionization already has $[\text{H}_2\text{O}]$ folded in. The resulting $K_a$ is a stripped-down constant with units of concentration, reporting the ratio of ionized to un-ionized acid at equilibrium once the (constant) role of solvent water is factored out. The key physical content is this: $K_a$ measures how far the proton-transfer equilibrium sits toward products (ionized) versus reactants (un-ionized) at standard conditions. A large $K_a$ means the acid is substantially ionized in water — HA converts almost completely to A⁻ and H₃O⁺. A tiny $K_a$ means almost none of the acid ionizes; the vast majority of molecules remain as neutral HA. Because $K_a$ values for real acids range from roughly $10^{10}$ (very strong) to $10^{-50}$ (essentially never ionizes, like an alkane C–H), plotting or tabulating $K_a$ directly is useless — the numbers refuse to fit on one page or one mental number-line. The transform $\text{pK}_a = -\log_{10}K_a$ solves this by compressing that range logarithmically, and by flipping the sign so that stronger acids get smaller (often negative) pKa values, matching the intuitive sense that "acidic" things should have low numbers, like low pH.

Figure

Proton transfer from HA to water: the curved-arrow mechanism defining Ka

It helps to see the logarithmic compression concretely, side by side, because the whole motivation for pKa is visual/numerical relief from an unmanageable range of raw $K_a$ values.

Figure

The Ka range compressed onto the pKa scale

The picture to keep is: pKa is a bookkeeping device, not a new physical quantity. Everything physical is already contained in $K_a$ (equivalently, in $\Delta G^\circ$ ); pKa is simply the version of that number that fits into a comparative table and into ordinary human working memory.

The core ideas

For a generic monoprotic acid HA in water, the equilibrium is

\text{HA(aq)} + \text{H}_2\text{O(l)} \;\rightleftharpoons\; \text{A}^-\text{(aq)} + \text{H}_3\text{O}^+\text{(aq)}

where: HA is the acid, A⁻ its conjugate base, and H₃O⁺ the hydronium ion formed when water acts as the proton acceptor. The equilibrium constant, with solvent water's concentration (55.5 M, essentially invariant in dilute solution) absorbed into the constant, is

K_a = \dfrac{[\text{A}^-][\text{H}_3\text{O}^+]}{[\text{HA}]}

where: brackets denote equilibrium molar concentrations, and $K_a$ carries units of concentration (mol/L) because one fewer concentration term appears in the denominator than would appear in a naively-written mass-action expression that kept $[\text{H}_2\text{O}]$ explicit. The defining logarithmic transform is

\text{pK}_a = -\log_{10}(K_a)

where: the negative sign flips the direction so that a large $K_a$ (strong acid, ionizes readily) yields a small or negative pKa, matching the same convention used for pH. This is connected to thermodynamics through the standard relation between an equilibrium constant and the standard Gibbs free energy of reaction:

\Delta G^\circ = -RT\ln K_a

where: $R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$ , $T$ is absolute temperature in kelvin, and $\Delta G^\circ$ is the standard free energy change for the ionization reaction as written above. Converting the natural log to base 10 ( $\ln x = 2.303\log_{10}x$ ) and substituting the definition of pKa gives the single most useful "translation" equation in all of acid–base chemistry:

\Delta G^\circ = 2.303\,RT\cdot \text{pK}_a

where: this says explicitly that pKa is a free energy, just rescaled by the constant factor $2.303RT$ ; at $T = 298\ \text{K}$ , $2.303RT = 5.71\ \text{kJ/mol}$ , so each pKa unit corresponds to about 5.7 kJ/mol of standard free energy. Reading this equation is the entire conceptual payoff of the article: pKa is not an independent "acidity number" invented separately from thermodynamics — it is thermodynamics, relabeled. A pKa difference of 10 units between two acids means a free energy difference of roughly 57 kJ/mol between how favorably each ionizes, which is why even modest-looking pKa gaps correspond to gigantic differences in the position of equilibrium (a point developed fully when comparing conjugate acid-base pairs directly).

Derivation AFrom the equilibrium expression to the pKa number

Goal. Show explicitly, step by step, how the measurable equilibrium concentrations of a real acid convert into a single pKa value, and confirm the arithmetic with an asymmetric, non-round numerical example.

Step 1 — Write the mass-action expression. For a weak monoprotic acid HA dissolved in water, mechanistically donating a proton via the concerted proton-transfer step already discussed (lone pair of water attacks H, H–A bond electrons flow onto A), the equilibrium constant is

K_a = \frac{[\text{A}^-][\text{H}_3\text{O}^+]}{[\text{HA}]}

This expression already assumes $[\text{H}_2\text{O}]$ has been folded into $K_a$ , which is legitimate because water is both solvent and reactant in enormous excess — its concentration barely changes as the small amount of HA ionizes.

Step 2 — Set up an ICE table for a concrete, asymmetric acid. Take a hypothetical weak acid HA at initial concentration $C_0 = 0.180\ \text{M}$ (chosen non-round on purpose), with negligible initial A⁻ or H₃O⁺ (ignore the tiny autoionization background of pure water). Let $x$ be the amount that ionizes at equilibrium:

	HA	A⁻	H₃O⁺
initial	0.180	0	0
change	$-x$	$+x$	$+x$
equilibrium	$0.180-x$	$x$	$x$

Suppose the experimentally measured equilibrium pH is 2.68 (a deliberately non-round, realistic value for a moderately weak acid at this concentration). Then

[\text{H}_3\text{O}^+] = 10^{-2.68} = 2.09\times10^{-3}\ \text{M}

so $x = 2.09\times10^{-3}\ \text{M}$ , and correspondingly $[\text{A}^-] = 2.09\times10^{-3}\ \text{M}$ as well, by the 1:1 stoichiometry of the proton-transfer equation.

Step 3 — Compute the equilibrium HA concentration.

[\text{HA}]_{\text{eq}} = 0.180 - 0.00209 = 0.1779\ \text{M}

Because $x \ll C_0$ here, the approximation $[\text{HA}]_{\text{eq}} \approx C_0$ would only introduce a 1.2% error — worth noting, but the exact subtraction is used below to keep the arithmetic fully honest.

Step 4 — Assemble Ka.

K_a = \frac{(2.09\times10^{-3})(2.09\times10^{-3})}{0.1779} = \frac{4.368\times10^{-6}}{0.1779} = 2.456\times10^{-5}

Step 5 — Take the negative base-10 logarithm to get pKa.

\text{pK}_a = -\log_{10}(2.456\times10^{-5}) = -(\,-4.610\,) = 4.61

This value (4.61) sits close to real weak organic acids such as acetic acid (pKa 4.76), which is a useful sanity check: the invented numbers were chosen to land in a chemically sensible neighborhood, not an implausible one.

Step 6 — Limiting-case check. Consider what happens as the acid becomes essentially non-ionizing, i.e. $x \to 0$ while $C_0$ stays fixed. Then $[\text{H}_3\text{O}^+]\to 0$ and $[\text{A}^-]\to 0$ , so $K_a \to 0$ and consequently $\text{pK}_a \to +\infty$ — consistent with the physical statement that a proton which essentially never leaves HA (like a C–H bond in methane) has an enormous, even undefined-in-practice, pKa. Conversely, in the limit of a strong acid where ionization is essentially complete, $x \to C_0$ , so $[\text{HA}]_{\text{eq}} \to 0$ in the denominator, driving $K_a \to \infty$ and $\text{pK}_a \to -\infty$ — matching the fact that strong acids are reported with very negative or undefined pKa values (HCl is often quoted around $-6$ to $-7$ , and superacids run to $-20$ or below).

Go deeper · Derivation B · 2 minFrom ΔG° to pKa and back: the thermodynamic identity

Derivation BFrom ΔG° to pKa and back: the thermodynamic identity

Goal. Derive the free-energy/pKa relationship from the statistical thermodynamic definition of an equilibrium constant, and verify it numerically with asymmetric inputs.

Step 1 — Start from the definition of the standard equilibrium constant in terms of chemical potentials. At equilibrium, the sum of chemical potentials of products equals the sum of chemical potentials of reactants, each referenced to its standard state:

\sum_{\text{products}}\mu_i^\circ + RT\ln\left(\prod_{\text{products}} a_i\right) = \sum_{\text{reactants}}\mu_j^\circ + RT\ln\left(\prod_{\text{reactants}} a_j\right)

where $a_i$ are activities (approximated here by concentrations relative to the 1 M standard state).

Step 2 — Collect standard-state terms into ΔG° and equilibrium terms into the reaction quotient at equilibrium (which equals K). Rearranging,

\Delta G^\circ \equiv \sum \mu^\circ_{\text{products}} - \sum \mu^\circ_{\text{reactants}} = -RT\ln K_a

This is the general thermodynamic bridge between any equilibrium constant and the corresponding standard free energy change — the same relation used for every equilibrium in chemistry, not something special to acids.

Step 3 — Convert natural log to base-10 log. Since $\ln x = \ln(10)\cdot\log_{10}x = 2.303\log_{10}x$ ,

\Delta G^\circ = -RT(2.303)\log_{10}K_a

Step 4 — Substitute the definition pKa = −log₁₀(Ka), i.e. log₁₀(Ka) = −pKa.

\Delta G^\circ = -RT(2.303)(-\text{pK}_a) = 2.303\,RT\cdot\text{pK}_a

This confirms the equation stated above and shows it is not a separate empirical fact but a direct algebraic consequence of the standard free-energy/equilibrium-constant relation combined with the definition of pKa.

Step 5 — Numerical check with an asymmetric, non-round example. Take trichloroacetic acid, a real compound with pKa $= 0.66$ at $T = 298\ \text{K}$ (deliberately an off-round, small pKa rather than a tidy textbook integer). Compute the standard free energy of ionization:

\Delta G^\circ = 2.303 \times 8.314\ \text{J mol}^{-1}\text{K}^{-1} \times 298\ \text{K} \times 0.66

= 2.303 \times 8.314 \times 298 \times 0.66\ \text{J/mol}

= 5708.4\ \text{J/mol} \times 0.66 = 3767.5\ \text{J/mol} \approx 3.77\ \text{kJ/mol}

A small positive free energy — meaning ionization is only mildly favorable at standard 1 M concentrations, consistent with trichloroacetic acid being a strong-ish but not fully dissociating weak acid, with a substantial fraction remaining as HA even though $K_a > 1$ isn't quite reached ( $K_a = 10^{-0.66} = 0.219$ , i.e. less than 1, confirming $\Delta G^\circ$ should indeed be slightly positive).

Step 6 — Limiting-case check. As $T \to \infty$ at fixed pKa, $\Delta G^\circ \to \infty$ in magnitude — but this must be interpreted carefully: pKa itself is temperature-dependent in reality (through $K_a(T)$ ), so the correct physical limiting statement is that the conversion factor $2.303RT$ grows without bound, meaning that at very high temperature, a given equilibrium constant corresponds to an ever-larger apparent free energy scale — reflecting that $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$ becomes entropy-dominated. At $T \to 0$ , the conversion factor $2.303RT \to 0$ , so any finite $\Delta G^\circ$ would force $\text{pK}_a \to \pm\infty$ unless $\Delta G^\circ \to 0$ as well — consistent with the third-law expectation that equilibrium constants become extremely sharp (either fully forward or fully reverse) as thermal energy vanishes.

Worked examples

Example 1 (Foundational): Converting a textbook Ka to pKa and interpreting it. Acetic acid has a well-established $K_a = 1.74 \times 10^{-5}$ at 25 °C. Find pKa and state, mechanistically, what the number means. Apply the definition directly:

\text{pK}_a = -\log_{10}(1.74\times10^{-5})

Break the logarithm into its exponent and mantissa parts:

\log_{10}(1.74\times10^{-5}) = \log_{10}(1.74) + \log_{10}(10^{-5}) = 0.2405 - 5 = -4.7595

\text{pK}_a = -(-4.7595) = 4.76

Mechanistic interpretation: this means that in the proton-transfer equilibrium CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺, at equilibrium the ratio $[\text{CH}_3\text{COO}^-][\text{H}_3\text{O}^+]/[\text{CH}_3\text{COOH}]$ equals $1.74\times10^{-5}$ M — a small number, meaning the reaction lies overwhelmingly toward the un-ionized acid side. In a 0.1 M solution, only about 1.3% of molecules are ionized at any instant — the vast majority of acetic acid molecules in a bottle of vinegar are neutral CH₃COOH, not acetate. The pKa of 4.76 is simply a compact label for "moderately weak acid, mostly un-ionized in water near neutral pH," and by the $2.303RT$ relation corresponds to $\Delta G^\circ \approx 27.2$ kJ/mol — a real, physically meaningful, moderately unfavorable free energy of ionization at standard 1 M reference concentrations.

Example 2 (Applied): Determining the ionization state of ibuprofen at physiological pH from its pKa. Ibuprofen, a carboxylic acid drug, has pKa $= 4.91$ . At the pH of blood plasma (pH $= 7.40$ ), what fraction of ibuprofen exists as the neutral (protonated) form versus the ionized carboxylate form, and why does this matter pharmacologically? This uses the Henderson–Hasselbalch relation, which is itself a direct rearrangement of the $K_a$ expression — worth deriving on the spot rather than merely quoting. Starting from

K_a = \frac{[\text{A}^-][\text{H}_3\text{O}^+]}{[\text{HA}]}

take $-\log_{10}$ of both sides:

-\log_{10}K_a = -\log_{10}[\text{H}_3\text{O}^+] - \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

\text{pK}_a = \text{pH} - \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

\text{pH} - \text{pK}_a = \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

Now substitute pH $= 7.40$ and pKa $= 4.91$ :

7.40 - 4.91 = 2.49 = \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

\frac{[\text{A}^-]}{[\text{HA}]} = 10^{2.49} = 309

So for every 1 molecule of neutral ibuprofen, there are 309 molecules of the ionized carboxylate — meaning the fraction neutral is

f_{\text{HA}} = \frac{1}{1+309} = \frac{1}{310} = 0.32\%

Pharmacologically this matters directly: only the small neutral fraction (0.32%) is lipophilic enough to cross a lipid bilayer efficiently by passive diffusion, so absorption across the stomach lining and cell membranes depends sharply on the interplay between pKa and local pH — a principle (the pH-partition hypothesis) built entirely on the Henderson–Hasselbalch consequence of the pKa definition, and one that governs drug absorption, distribution, and renal clearance throughout pharmacology.

Example 3 (Exam/competition level): Back-calculating pKa from a buffer-preparation constraint, with an added consistency check via ΔG°. A chemist wants to prepare a buffer at pH 5.20 using a weak acid HX and its sodium salt NaX, mixing them so that $[\text{X}^-]/[\text{HX}] = 1.85$ (a deliberately non-round ratio, reflecting a real weighing-out scenario rather than a convenient 1:1 mix). Given that the resulting buffer indeed holds at pH 5.20, find pKa of HX, then find $\Delta G^\circ$ for its ionization at 37 °C (human body temperature, 310 K, chosen instead of the usual 298 K to test whether the student can adapt the constant correctly). Rearranging Henderson–Hasselbalch:

\text{pK}_a = \text{pH} - \log_{10}\left(\frac{[\text{X}^-]}{[\text{HX}]}\right) = 5.20 - \log_{10}(1.85)

\log_{10}(1.85) = 0.2672

\text{pK}_a = 5.20 - 0.2672 = 4.93

Now compute $\Delta G^\circ$ at $T = 310\ \text{K}$ rather than the default 298 K, so the conversion constant must be recalculated rather than reused from memory:

2.303\,RT = 2.303 \times 8.314\ \text{J mol}^{-1}\text{K}^{-1} \times 310\ \text{K} = 5934.6\ \text{J/mol} = 5.935\ \text{kJ/mol}

\Delta G^\circ = 5.935\ \text{kJ/mol} \times 4.93 = 29.26\ \text{kJ/mol}

A positive free energy of the expected order of magnitude for a weak carboxylic-acid-like ionization, confirming internal consistency: pKa near 4.9 correctly predicts a modestly unfavorable (endergonic), but not enormous, standard free energy of proton transfer to water — exactly the regime chemists call a "weak acid," neither essentially non-ionizing (pKa > 20, ΔG° > 100+ kJ/mol) nor essentially fully ionized (pKa < 0, ΔG° < 0).

Limiting cases, scope & common traps

Regime	pKa range	Physical meaning	Example
Strong acid	pKa < 0 (often ≪ 0)	Ionization essentially complete in water; $K_a \gg 1$	HCl (≈ −6), H₂SO₄ (first proton, ≈ −3)
Weak acid	0 – 12	Partial ionization; equilibrium mixture of HA and A⁻	CH₃COOH (4.76), phenol (10.0)
Very weak acid / "non-acid"	15 – 25	Ionization negligible under normal aqueous conditions; requires strong bases to deprotonate at all	H₂O (15.7), acetone α-CH (≈ 20)
Effectively non-acidic C–H	30 – 50+	No meaningful aqueous ionization; only observed with extremely strong non-aqueous bases	NH₃ (≈ 38), CH₄ (≈ 50)

Two scope caveats deserve explicit emphasis. First, pKa values above roughly 14–15 (the pKa of water itself, or of the conjugate acid of hydroxide) cannot be measured directly in aqueous solution, because water itself would be deprotonated by any base strong enough to react with such a weak acid — these values are extrapolated from measurements in other solvents (DMSO, for instance) or from computational estimates, and different sources sometimes disagree by several units for this reason. Second, pKa is solvent-dependent: unless stated otherwise, "pKa" by convention means the aqueous value, but the identical molecule can have a substantially different pKa in DMSO (where, notably, ion pairs are not stabilized the same way, and many acids appear far weaker — acetic acid's pKa jumps from 4.76 in water to about 12.6 in DMSO). Quoting a bare pKa number without implicitly fixing the solvent and temperature is a category error, even though convention usually makes water and 25 °C the silent default.

The chemist behind it

The modern pH/pKa formalism traces most directly to Søren Peter Lauritz Sørensen, a Danish chemist working at the Carlsberg Laboratory in Copenhagen — an industrial brewing-science institute, not a university, which speaks to how practical the original motivation was. Sørensen needed a workable way to characterize how acidity affected enzyme activity during fermentation, and in 1909 introduced the notation "pH" (from the French puissance d'hydrogène, "power of hydrogen") specifically to tame the same problem pKa later solved for acid strength: hydrogen ion concentrations in real solutions span many orders of magnitude and are unwieldy to tabulate directly. The logarithmic pH scale he introduced was rapidly generalized by other chemists to any equilibrium constant worth compressing, including acid dissociation constants, giving rise to the "p" notation family (pKa, pKb, pKw, pOH) used throughout chemistry today. Sørensen's practical, industrially-motivated innovation — solve an annoying numerical range problem with a clean logarithmic transform — is exactly the spirit in which pKa should be understood: not as an exotic new physical quantity, but as an act of numerical hygiene applied to an already fully specified equilibrium constant.

Origins · 1 minSøren Peter Lauritz Sørensen and how this was discovered

Søren Peter Lauritz Sørensen

1868–1939 · Carlsberg Laboratory, Copenhagen, early 20th century

Trained as a chemist and briefly worked on geological/mineralogical topics before joining Carlsberg's research laboratory, where problems of protein chemistry, enzyme kinetics, and fermentation control demanded quantitative acidity measurement. His 1909 paper introducing pH addressed a concrete brewing-industry problem — controlling enzyme and yeast activity — and the notation proved so useful it was exported far beyond its origin, eventually underlying the entire pKa formalism used in organic and biochemistry.

History

- 1884 — Svante Arrhenius proposes that acids ionize in water to give H⁺, establishing the conceptual basis for acid dissociation equilibria.

- 1887 — Wilhelm Ostwald applies mass-action law to weak electrolytes, giving the first quantitative dissociation constants.

- 1909 — Søren Sørensen introduces the pH notation at the Carlsberg Laboratory, establishing the logarithmic convention later extended to pKa.

- 1923 — Brønsted and Lowry independently define acids and bases via proton donation/acceptance, giving pKa its modern conjugate-pair mechanistic meaning.

- 1930s–present — Systematic tabulation of pKa values (Hammett, Bordwell, and successors) turns pKa into the standard quantitative currency of organic reactivity.

Is pKa the same thing as pH?

No — they answer different questions. pH describes the actual hydrogen ion concentration in a specific solution right now: $\text{pH} = -\log_{10}[\text{H}_3\text{O}^+]$ , and it changes every time you add acid, base, or water. pKa is a fixed property of a particular ionizable proton on a particular molecule (in a given solvent and temperature): it describes the equilibrium constant for that proton's transfer to water, and does not change when you dilute the solution or add extra acid elsewhere. The two connect through Henderson–Hasselbalch, $\text{pH} = \text{pKa} + \log_{10}([\text{A}^-]/[\text{HA}])$ , which is exactly how a buffer's pH is calculated from the fixed pKa of its acid component.

Why does a smaller (or more negative) pKa mean a stronger acid?

Because pKa is defined as $-\log_{10}K_a$ , and a stronger acid ionizes more completely, giving a larger $K_a$ . Taking the negative logarithm of a large number gives a small or negative result, so strong acids land at low/negative pKa and weak acids land at high pKa. Mechanistically, a strong acid's conjugate base is comparatively stable (delocalized charge, electronegative atom, resonance, or induction), so the proton-transfer equilibrium shifts far toward products, driving $K_a$ up and pKa down — this connects directly to the idea that conjugate-base stability is the master principle behind acid strength.

Can pKa be negative, and what does that physically mean?

Yes. A negative pKa simply means $K_a > 1$ , i.e. the acid is ionized to an extent greater than 1 (in the sense of the equilibrium expression), meaning the proton-transfer reaction is thermodynamically favorable even referenced to 1 M standard states — the molecule essentially always gives up its proton to water. Hydrochloric acid (pKa around −6 to −7 depending on the estimate) and sulfuric acid's first ionization (around −3) are common examples; these acids are conventionally described as "fully dissociated" in dilute aqueous solution precisely because their pKa values are so far below the ambient pH range chemists usually work in.

Why is pKa usually quoted for water as solvent — does it change in other solvents?

By convention, an unlabeled pKa value means the aqueous pKa, because water is cheap, universal, and biologically dominant, so it became the default reference solvent historically. But pKa absolutely changes with solvent, sometimes drastically: water strongly stabilizes charged species (both the ionized A⁻ and H₃O⁺) through hydrogen bonding and its high dielectric constant, so many acids appear far weaker in solvents that stabilize charge poorly, such as DMSO. Acetic acid's pKa rises from 4.76 in water to about 12.6 in DMSO — the intrinsic proton affinity hasn't changed, but the solvent's ability to stabilize the resulting ions has, which is why Bordwell's DMSO pKa tables (widely used for carbanion and radical stability comparisons) must never be directly compared numerically to aqueous pKa tables.

Does a compound need to have measurable Ka in water to be assigned a pKa?

Not necessarily — many pKa values quoted for very weak "acids" (alkane C–H bonds, ammonia N–H, and similar) are extrapolated or computed rather than measured directly in water, because the corresponding equilibrium concentration of ionized species in aqueous solution would be immeasurably, even physically meaninglessly, small. These extrapolated values (often obtained via non-aqueous measurements bridged by known reference compounds, or via computational thermodynamics) are still useful and self-consistent for ranking relative acidities, even though no titration curve in a beaker of water could ever confirm them directly.

Why does the article emphasize that pKa applies to "one specific proton," not a whole molecule?

Because most real molecules — amino acids, nucleotides, many drugs — have several distinct ionizable sites, each governed by its own independent (or nearly independent) proton-transfer equilibrium and its own pKa. Citric acid has three carboxylic acid pKa values; a generic amino acid like glycine has separate pKa values for its carboxylic acid (~2.3) and its ammonium group (~9.6). Treating "the pKa of glycine" as a single number would erase exactly the information — which proton ionizes under which pH conditions — that pKa exists to communicate.

How is pKa connected to what comes next — predicting reaction direction?

Once you know the pKa of the acid you start with and the pKa of the conjugate acid formed on the product side of a proton transfer, the equilibrium constant for the whole reaction is just the ratio of the two $K_a$ values, so the pKa difference (not either value alone) tells you which side is favored and by how much. This is the immediate next step built directly on the definitions here, and it in turn rests on the even deeper structural question of why one conjugate base is more stable than another — the master principle governing every pKa value ever tabulated.