# Acid dissociation constant The **acid dissociation constant**, *K*a, is the [[Equilibrium_constant|equilibrium constant]] for the reaction in which an [[Acid|acid]] HA hands a [[Proton|proton]] to [[Water|water]], `HA + H2O ⇌ H3O+ + A−`, written `Ka = [H3O+][A−]/[HA]`.[^os-ka] Its negative logarithm, `pKa = −log10 Ka`, is the working measure of [[Acid_strength|acid strength]]: the smaller the pKa, the more completely the acid ionizes at a given concentration. Acetic acid has Ka = 1.8×10⁻⁵ and pKa 4.74, so in a 0.10 mol/L solution only about 1.3 percent of its molecules have given up their proton at any instant.[^os-ka] That percentage is not a property of the acid alone. In the microsim below the reader slides the starting concentration C₀ of acetic acid across five decades, from 10⁻⁵ to 1 mol/L, and watches the fraction ionized climb as the solution is diluted. Two curves are drawn: the exact root of `Ka = x²/(C0 − x)`, and the textbook shortcut `x ≈ sqrt(Ka·C0)` that assumes x is small next to C₀. The question the sim answers is when that assumption is honest; a red band marks the concentrations below about 7×10⁻³ mol/L where the shortcut fails the 5 percent test, and two [[PH|pH]] readouts show how far apart the answers drift. On Wikitube's [[Chemistry]] flagship this page is the main article for the Part VIII section *Weak acids: the dissociation constant*, between [[PH]], whose sim moves the neutral point of water, and [[Buffer_solution]], whose sim shows what a conjugate pair does when base is added. ## Theoretical background In the [[Brønsted–Lowry_acid–base_theory|Brønsted–Lowry]] picture an acid is a proton donor and a base a proton acceptor, and every acid–base reaction is a competition between two bases for one proton. When HA dissolves in water the competitors are the [[Conjugate_(acid-base_theory)|conjugate]] base A⁻ and the water molecule; Ka records who wins. A strong acid such as HCl loses the competition so completely that no measurable HA survives, while a weak acid such as acetic acid keeps most of its protons.[^os-ka] Because the reaction is a genuine [[Chemical_equilibrium|equilibrium]], adding either product pushes it back: dissolving sodium acetate in acetic acid lowers the [[Hydronium|hydronium]] concentration, the [[Common-ion_effect|common-ion effect]] on which buffers are built, and diluting the solution pulls the equilibrium toward the ions, which is the effect the microsim shows. The constant is also a thermodynamic quantity, fixed by the standard Gibbs energy of the proton transfer, which ties the acid-strength ladder to temperature, and it belongs to the acid in a particular solvent rather than to the acid alone. ## Definitions For a monoprotic acid the definition is `Ka = [H3O+][A−]/[HA]`, with concentrations at equilibrium in mol/L and the solvent water omitted because its concentration is effectively constant.[^os-ka] The logarithmic form `pKa = −log10 Ka` turns a range of twenty powers of ten into a number between about −10 and 50 that can be tabulated and compared; acetic acid's 1.8×10⁻⁵ becomes 4.74, formic acid's 1.8×10⁻⁴ becomes 3.74, and hydrocyanic acid's 4.9×10⁻¹⁰ becomes 9.31.[^os-appH] A [[Base_(chemistry)|base]] has the parallel constant `Kb = [BH+][OH−]/[B]`, and for any conjugate pair `Ka·Kb = Kw`, so that `pKa + pKb = pKw = 14.00` at 25 °C.[^os-ka] A pKa below about 7 marks an acid that is mostly ionized at neutral pH; one above 7 marks an acid that is mostly intact there. The same symbol serves each successive proton of a polyprotic acid, numbered pKa1, pKa2 and so on. ## Equilibrium constant Ka is a member of the general family of equilibrium constants. Strictly it is defined with activities rather than concentrations, so the thermodynamic constant is [[Dimensionless_quantity|dimensionless]] and independent of ionic strength; the concentration constants tabulated for practical work drift slowly with the salt content of the solution. Several notations are in use. ### Cumulative and stepwise constants A polyprotic acid loses its protons in steps, each with its own stepwise constant, K₁ for H₂A → HA⁻ and K₂ for HA⁻ → A²⁻. The cumulative constant for losing both protons at once is their product, β₂ = K₁K₂, so that `log β2 = log K1 + log K2`. ### Association and dissociation constants Coordination chemists usually write the reverse reaction, the association of a proton with a base, whose constant is the reciprocal of the dissociation constant: `K_assoc = 1/Ka`, `log K_assoc = pKa`. Both conventions describe the same equilibrium, and a table must say which it uses. ### Temperature dependence Like every equilibrium constant, Ka obeys the [[Van_'t_Hoff_equation|van 't Hoff equation]], `d ln Ka/dT = ΔH°/(RT²)`, so an endothermic dissociation strengthens with heating. The clearest case is water, whose ion product rises from 1.0×10⁻¹⁴ at 25 °C to 2.4×10⁻¹³ at 80 °C because its self-ionization absorbs heat.[^os-kw] Many carboxylic acids have dissociation enthalpies near zero at room temperature, so their pKa values move by only hundredths over tens of degrees. ### Dimensionality Written in concentrations, Ka has the nominal unit of mol/L for a monoprotic acid; written in activities relative to the standard state it has none. The convention matters when constants are combined: `Ka·Kb = Kw` balances only if both sides use the same concentration scale. ## Strong acids and bases A strong acid is one whose Ka is so large that dissociation is essentially complete in water; hydrochloric, nitric and perchloric acids and the first proton of sulfuric acid are the everyday members.[^os-ka] Water cannot rank them: any acid much stronger than hydronium simply converts to hydronium, so all strong acids look alike in water, the levelling effect, and their negative pKa values are estimated in less basic solvents. Strong bases such as [[Sodium_hydroxide|sodium hydroxide]] are the mirror case. The second proton of sulfuric acid is not strong at all: HSO₄⁻ has Ka = 1.2×10⁻², weak enough that its solutions must be treated by the weak-acid method.[^os-nahso4] ## Monoprotic acids The weak-acid calculation is an ICE table. If C₀ mol/L of HA is dissolved and x mol/L ionizes, the equilibrium concentrations are [H3O⁺] = [A⁻] = x and [HA] = C₀ − x, so `Ka = x²/(C0 − x)`.[^os-ka] Solving the quadratic and discarding the negative root gives the exact answer, `x = (−Ka + sqrt(Ka² + 4·Ka·C0))/2`. The textbook shortcut assumes x ≪ C₀, replaces C₀ − x by C₀ and returns `x ≈ sqrt(Ka·C0)`; the Portal Book's rule is that the shortcut is acceptable when x is less than 5 percent of C₀.[^os-ka] Percent ionization, `100·x/C0`, is the natural display, and it is not a constant: it falls as C₀ rises.[^os-ka] The sim is a single log slider on C₀ from 10⁻⁵ to 1 mol/L, default 0.10, with Ka fixed at the book's 1.80×10⁻⁵ for acetic acid.[^os-ka-acetic] The canvas plots percent ionization against log C₀ twice, from the exact root and from the shortcut, and a marker rides both curves with `pH_exact` and `pH_approx` beside it. At the default 0.10 mol/L the exact root gives x = 1.33×10⁻³ mol/L, 1.33 percent ionized, pH 2.88, and the shortcut 1.34 percent and pH 2.87; the book's pH 2.89 and 1.3 percent are the test the sim must pass. At C₀ = 6.8×10⁻³ mol/L the exact fraction reaches 5.0 percent, and from there down the axis is shaded red: at 10⁻³ mol/L the exact answer is 12.5 percent ionized (pH 3.90) against the shortcut's 13.4 percent (pH 3.87), and at 10⁻⁵ mol/L the exact answer is 72 percent while the shortcut returns 134 percent, more acid ionized than was dissolved. The threshold and the low-concentration numbers are derived from the book's Ka, not printed in it. Below about 10⁻⁶ mol/L the model itself fails, because the 10⁻⁷ mol/L of hydronium that water supplies on its own becomes comparable to x; the sim greys out that end of the slider and says why.[^os-ka] The same test catches the sulfate case: for 0.50 mol/L sodium hydrogen sulfate x is about 15 percent of C₀, so only the quadratic is honest.[^os-nahso4] ## Polyprotic acids An acid with more than one acidic proton dissociates in stages, each stage weaker than the last because a proton must leave an increasingly negative ion. Carbonic acid has Ka1 = 4.3×10⁻⁷ and Ka2 = 4.7×10⁻¹¹; phosphoric acid has Ka1 = 7.5×10⁻³, Ka2 = 6.2×10⁻⁸ and Ka3 = 4.2×10⁻¹³; sulfurous acid has 1.6×10⁻² and 6.4×10⁻⁸.[^os-appH] Because successive constants typically differ by four or more powers of ten, the first dissociation fixes the hydronium concentration almost alone and the later ones can be treated afterwards with that value as an input: for 0.033 mol/L carbonic acid the first step gives [H3O⁺] = 1.2×10⁻⁴ mol/L, and in a saturated hydrogen sulfide solution near 0.1 mol/L the first step gives 9.4×10⁻⁵ mol/L while the doubly charged sulfide ion sits near 10⁻¹⁹ mol/L.[^os-polyprotic] The gap between the constants is also what makes the intermediate ions, bicarbonate and hydrogen phosphate, good buffers at very different pH values, a point taken up in the [[Buffer_solution]] article. ### Isoelectric point A molecule carrying both an acidic and a basic group, such as an amino acid, is a polyprotic acid whose fully protonated form is a cation and whose fully deprotonated form is an anion. At one pH the average charge is zero; for two relevant pKa values that isoelectric point is their mean, `pI = (pKa1 + pKa2)/2`, and there the molecule does not migrate in an electric field. ## Bases and basicity The strength of a base is measured by Kb for `B + H2O ⇌ BH+ + OH−`, and the calculation is the acid calculation with hydroxide in place of hydronium.[^os-ka] [[Ammonia]], Kb = 1.8×10⁻⁵, is a weak base of almost exactly acetic acid's weakness as an acid; in 0.0325 mol/L ammonia the shortcut gives [OH⁻] = 7.56×10⁻⁴ mol/L, 2.33 percent ionized.[^os-nh3] Amines and alkaloids are weak bases of the same kind; 0.010 mol/L caffeine reaches pH 11.16.[^os-nh3] ### Basicity expressed as dissociation constant of conjugate acid Modern tables list the Ka of the conjugate acid instead of Kb, since `Ka·Kb = Kw` holds the same information. The ammonium ion has Ka = 5.6×10⁻¹⁰, slightly larger than the 4.9×10⁻¹⁰ of hydrocyanic acid, so ammonium is a slightly stronger acid than HCN and ammonia a slightly weaker base than cyanide.[^os-nh3] One pKa scale then ranks acids and bases together. ## Amphoteric substances Hydrogen carbonate, hydrogen sulfate, dihydrogen phosphate and water can both donate and accept a proton, and which role dominates is decided by comparing the species' Ka with its Kb: hydrogen sulfate, with Ka = 1.2×10⁻² and a negligible Kb, makes an acidic solution, while hydrogen carbonate, with a tiny Ka and a larger Kb, makes a basic one.[^os-nahso4][^os-appH] ### Water self-ionization Water is the reference case: `2H2O ⇌ H3O+ + OH−` with `Kw = 1.0×10⁻¹⁴` at 25 °C, so that pKw = 14.00 and `pH + pOH = pKw`.[^os-kw] The [[Self-ionization_of_water|self-ionization]] grows with temperature, and the [[PH]] microsim moves the neutral point of pure water from 7.00 to about 6.13 between 25 and 100 °C on that account.[^os-kw] ## Acidity in nonaqueous solutions A pKa is a property of the acid *in a solvent*. In a solvent that solvates anions less well than water the conjugate base is less stabilized and the acid looks weaker: in dimethyl sulfoxide, whose acidity scale Bordwell built from hundreds of equilibrium measurements, acetic acid has a pKa of about 12.3 against 4.74 in water.[^bordwell1988] The order of acids can also change between solvents, so comparing values across them needs either a reference acid measured in both or the unified scale, anchored to the gas-phase proton, proposed by Himmel and colleagues in 2010.[^himmel2010] ### Mixed solvents Water–methanol, water–ethanol and water–dioxane mixtures dissolve acids that will not dissolve in water alone. As the organic fraction rises the dielectric constant falls and the measured pKa of a neutral acid rises; values are reported with the solvent composition, and extrapolation back to pure water is common but approximate. ## Factors that affect p<i>K</i>_a values Two things set the constant: how easily the H–A bond gives up its proton and how well the solvent and the molecule itself stabilize the resulting anion. Electron-withdrawing substituents near the acidic hydrogen spread the negative charge and lower the pKa, which is why formic acid (Ka = 1.8×10⁻⁴) is ten times stronger than acetic acid (1.8×10⁻⁵), whose methyl group pushes electron density toward the carboxylate.[^os-appH] Resonance does the same work for carboxylic acids and phenols, spreading the charge over two oxygens or a ring. For binary acids the [[Chemical_bond|bond]] strength dominates: hydrofluoric acid, with the strongest bond to hydrogen among the halogen acids, is the only weak one, Ka = 6.4×10⁻⁴, while its heavier relatives are strong.[^os-appH] Among oxyacids the constant climbs with the number of oxygen atoms not bonded to hydrogen and with the [[Electronegativity|electronegativity]] of the central atom, so hypochlorous acid, HClO, sits at Ka = 2.9×10⁻⁸ while perchloric acid is among the strongest acids known.[^os-appH] ### Thermodynamics The constant is a Gibbs energy in disguise: `ΔG° = −RT ln Ka = 2.303·RT·pKa`, so at 298.15 K each unit of pKa corresponds to 5.71 kJ/mol of standard [[Gibbs_free_energy|Gibbs energy]] (computed with R = 8.314 J/(mol·K)). Splitting ΔG° into [[Enthalpy|enthalpy]] and [[Entropy|entropy]] shows that many weak acids owe their weakness less to a strong bond than to the entropy cost of organizing water around two ions. ## Experimental determination The classic method is potentiometric [[Titration|titration]]: the acid is titrated with strong base while a glass electrode records pH, and at half-equivalence, where [HA] = [A⁻], the measured pH equals pKa, a relation the Portal Book uses for acetic acid (pH 4.74 at 12.50 mL of a 25.00 mL titration).[^os-titration] Spectrophotometry serves when the acid and its anion absorb light differently, since the [[Absorbance|absorbance]] at fixed wavelength tracks the ionized fraction; [[Nuclear_magnetic_resonance|NMR]] chemical shifts do the same for nuclei near the acidic site; and capillary electrophoresis exploits the change in mobility with charge. A 2013 review by Reijenga and co-workers surveys these methods, their sample requirements and the growing role of computational prediction for compounds that cannot be measured.[^reijenga2013] Whatever the method, the value reported must state the temperature and the ionic strength, or the extrapolation to zero ionic strength, because both can move the result by tenths of a unit, and the solvent if it is not water. ### Micro-constants When a molecule has two ionizable groups of similar pKa, the measured macro-constants describe the loss of "a" proton without saying which. Four micro-constants describe the individual sites; they are related to the two macro-constants but cannot be extracted from a titration alone and need a site-specific probe such as NMR. ## Applications and significance The constant decides how a substance is distributed between its charged and neutral forms at any pH, through the [[Henderson–Hasselbalch_equation|Henderson–Hasselbalch equation]] `pH = pKa + log10([A−]/[HA])`.[^henderson1908] That ratio governs buffer design, the absorption of drugs across membranes, which pass mostly in the neutral form, and the speciation of carbon dioxide in seawater, where the fall in pH shifts carbonate toward bicarbonate.[^doney2009] In [[Analytical_chemistry|analytical chemistry]] it fixes which indicator to use; in [[Corrosion|corrosion]] and geochemistry it sets which metal species exist at a given pH. ## Values for common substances From the Portal Book's Appendix H (25 °C); the pKa column is computed.[^os-appH] | Acid | Formula | Ka | pKa | |---|---|---|---| | Hydrogen sulfate ion | HSO₄⁻ | 1.2×10⁻² | 1.92 | | Phosphoric acid (1) | H₃PO₄ | 7.5×10⁻³ | 2.12 | | Hydrofluoric acid | HF | 6.4×10⁻⁴ | 3.19 | | Nitrous acid | HNO₂ | 4.6×10⁻⁴ | 3.34 | | Formic acid | HCO₂H | 1.8×10⁻⁴ | 3.74 | | Acetic acid | CH₃CO₂H | 1.8×10⁻⁵ | 4.74 | | Carbonic acid (1) | H₂CO₃ | 4.3×10⁻⁷ | 6.37 | | Phosphoric acid (2) | H₂PO₄⁻ | 6.2×10⁻⁸ | 7.21 | | Hypochlorous acid | HClO | 2.9×10⁻⁸ | 7.54 | | Ammonium ion | NH₄⁺ | 5.6×10⁻¹⁰ | 9.25 | | Hydrocyanic acid | HCN | 4.9×10⁻¹⁰ | 9.31 | | Carbonic acid (2) | HCO₃⁻ | 4.7×10⁻¹¹ | 10.33 | The ammonium value is from the chapter text rather than the appendix.[^os-nh3] ## See also - [[Acid_strength]] - [[Ionization]] - [[Conjugate_(acid-base_theory)]] - [[PH]] - [[Buffer_solution]] - [[Titration]] - [[Equilibrium_constant]] - [[Henderson–Hasselbalch_equation]] ## Notes The 5 percent boundary of 6.8×10⁻³ mol/L, the percent-ionization values below 0.010 mol/L and the pKa column of the table are computed from the Portal Book's constants, not printed in it. The microsim uses concentrations, not activities. ## References [^os-ka]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14 "Acid-Base Equilibria", §14.3 "Relative Strengths of Acids and Bases", pp. 675–686: the definition of Ka and Kb, Ka·Kb = Kw, percent ionization (0.10 mol/L acetic acid at pH 2.89 → 1.3 %), the ICE-table solution, the "x is small" shortcut and its 5 % test, strong acids, and the neglect of water's own 10⁻⁷ mol/L (p. 682). https://openstax.org/books/chemistry-atoms-first-2e/pages/14-3-relative-strengths-of-acids-and-bases [^os-ka-acetic]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, p. 716: Ka(CH₃CO₂H) = 1.80×10⁻⁵. [^os-appH]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Appendix H "Ionization Constants of Weak Acids", pp. 1111–1114. https://openstax.org/books/chemistry-atoms-first-2e/pages/h-ionization-constants-of-weak-acids [^os-nh3]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.3, p. 679 (Kb(NH₃) = 1.8×10⁻⁵; Ka(NH₄⁺) = 5.6×10⁻¹⁰ compared with Ka(HCN) = 4.9×10⁻¹⁰) and pp. 685–686 (0.0325 mol/L NH₃ with Kb = 1.76×10⁻⁵ → [OH⁻] = 7.56×10⁻⁴ mol/L, 2.33 %; 0.010 mol/L caffeine → pH 11.16). https://openstax.org/books/chemistry-atoms-first-2e/pages/14-3-relative-strengths-of-acids-and-bases [^os-nahso4]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.3, p. 681 (Ka(HSO₄⁻) = 1.2×10⁻²) and p. 686 (0.50 mol/L NaHSO₄: x ≈ 15 % of C₀, so the quadratic must be solved). [^os-polyprotic]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.5 "Polyprotic Acids", pp. 694–695: 0.033 mol/L H₂CO₃ → [H3O⁺] = 1.2×10⁻⁴ mol/L; saturated H₂S (≈0.1 mol/L) → [H3O⁺] = 9.4×10⁻⁵ mol/L and [S²⁻] ≈ 1×10⁻¹⁹ mol/L. [^os-kw]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.1–14.2, pp. 667–670: Kw = 1.0×10⁻¹⁴ at 25 °C and 2.4×10⁻¹³ at 80 °C; the self-ionization is endothermic; pH + pOH = pKw. https://openstax.org/books/chemistry-atoms-first-2e/pages/14-2-ph-and-poh [^os-titration]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7 "Acid-Base Titrations", pp. 702–705: pH = pKa at half-equivalence in the titration of 25.00 mL of 0.100 mol/L acetic acid (Table 14.2). https://openstax.org/books/chemistry-atoms-first-2e/pages/14-7-acid-base-titrations [^bordwell1988]: Bordwell, Frederick G. (1988). "Equilibrium acidities in dimethyl sulfoxide solution." *Accounts of Chemical Research* 21 (12): 456–463. https://doi.org/10.1021/ar00156a004 [^himmel2010]: Himmel, Daniel; Goll, Sascha K.; Leito, Ivo; Krossing, Ingo (2010). "A Unified pH Scale for All Phases." *Angewandte Chemie International Edition* 49 (38): 6885–6888. https://doi.org/10.1002/anie.201000252 [^reijenga2013]: Reijenga, Jetse; van Hoof, Arno; van Loon, Antonie; Teunissen, Bram (2013). "Development of Methods for the Determination of pKa Values." *Analytical Chemistry Insights* 8: 53–71. https://doi.org/10.4137/ACI.S12304 [^henderson1908]: Henderson, Lawrence J. (1908). "Concerning the Relationship Between the Strength of Acids and Their Capacity to Preserve Neutrality." *American Journal of Physiology* 21 (2): 173–179. https://doi.org/10.1152/ajplegacy.1908.21.2.173 [^doney2009]: Doney, Scott C.; Fabry, Victoria J.; Feely, Richard A.; Kleypas, Joan A. (2009). "Ocean Acidification: The Other CO₂ Problem." *Annual Review of Marine Science* 1: 169–192. https://doi.org/10.1146/annurev.marine.010908.163834 ## Further reading - Flowers, Paul; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax, Chapter 14 and Appendices H–I — the Portal Book behind this page. - Reijenga, J.; et al. (2013). "Development of Methods for the Determination of pKa Values." *Analytical Chemistry Insights* 8: 53–71. ## External links - [Appendix H, Ionization Constants of Weak Acids — OpenStax Chemistry: Atoms First 2e](https://openstax.org/books/chemistry-atoms-first-2e/pages/h-ionization-constants-of-weak-acids) - [§14.3 Relative Strengths of Acids and Bases — OpenStax Chemistry: Atoms First 2e](https://openstax.org/books/chemistry-atoms-first-2e/pages/14-3-relative-strengths-of-acids-and-bases) <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Acid_dissociation_constant.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Acid dissociation constant* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Acid_dissociation_constant.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Acid_dissociation_constant.html" data-title="Acid dissociation constant"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Acid_dissociation_constant) : [Wikitube](https://en.wikitube.io/wiki/Acid_dissociation_constant) · pinned revision [1367582159](https://en.wikipedia.org/w/index.php?oldid=1367582159) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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