{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"weak-acid-ph"},"result":{"entity_type":"calculator","id":"weak-acid-ph","calculator_id":"weak-acid-ph","canonical_url":"https://tttkmbb.com/chemistry/weak-acid-ph","name":"Weak Acid pH Calculator","title":"Weak Acid pH Calculator – Exact pH of a Weak Acid or Weak Base from Ka/pKa (Kb/pKb) and Concentration","category":"chemistry","category_name":"Chemistry","tool_name":"calculate_weak_acid_ph","featured_mcp_tool":false,"description":"Computes pH, pOH, [H⁺], [OH⁻] and percent ionization of a monoprotic weak acid or monobasic weak base from its dissociation constant (Ka/pKa or Kb/pKb) and nominal concentration by solving the equilibrium quadratic exactly, and compares the result with the √(K·C) approximation.","use_when":"You know the Ka (pKa) of a weak acid such as acetic acid, or the Kb (pKb) of a weak base such as ammonia, and its concentration, and need the pH or the degree of ionization of the solution.","do_not_use_when":"The acid or base is strong and fully dissociated (use ph), the solution also contains the conjugate salt (a buffer: use henderson-hasselbalch), or the acid is polyprotic with a second dissociation that matters (H2SO4, H3PO4 at low concentration).","inputs":[{"name":"species","label":"Species","type":"enum","required":false,"default":"weak_acid","values":[{"value":"weak_acid","label":"Weak acid (uses Ka)","aliases":["acid"]},{"value":"weak_base","label":"Weak base (uses Kb)","aliases":["base"]}],"description":"Whether the solute is a weak acid (Ka) or a weak base (Kb).","example":"weak_acid"},{"name":"ka","label":"Ka","type":"number","required":false,"max":10000000000,"exclusive_min":0,"description":"Acid dissociation constant (acetic acid 1.8×10⁻⁵, HF 6.3×10⁻⁴, HCN 6.2×10⁻¹⁰). Alternative to pka; for a weak base it is read as the Ka of the conjugate acid.","example":0.000018},{"name":"pka","label":"pKa","type":"number","required":false,"min":-10,"max":25,"description":"−log10 Ka (acetic acid 4.76, NH4⁺ 9.25). Alternative to ka."},{"name":"kb","label":"Kb","type":"number","required":false,"max":10000000000,"exclusive_min":0,"description":"Base dissociation constant (ammonia 1.8×10⁻⁵, methylamine 4.4×10⁻⁴). Alternative to pkb; for a weak acid it is read as the Kb of the conjugate base."},{"name":"pkb","label":"pKb","type":"number","required":false,"min":-10,"max":25,"description":"−log10 Kb (ammonia 4.75). Alternative to kb."},{"name":"concentration_mol_l","label":"Nominal concentration","type":"number","unit":"mol/L","required":true,"max":100,"exclusive_min":0,"description":"Analytical (formal) concentration of the acid or base before dissociation.","example":0.1}],"outputs":[{"name":"ph","label":"pH","type":"number","decimals":3,"description":"−log10[H⁺]."},{"name":"poh","label":"pOH","type":"number","decimals":3,"description":"−log10[OH⁻] = 14 − pH at 25 °C."},{"name":"h_concentration_mol_l","label":"[H⁺]","type":"number","unit":"mol/L","decimals":15,"description":"Hydrogen-ion concentration at equilibrium."},{"name":"h_concentration_text","label":"[H⁺] (scientific)","type":"string","decimals":4,"description":"[H⁺] in scientific notation, mol/L."},{"name":"oh_concentration_mol_l","label":"[OH⁻]","type":"number","unit":"mol/L","decimals":15,"description":"Hydroxide-ion concentration at equilibrium (Kw / [H⁺])."},{"name":"oh_concentration_text","label":"[OH⁻] (scientific)","type":"string","decimals":4,"description":"[OH⁻] in scientific notation, mol/L."},{"name":"percent_ionization","label":"Percent ionization","type":"number","unit":"%","decimals":2,"description":"100 × dissociated fraction: [H⁺]/C for an acid, [OH⁻]/C for a base."},{"name":"approximate_ph","label":"pH by √(K·C) approximation","type":"number","decimals":3,"description":"pH obtained by assuming the dissociated amount is negligible against C ([H⁺] ≈ √(Ka·C), or [OH⁻] ≈ √(Kb·C))."},{"name":"approximation_valid","label":"Approximation valid","type":"boolean","decimals":4,"description":"true when C / K > 100 and ionization is below 5 %, the usual textbook criterion for using √(K·C)."},{"name":"dissociation_constant_used","label":"K used","type":"number","decimals":12,"description":"Ka (acid) or Kb (base) used in the quadratic."},{"name":"pka_used","label":"pKa","type":"number","decimals":3,"description":"pKa of the acid, or of the conjugate acid when a weak base is entered (pKa = 14 − pKb)."},{"name":"pkb_used","label":"pKb","type":"number","decimals":3,"description":"pKb of the base, or of the conjugate base when a weak acid is entered (pKb = 14 − pKa)."}],"input_schema":{"type":"object","properties":{"species":{"description":"Whether the solute is a weak acid (Ka) or a weak base (Kb).","type":"string","enum":["weak_acid","weak_base"],"default":"weak_acid","examples":["weak_acid"]},"ka":{"description":"Acid dissociation constant (acetic acid 1.8×10⁻⁵, HF 6.3×10⁻⁴, HCN 6.2×10⁻¹⁰). Alternative to pka; for a weak base it is read as the Ka of the conjugate acid.","type":"number","maximum":10000000000,"exclusiveMinimum":0,"examples":[0.000018]},"pka":{"description":"−log10 Ka (acetic acid 4.76, NH4⁺ 9.25). Alternative to ka.","type":"number","minimum":-10,"maximum":25},"kb":{"description":"Base dissociation constant (ammonia 1.8×10⁻⁵, methylamine 4.4×10⁻⁴). Alternative to pkb; for a weak acid it is read as the Kb of the conjugate base.","type":"number","maximum":10000000000,"exclusiveMinimum":0},"pkb":{"description":"−log10 Kb (ammonia 4.75). Alternative to kb.","type":"number","minimum":-10,"maximum":25},"concentration_mol_l":{"description":"Analytical (formal) concentration of the acid or base before dissociation. Unit: mol/L.","type":"number","maximum":100,"exclusiveMinimum":0,"examples":[0.1],"x-unit":"mol/L"}},"additionalProperties":false,"required":["concentration_mol_l"]},"output_schema":{"type":"object","properties":{"ph":{"description":"−log10[H⁺].","type":"number"},"poh":{"description":"−log10[OH⁻] = 14 − pH at 25 °C.","type":"number"},"h_concentration_mol_l":{"description":"Hydrogen-ion concentration at equilibrium. Unit: mol/L.","type":"number","x-unit":"mol/L"},"h_concentration_text":{"description":"[H⁺] in scientific notation, mol/L.","type":"string"},"oh_concentration_mol_l":{"description":"Hydroxide-ion concentration at equilibrium (Kw / [H⁺]). Unit: mol/L.","type":"number","x-unit":"mol/L"},"oh_concentration_text":{"description":"[OH⁻] in scientific notation, mol/L.","type":"string"},"percent_ionization":{"description":"100 × dissociated fraction: [H⁺]/C for an acid, [OH⁻]/C for a base. Unit: %.","type":"number","x-unit":"%"},"approximate_ph":{"description":"pH obtained by assuming the dissociated amount is negligible against C ([H⁺] ≈ √(Ka·C), or [OH⁻] ≈ √(Kb·C)).","type":"number"},"approximation_valid":{"description":"true when C / K > 100 and ionization is below 5 %, the usual textbook criterion for using √(K·C).","type":"boolean"},"dissociation_constant_used":{"description":"Ka (acid) or Kb (base) used in the quadratic.","type":"number"},"pka_used":{"description":"pKa of the acid, or of the conjugate acid when a weak base is entered (pKa = 14 − pKb).","type":"number"},"pkb_used":{"description":"pKb of the base, or of the conjugate base when a weak acid is entered (pKb = 14 − pKa).","type":"number"}}},"formula":"Acid: [H⁺] = (−Ka + √(Ka² + 4·Ka·C)) / 2, pH = −log10[H⁺], pOH = 14 − pH. Base: [OH⁻] = (−Kb + √(Kb² + 4·Kb·C)) / 2, pOH = −log10[OH⁻], pH = 14 − pOH. percent_ionization = 100 × [H⁺]/C (or [OH⁻]/C); approximate: [H⁺] ≈ √(Ka·C); Ka = 10^(−pKa); pKa + pKb = 14","method":"Exact solution of K = x² / (C − x) for a single dissociation step, evaluated in the equivalent form 2·K·C / (K + √(K² + 4·K·C)) to avoid rounding loss. Assumes 25 °C (Kw = 1.0×10⁻¹⁴), unit activity coefficients and neglects the H⁺ from water, which only matters when the result is within about a factor of 10 of 10⁻⁷ mol/L.","sources":[{"name":"Wikipedia – Acid dissociation constant","url":"https://en.wikipedia.org/wiki/Acid_dissociation_constant","type":"reference","retrieved_at":"2026-09-24"},{"name":"OpenStax Chemistry 2e – 14.3 Relative Strengths of Acids and Bases","url":"https://openstax.org/books/chemistry-2e/pages/14-3-relative-strengths-of-acids-and-bases","type":"textbook","retrieved_at":"2026-09-24"},{"name":"Wikipedia – pH","url":"https://en.wikipedia.org/wiki/PH","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"0.10 M acetic acid, Ka 1.8×10⁻⁵","inputs":{"species":"weak_acid","ka":0.000018,"concentration_mol_l":0.1},"expected":{"ph":2.875,"poh":11.125,"h_concentration_mol_l":0.0013327,"h_concentration_text":"1.333e-3","percent_ionization":1.33,"approximate_ph":2.872,"approximation_valid":true,"pka_used":4.745},"url":"https://tttkmbb.com/api/v1/calculate/weak-acid-ph?species=weak_acid&ka=0.000018&concentration_mol_l=0.1"},{"name":"0.10 M ammonia, Kb 1.8×10⁻⁵","inputs":{"species":"weak_base","kb":0.000018,"concentration_mol_l":0.1},"expected":{"poh":2.875,"ph":11.125,"oh_concentration_mol_l":0.0013327,"percent_ionization":1.33,"approximate_ph":11.128,"approximation_valid":true,"pkb_used":4.745,"pka_used":9.255},"url":"https://tttkmbb.com/api/v1/calculate/weak-acid-ph?species=weak_base&kb=0.000018&concentration_mol_l=0.1"}],"faq":[{"q":"When is the √(Ka·C) shortcut good enough?","a":"When C/Ka exceeds about 100 (equivalently ionization under 5 %) the error is below 0.02 pH units; for dilute or relatively strong weak acids (HF, HNO2, chloroacetic acid) the exact quadratic reported here differs noticeably."},{"q":"I only have the pKa of the conjugate acid of my base.","a":"Enter species=weak_base with that pka: the calculator converts with Kb = Kw / Ka (pKb = 14 − pKa), e.g. NH4⁺ pKa 9.25 gives Kb 1.8×10⁻⁵ for ammonia."},{"q":"Why is the pH of a very dilute weak acid not what this gives?","a":"Below about 10⁻⁶ mol/L of H⁺ the autoionisation of water contributes comparably and the true pH approaches 7 from below; the calculator flags this case in a note but does not solve the full charge-balance cubic."}],"tags":["weak acid ph","weak base ph","ka","pka","percent ionization","acid dissociation constant"],"related":[{"calculator_id":"ph","reason":"pH of strong acids and bases from their concentration."},{"calculator_id":"henderson-hasselbalch","reason":"pH when the conjugate base or acid is also present (buffer)."},{"calculator_id":"titration","reason":"Titrant volume to neutralise this acid or base."}],"links":{"html":"https://tttkmbb.com/chemistry/weak-acid-ph","markdown":"https://tttkmbb.com/chemistry/weak-acid-ph.md","json":"https://tttkmbb.com/chemistry/weak-acid-ph.json","api":"https://tttkmbb.com/api/v1/calculate/weak-acid-ph","schema":"https://tttkmbb.com/api/v1/calculators/weak-acid-ph","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:46:15Z","next_actions":[{"tool":"run_calculator","calculator_id":"weak-acid-ph","reason":"Run Weak Acid pH Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/chemistry/weak-acid-ph.md"}}