# Buffer solution A **buffer solution** is an aqueous [[Solution_(chemistry)|solution]] containing a weak [[Acid|acid]] together with its [[Conjugate_(acid-base_theory)|conjugate]] base, or a weak [[Base_(chemistry)|base]] with its conjugate acid, in comparable amounts, so that its [[PH|pH]] changes only slightly when a small amount of strong acid or base is added.[^os-buffers] The weak acid absorbs added hydroxide and the conjugate base absorbs added hydronium, and as long as both partners remain in appreciable quantity the pH stays near the acid's p*K*a, following the [[Henderson–Hasselbalch_equation|Henderson–Hasselbalch equation]] `pH = pKa + log10([A−]/[HA])`.[^os-buffers] In the microsim below two beakers stand side by side. The left one holds 100 mL of a buffer, 0.10 mol/L acetic acid with 0.10 mol/L sodium acetate, at pH 4.74; the right one holds water already adjusted to the same pH 4.74 with a trace of strong acid. The reader slides the volume of 0.10 mol/L [[Sodium_hydroxide|sodium hydroxide]] added to both, from 0 to 120 mL, and two pH traces are drawn. The buffer's trace stays nearly flat by `pH = pKa + log10(n_A−/n_HA)` until the acid is almost used up, near 90 mL, and only then climbs; the unbuffered trace leaps with the first millilitre, from 4.74 to 10.99, as the book's Example 14.20 predicts.[^os-buffers] The equation the sim answers is the ratio one: how much base does it take to move the ratio of acetate to acetic acid, and therefore the pH, by a given amount. On Wikitube's [[Chemistry]] flagship this page is the main article for the Part VIII section *Buffers*, following [[Acid_dissociation_constant]] and preceding [[Titration]], whose curve is the buffer's own trace continued through the equivalence point. ## Principles A buffer works by [[Le_Chatelier's_principle|Le Chatelier's principle]] applied to the weak-acid [[Chemical_equilibrium|equilibrium]] `HA + H2O ⇌ H3O+ + A−`. Added hydroxide removes hydronium, and the reservoir of HA replaces it by ionizing a little more; added hydronium is consumed by the reservoir of A⁻. In either direction the reaction that matters is nearly complete, `OH− + HA → A− + H2O` or `H3O+ + A− → HA + H2O`, so the added strong reagent is converted into a small change in the *ratio* of the two partners rather than a large change in free hydronium.[^os-buffers] Because pH depends on the logarithm of that ratio, the change is small twice over: the ratio moves by a few percent, and the logarithm of a few percent is a few hundredths of a unit. The Portal Book's Example 14.20 is the sim's default state and its test. The buffer holds 0.010 mol of acetic acid and 0.010 mol of acetate in 100 mL, pH 4.74; adding 1.0 mL of 0.10 mol/L NaOH, 1.0×10⁻⁴ mol, converts that much acid to acetate, leaving 0.0099 mol against 0.0101 mol, and the pH becomes 4.75.[^os-buffers] Unbuffered water at pH 4.74 receiving the same millilitre ends with 9.9×10⁻⁴ mol/L of free hydroxide, pOH 3.00 and pH 10.99: the same drop of base moves one beaker by 0.01 unit and the other by 6.25 units.[^os-buffers] The book's check problem runs the other way, 1.0 mL of 0.10 mol/L HCl into 100 mL of unbuffered water at pH 4.74, and lands at pH 3.00.[^os-buffers] Weak-acid buffers such as acetate suit pH values below 7, and weak-base buffers such as ammonia with ammonium chloride suit values above it, because each is useful only within about one unit of its own pKa.[^os-buffers] ### Buffer capacity A buffer is not inexhaustible. Its capacity is the amount of strong acid or base it can absorb per unit change of pH, a quantity Van Slyke defined in 1922 as `β = dn/d(pH)`, with n the moles of base added per litre.[^vanslyke1922] For a single weak-acid pair at total concentration C the capacity is `β = 2.303·(Kw/[H+] + [H+] + C·Ka·[H+]/(Ka + [H+])²)`, which peaks where [H⁺] = Ka, that is at pH = pKa, with a maximum of `β_max = 2.303·C/4 ≈ 0.58·C` (a textbook result, computed here). For the sim's buffer, C = 0.20 mol/L, that is about 0.115 mol of base per litre per pH unit; the 1.0×10⁻³ mol/L delivered by the first millilitre therefore moves the pH by 0.0087, which rounds to the book's 4.74 → 4.75.[^os-buffers] Capacity falls away as the ratio departs from one. The Portal Book's working rule is that a buffer has lost its usefulness once one partner falls below about 10 percent of the other, and its Figure 14.17 shows a rise of a full pH unit once the acid has dropped to 11 percent of the acetate.[^os-buffers] In the sim that point arrives at about 82 mL of base, where the remaining 0.0018 mol of acid stands against 0.0182 mol of acetate; the trace, which has climbed only from 4.74 to about 5.7 in the first 80 mL, then steepens, passing 6.0 near 90 mL and 7.0 near 99 mL before jumping through the equivalence at 100 mL, where the last acid is consumed, to pH 8.9 and on toward 12 as free hydroxide accumulates. The two traces are the article's whole lesson: the same millilitre, 0.01 pH in one beaker and 6.25 in the other. ## Calculating buffer pH The working equation comes from the acid dissociation constant rearranged and put into logarithms. From `Ka = [H3O+][A−]/[HA]`, `[H3O+] = Ka·[HA]/[A−]`, and taking the negative logarithm of both sides gives `pH = pKa + log10([A−]/[HA])`, the Henderson–Hasselbalch equation, first published by Lawrence Henderson in 1908 in concentration form and put into the logarithmic form by Karl Hasselbalch in 1917.[^henderson1908][^hasselbalch1917] It rests on the same "x is small" assumption as the weak-acid shortcut: the equilibrium concentrations of HA and A⁻ are taken equal to the amounts mixed, which holds when both are large compared with Ka and with Kw/Ka.[^os-buffers] Because volumes cancel in the ratio, the equation can be written in moles, `pH = pKa + log10(n_A−/n_HA)`, and dilution does not change the pH of a buffer until the concentrations become small enough for the assumption to fail. ### Monoprotic acids For the acetate buffer the stoichiometry is a subtraction. After V mL of 0.10 mol/L NaOH, `n_HA = 0.010 − 0.10·V/1000` and `n_A− = 0.010 + 0.10·V/1000`, so the Henderson–Hasselbalch trace is `pH = 4.74 + log10((0.010 + 1.0×10⁻⁴·V)/(0.010 − 1.0×10⁻⁴·V))`: 4.75 at 1.0 mL, 5.22 at 50 mL, 6.02 at 90 mL and 7.04 at 99 mL (values computed here from the book's pKa). At 100 mL the denominator is zero and the equation is undefined, and just before it the assumption behind the equation has already failed, because the small amount of hydroxide produced by hydrolysis of acetate is no longer negligible against the vanishing acid.[^os-buffers] The sim therefore does not use Henderson–Hasselbalch to draw its buffer trace. It solves the charge balance `[H+] + [Na+] = [OH−] + C_A·Ka/(Ka + [H+])`, where C_A is the total acetate-plus-acetic-acid concentration after dilution and [Na⁺] counts both the sodium acetate and the sodium hydroxide, by sixty steps of bisection in log10[H⁺] for each of 240 volumes. That equation is exact within the concentration model, survives the point n_HA → 0, and reproduces the Henderson–Hasselbalch numbers wherever the latter is valid: 4.745 at 0 mL, 4.754 at 1.0 mL, 6.02 at 90 mL, 7.04 at 99 mL, then 8.87 at exactly 100 mL, where the beaker is simply 0.10 mol/L sodium acetate in 200 mL, 10.70 at 101 mL and 11.96 at 120 mL (all computed here). The HUD shows the Henderson–Hasselbalch form because it is the equation a reader should carry away, and a footnote on the canvas says that the trace is drawn from the charge balance so it does not break at 100 mL. The unbuffered beaker is drawn from the same charge balance with C_A = 0 and a starting 1.8×10⁻⁵ mol/L of strong acid, which is what pH 4.74 means for pure water.[^os-buffers] ### Polyprotic acids A polyprotic acid supplies one buffer pair per dissociation step, each centred on its own pKa. Phosphoric acid's second step, H₂PO₄⁻/HPO₄²⁻, has Ka2 = 6.2×10⁻⁸ and pKa2 = 7.21, which is why phosphate buffers hold the pH of most biochemical experiments; its first and third steps, pKa1 = 2.12 and pKa3 = 12.38, buffer at the ends of the scale.[^os-appH] Carbonic acid's first step, pKa1 = 6.37, together with the fact that carbonic acid is in equilibrium with dissolved carbon dioxide, is the chemistry of the [[Bicarbonate_buffer_system|bicarbonate buffer]] in blood: arterial pH is held between 7.35 and 7.45, and at the normal 7.40 the bicarbonate-to-carbonic-acid ratio is 20:1, with the lungs adjusting the carbonic acid side through breathing and the kidneys the bicarbonate side.[^openstax-ap] Because the steps of a polyprotic acid are usually separated by several pKa units, each pair can be treated with the monoprotic equation while the pH is within a unit of its pKa; between the steps, near the intermediate ion's own pH, the two neighbouring constants both matter and the full charge balance is again the honest method. ## Applications Buffers appear wherever a reaction's rate, a measurement's reading or an organism's survival depends on pH. Chemists use them to hold a constant pH while studying a reaction, to calibrate pH meters, and to set the conditions of [[Titration|titrations]] and separations; biologists keep cells, [[Enzyme|enzymes]] and nucleic acids in buffered media because most proteins denature outside a narrow pH window; and the body's own buffers, of which bicarbonate is the largest in blood, are a working example of chemical [[Homeostasis|homeostasis]].[^openstax-ap] In [[Analytical_chemistry|analytical chemistry]] the standard buffers assigned by IUPAC are the reference points of the pH scale itself, and a laboratory meter is meaningful only against them. ### Simple buffering agents The classical buffers are the conjugate pairs of the common weak acids and bases. Acetic acid with sodium acetate covers pH 3.7 to 5.7, one unit either side of pKa 4.74; ammonia with ammonium chloride covers 8.2 to 10.2 around the ammonium pKa of 9.25; dihydrogen and monohydrogen phosphate cover 6.2 to 8.2 around pKa2 7.21; and citric acid, with three closely spaced dissociations, gives a broad range in the acid region.[^os-appH] Each is prepared either by mixing the acid and a salt of its conjugate base, or by partly neutralizing the acid with strong base, which produces the conjugate base in place; the sim's beaker can be read as the second recipe, since every millilitre of NaOH turns acetic acid into acetate. The useful range in each case is pKa ± 1, the span over which neither partner drops below a tenth of the other.[^os-buffers] ### "Universal" buffer mixtures A single conjugate pair buffers over about two pH units. To cover the whole scale, mixtures of several acids with well-spaced pKa values are titrated with strong base, so that as one pair is exhausted the next takes over. The best known is the Britton–Robinson buffer of 1931, a mixture of phosphoric, acetic and boric acids titrated with sodium hydroxide, which gives a nearly linear relation between added base and pH from about 2 to 12.[^britton1931] Universal mixtures trade capacity for range, since only one component is active at any pH, and their ionic strength changes along the series, which is why they serve for surveys and indicator work rather than for precise thermodynamic measurements. ### Common buffer compounds used in biology Biological work needs buffers between pH 6 and 8 that do not bind metal ions, do not cross cell membranes, absorb no light in the ultraviolet used for assays and are chemically inert. Phosphate, the traditional choice, meets the pH requirement but precipitates calcium and magnesium and takes part in metabolism; Tris, the amine buffer of molecular biology, has a pKa that shifts markedly with temperature. In 1966 Norman Good and colleagues set out these design criteria and synthesized a family of zwitterionic sulfonic-acid and amine buffers, now called Good's buffers, including MES, PIPES, MOPS and HEPES, chosen for pKa values in the physiological range, high water solubility, minimal membrane permeability and negligible metal binding.[^good1966] HEPES in particular became the standard buffer for cell culture, and the Good criteria remain the checklist against which a new biological buffer is judged. In every case the buffer is used at a concentration, typically 10 to 100 mmol/L, that gives enough capacity for the acid or base the experiment will produce without dominating the ionic strength. ## See also - [[Henderson–Hasselbalch_equation]] - [[Bicarbonate_buffer_system]] - [[Acid_dissociation_constant]] - [[PH]] - [[Titration]] - [[Common-ion_effect]] - [[Equilibrium_constant]] ## Notes All pH values on the buffer trace after the first millilitre (5.22, 6.02, 7.04, 8.87, 10.70, 11.96), the 82 mL exhaustion point and the buffer capacity of 0.115 mol/L per pH unit are computed here from the Portal Book's Ka = 1.8×10⁻⁵; the book's printed tests are 4.74 → 4.75 for the buffer, 4.74 → 10.99 for the unbuffered water and 4.74 → 3.00 for the acid check problem. The Portal Book's printed pKa for the blood buffer was lost in text extraction and its prose value does not agree with its own worked ratio, so no blood number is used as a sim test. ## References [^os-buffers]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14 "Acid-Base Equilibria", §14.6 "Buffers", pp. 697–701: how buffers work; Example 14.20 (100 mL of 0.10 mol/L CH₃CO₂H and 0.10 mol/L NaCH₃CO₂, pH 4.74 → 4.75 on adding 1.0 mL of 0.10 mol/L NaOH; unbuffered water 4.74 → 10.99) and its check problem (4.74 → 3.00 with 1.0 mL of 0.10 mol/L HCl); the 10 % rule and Figure 14.17; weak-acid buffers for pH < 7; the Henderson–Hasselbalch equation and its assumption. https://openstax.org/books/chemistry-atoms-first-2e/pages/14-6-buffers [^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 (acetic acid 1.8×10⁻⁵; phosphoric acid 7.5×10⁻³, 6.2×10⁻⁸, 4.2×10⁻¹³; carbonic acid 4.3×10⁻⁷); pKa values computed from them. Ammonium Ka = 5.6×10⁻¹⁰ from Chapter 14, p. 679. https://openstax.org/books/chemistry-atoms-first-2e/pages/h-ionization-constants-of-weak-acids [^vanslyke1922]: Van Slyke, Donald D. (1922). "On the measurement of buffer values and on the relationship of buffer value to the dissociation constant of the buffer and the concentration and reaction of the buffer solution." *Journal of Biological Chemistry* 52 (2): 525–570. https://doi.org/10.1016/S0021-9258(18)85845-8 [^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 [^hasselbalch1917]: Hasselbalch, K. A. (1917). "Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl." *Biochemische Zeitschrift* 78: 112–144. [^openstax-ap]: OpenStax (2022). *Anatomy and Physiology 2e*. §26.4 "Acid-Base Balance" and §26.5 "Disorders of Acid-Base Balance": arterial blood pH 7.35–7.45; the 20:1 bicarbonate to carbonic acid ratio at pH 7.40; respiratory and renal regulation. https://openstax.org/books/anatomy-and-physiology-2e/pages/26-5-disorders-of-acid-base-balance [^britton1931]: Britton, H. T. S.; Robinson, R. A. (1931). "CXCVIII.—Universal buffer solutions and the dissociation constant of veronal." *Journal of the Chemical Society (Resumed)*: 1456–1462. https://doi.org/10.1039/JR9310001456 [^good1966]: Good, Norman E.; Winget, G. Douglas; Winter, Wilhelmina; Connolly, Thomas N.; Izawa, Seikichi; Singh, Raizada M. M. (1966). "Hydrogen Ion Buffers for Biological Research." *Biochemistry* 5 (2): 467–477. https://doi.org/10.1021/bi00866a011 ## External links - [§14.6 Buffers — OpenStax Chemistry: Atoms First 2e](https://openstax.org/books/chemistry-atoms-first-2e/pages/14-6-buffers), the Portal Book section behind the sim's numbers - [§26.4 Acid-Base Balance — OpenStax Anatomy and Physiology 2e](https://openstax.org/books/anatomy-and-physiology-2e/pages/26-4-acid-base-balance) <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Buffer_solution.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Buffer solution* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Buffer_solution.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Buffer_solution.html" data-title="Buffer solution"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Buffer_solution) : [Wikitube](https://en.wikitube.io/wiki/Buffer_solution) · pinned revision [1371829235](https://en.wikipedia.org/w/index.php?oldid=1371829235) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K41 · sim pending (matter/Buffer_solution).*