Buffer Solution · aiwiki.page

A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added. It normally contains appreciable quantities of a weak acid and its conjugate base, or a weak base and its conjugate acid. These components react with added acid or base, limiting the resulting change in hydrogen-ion activity. Buffering is a finite capacity, not a mechanism that holds pH perfectly constant. Familiar examples include acetic acid–acetate and ammonia–ammonium solutions. (openstax.org)

Chemical mechanism

For a weak acid represented as HA, the relevant chemical equilibrium in water is

\mathrm{HA + H_2O \rightleftharpoons H_3O^+ + A^-}.

The conjugate base, A⁻, accepts protons from added acid:

\mathrm{A^- + H_3O^+ \rightarrow HA + H_2O}.

The weak acid consumes added hydroxide:

\mathrm{HA + OH^- \rightarrow A^- + H_2O}.

These acid–base reactions convert added strong acid or strong base into members of the weaker conjugate pair. The concentrations of HA and A⁻ change, but modest additions produce only a relatively small change in their ratio and therefore in pH. The equilibrium shifts can also be interpreted through Le Chatelier’s principle. (openstax.org)

Both components must be available in sufficient amounts. A weak-acid solution without a substantial reservoir of conjugate base is not equivalent to a deliberately formulated buffer: its ability to consume added acid is much smaller. (ulm.edu)

Quantitative description

The Henderson–Hasselbalch equation relates buffer pH to acid strength and the relative amounts of the conjugate partners. Using thermodynamic activities, the relationship is

\mathrm{pH}=\mathrm{p}K_a+ \log_{10}\!\left(\frac{a_{\mathrm{A^-}}}{a_{\mathrm{HA}}}\right),

where $K_a$ is the acid dissociation constant, $\mathrm{p}K_a=-\log_{10}K_a$ , and $a$ denotes dimensionless activity. This follows by rearranging the acid-dissociation equilibrium expression and using the activity-based definition of pH. (goldbook.iupac.org)

For solutions in which activity corrections can be neglected,

\mathrm{pH}\approx\mathrm{p}K_a+ \log_{10}\!\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right).

Square brackets denote equilibrium molar concentrations. Replacing these with concentrations calculated directly from the preparation is an additional approximation, valid when subsequent dissociation changes the component amounts only slightly. The activity-based relationship itself does not require that approximation. (eprints.whiterose.ac.uk)

For a weak-base buffer, the same equation applies by treating the protonated base as the acid. Thus, for ammonia–ammonium,

\mathrm{pH}\approx\mathrm{p}K_a(\mathrm{NH_4^+})+ \log_{10}\!\left(\frac{[\mathrm{NH_3}]}{[\mathrm{NH_4^+}]}\right).

The relevant $pK_a$ is that of ammonium, not the $pK_b$ of ammonia. (lavelle.chem.ucla.edu)

Buffer range and capacity

A common working range is approximately

\mathrm{pH}=\mathrm{p}K_a\pm1,

corresponding to base-to-acid ratios between about 0.1 and 10. This is a practical convention rather than a sharp boundary. At a fixed total concentration, buffering by a simple conjugate pair is strongest near equal acid and base concentrations, where pH is approximately $pK_a$ . (lavelle.chem.ucla.edu)

Buffer capacity describes the amount of strong acid or base required to produce a specified pH change. Its differential form, often called the Van Slyke buffer value, is

\beta=\frac{\mathrm{d}b}{\mathrm{d}(\mathrm{pH})},

where $b$ is the amount of strong base added per unit volume; an equivalent positive quantity can be defined for acid addition with the sign reversed. This distinguishes capacity from the pH value itself. (nvlpubs.nist.gov)

Two solutions can therefore have nearly the same pH but very different capacities. Increasing both buffer-component concentrations while preserving their ratio increases the amount of acid or base they can accommodate. Resistance also differs by direction: an acid-rich mixture has more material available to consume added base, whereas a base-rich mixture has more available to consume added acid. Capacity declines as either partner approaches depletion. (openstax.org)

Preparation and common systems

Buffers can be prepared by mixing a weak acid with a soluble salt of its conjugate base, or by partially neutralizing a weak acid with strong base. Conversely, adding strong acid to a weak base or conjugate-base salt can generate the required acidic partner. The defining feature is the final composition, not the preparation route. (ulm.edu)

Common systems include:

Acetate buffers: acetic acid and acetate, useful around pH 4.75.
Ammonium buffers: ammonium and ammonia, useful around pH 9.25. These approximate values depend on conditions. (lavelle.chem.ucla.edu)
Phosphate buffers: commonly use dihydrogen phosphate and hydrogen phosphate as the conjugate pair; phosphate solutions also serve as pH reference standards. (tsapps.nist.gov)
Tris buffers: contain tris(hydroxymethyl)aminomethane and its protonated form. Their equilibrium behavior depends on temperature and solution composition. (pubs.acs.org)
Good’s buffers: compounds investigated for biological research with attention to useful dissociation constants, water solubility, membrane permeability, chemical stability, and unwanted interactions. (researchgate.net)

Applications and historical development

Buffers maintain experimental conditions in biochemistry, including studies of enzymes whose activity depends on pH. They also influence reaction kinetics and equilibrium processes by limiting changes in acidity during an experiment. (openstax.org)

Standard buffer solutions have a separate metrological role: they provide reference values for the calibration of pH measurement systems. Certified standards connect measurements to an agreed operational pH scale and support metrological traceability. Reference formulations include phthalate, phosphate, and borax solutions, with assigned values dependent on temperature. (nist.gov)

The quantitative treatment developed partly from research on physiological acid–base equilibria. Lawrence Joseph Henderson published an equation describing the carbonic-acid system in 1908; Karl Albert Hasselbalch introduced its logarithmic form in 1916. In 1966, Norman E. Good and colleagues published a systematic investigation of buffers designed for biological research. (openstax.org)

Limitations and chemical compatibility

Dilution generally preserves the acid-to-base ratio, so a buffer’s pH may change little while its capacity per unit volume decreases. Exact invariance is not expected: dilution changes activity coefficients, and sufficiently dilute solutions require explicit treatment of acid dissociation and water ionization. (ulm.edu)

Temperature changes dissociation equilibria and therefore buffer pH. Changes in ionic composition also alter activity coefficients, making concentration-only calculations less reliable. Buffers used in concentrated salt solutions or mixed solvents require equilibrium data appropriate to those conditions. (nvlpubs.nist.gov)

Buffer compounds are not necessarily chemically inert. They may bind metal ions, inhibit biological reactions, or absorb light used in analytical measurements. Good and colleagues explicitly evaluated such properties and did not claim that any one buffer was universally superior. Consequently, matching a buffer’s $pK_a$ to the intended pH establishes its acid–base suitability, but not its compatibility with every experimental system. (researchgate.net)

References

6 Buffers — Chemistry 2eopenstax.org
6 Buffers — Chemistryopenstax.org
Using activities to correct the Henderson-Hasselbalch equationeprints.whiterose.ac.uk
Experiment #9: The Henderson-Hasselbalch Equationulm.edu
Titrations and Buffers — UCLA Chemistry Teaching Noteslavelle.chem.ucla.edu
Revised standard values for pH measurements from 0 to 95 °Cnvlpubs.nist.gov
pH Metrology — NISTnist.gov
Standard Reference Material 2694a Certificatetsapps.nist.gov