pH is a dimensionless, logarithmic quantity that describes the acidity or basicity of a solution, principally in water. It is defined as the negative base-ten logarithm of hydrogen-ion activity: lower values indicate greater hydrogen-ion activity, and higher values indicate less. In dilute aqueous solutions at 25 °C, pH below 7 is acidic, pH above 7 is basic, and pH near 7 is neutral. Its rigorous definition uses activity rather than concentration. (goldbook.iupac.org)
Origin and definition
The Danish chemist Søren P. L. Sørensen introduced the pH scale in 1909 while working at the Carlsberg Laboratory. His work demonstrated the significance of acidity for biochemical reactions, including those involved in brewing. The scale provided a convenient numerical expression for hydrogen-ion concentrations spanning many orders of magnitude. (carlsberggroup.com)
The modern definition is
[ \mathrm{pH}=-\log_{10}a(\mathrm{H}^{+}), ]
where (a(\mathrm{H}^{+})) is the dimensionless chemical activity of hydrogen ions. On a molality basis,
[ a(\mathrm{H}^{+})= \gamma_{\mathrm{H}^{+}}\frac{m(\mathrm{H}^{+})}{m^\circ}, ]
with (m^\circ=1\ \mathrm{mol,kg^{-1}}) and (\gamma_{\mathrm{H}^{+}}) the activity coefficient. Activity accounts for nonideal interactions between dissolved species. Because individual-ion activities cannot be measured independently, practical pH values depend on conventions and comparison with assigned standards. (goldbook.iupac.org)
In water, hydrogen ions are hydrated rather than present as isolated protons. They are commonly represented as the hydronium ion, (\mathrm{H_3O^+}). For sufficiently dilute solutions, a useful approximation is
[ \mathrm{pH}\approx-\log_{10} \left(\frac{[\mathrm{H_3O^+}]}{1\ \mathrm{mol,L^{-1}}}\right). ]
The concentration approximation is widely used in introductory calculations but is not the fundamental definition. (openstax.org)
Logarithmic scale and neutrality
A decrease of one pH unit corresponds to a tenfold increase in hydrogen-ion activity. Thus, a solution at pH 3 has 100 times the hydrogen-ion activity of one at pH 5. These ratios describe hydrogen-ion activity, not necessarily the total amount of acid present. (goldbook.iupac.org)
Water undergoes proton transfer through self-ionization:
[ 2\mathrm{H_2O}\rightleftharpoons \mathrm{H_3O^+}+\mathrm{OH^-}. ]
Its equilibrium is described by the ionic product of water, (K_\mathrm{w}). In dilute solutions,
[ K_\mathrm{w}\approx[\mathrm{H_3O^+}][\mathrm{OH^-}], ]
using the conventional concentration expression. At 25 °C, this product is approximately (1.0\times10^{-14}). Defining pOH analogously for hydroxide gives (\mathrm{pH}+\mathrm{pOH}\approx14.00). (openstax.org)
Neutrality means equal hydronium and hydroxide concentrations in the dilute-solution treatment. Since (K_\mathrm{w}) varies with temperature, neutral pH is not always 7.00. The familiar 0–14 scale is also not an absolute boundary: sufficiently concentrated acidic or basic solutions can have values outside it, although nonideality becomes important. (openstax.org)
Acid strength and buffering
pH describes a solution, whereas acid strength describes an acid’s tendency to transfer a proton to its solvent. Strong acids dissociate essentially completely in dilute aqueous solution; weak acids establish an equilibrium between protonated and deprotonated forms. Their strength is characterized by an acid dissociation constant, (K_\mathrm{a}), often expressed as (\mathrm{p}K_\mathrm{a}=-\log_{10}K_\mathrm{a}). Consequently, pH depends on both acid strength and concentration, as well as other substances present. (openstax.org)
A buffer solution contains appreciable quantities of a weak acid and its conjugate base, or a weak base and its conjugate acid. These components consume small additions of strong acid or base, limiting the resulting pH change. An acetic acid–acetate mixture is a common example. (openstax.org)
For an acid–base pair (\mathrm{HA/A^-}), the Henderson–Hasselbalch equation is commonly written
[ \mathrm{pH}\approx\mathrm{p}K_\mathrm{a} +\log_{10}\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}. ]
This concentration form requires appropriate approximations. Equal concentrations give pH approximately equal to (\mathrm{p}K_\mathrm{a}). Buffer capacity is finite and depends on the quantities and proportions of the components; a buffer does not keep pH unchanged under unlimited addition of acid or base. (openstax.org)
Measurement and standards
Routine measurement uses a pH meter with a hydrogen-ion-sensitive glass electrode and a reference electrode, often combined in one probe. The instrument measures an electrical potential difference and relates it to pH through calibration with standard buffers. Primary standards provide metrological traceability through an unbroken chain of comparisons. NIST certifies pH reference materials using a primary electrochemical measurement involving a cell without transference. (goldbook.iupac.org)
Measurement uncertainty can arise from imperfect electrode response, liquid-junction potentials, and differences between the sample and calibration buffers. Some glass electrodes also respond to sodium ions in strongly alkaline solutions. Temperature and sample conditions therefore form part of the measurement’s context, rather than being incidental details. (nvlpubs.nist.gov)
An acid–base indicator provides an alternative based on the different colors of its protonated and deprotonated forms. Indicators change color over characteristic intervals rather than at a single exact pH. In titration, an appropriate indicator is selected so its transition occurs near the equivalence point; this point need not have pH 7. (openstax.org)
Environmental and laboratory significance
pH is routinely measured in natural waters during field sampling, continuous monitoring, and laboratory experiments. Recording it helps characterize a sample’s chemical condition and interpret changes over time. Reliable comparisons require attention to measurement procedures and conditions. (pubs.usgs.gov)
In the ocean, uptake of atmospheric carbon dioxide changes carbonate chemistry and lowers pH. Ocean acidification denotes this decrease; it does not require seawater to cross below neutral pH. A solution can become more acidic while remaining basic. (oceanservice.noaa.gov)
In analytical chemistry, pH changes provide information about acid–base composition during titration. Strong-acid–strong-base and weak-acid–strong-base systems produce different titration curves because their equilibria differ. Monitoring the curve can identify the equivalence region and distinguish it from the indicator’s observed endpoint. (openstax.org)