pH (Dimensionless, pH = −log10 aH⁺)

pH quantifies the acidity of a solution and is defined—within the ISO/ISQ framework and modern chemical thermodynamics—as the negative decadic logarithm of the hydrogen-ion activity: 

pH = −log10(a_H⁺)

Although numerically unitless, pH is a standardized logarithmic quantity belonging to ISO 80000-9 because it arises from chemical activities and is fundamental to molecular equilibria, reaction rates, biological function, and materials stability. Pair this overview with the concentration reference and the molality companion to follow hydrogen-ion behavior across activity, volume-based, and mass-based descriptions.

Historical Development

Introduced by S. P. L. Sørensen in 1909 to rationalize hydrogen-ion concentrations in biochemical systems, pH quickly became central to acid–base chemistry. Early operational definitions relied on color indicators and electromotive force (emf) measurements. The advent of the glass pH electrode and refinement of primary buffer standards transformed pH into a robust, traceable quantity in routine practice, while electrochemical cells without liquid junction (Harned cells) support primary pH assignments.

Conceptual Foundations

Activity vs. concentration

Thermodynamically, 

a_H⁺ = γ_H⁺ · (m_H⁺ / m°)

on the molality scale (with m° = 1 mol·kg⁻¹). In practice, direct evaluation of γH⁺ is challenging; operational pH scales rely on buffer standards that embody agreed activity values under specified conditions. Cross-reference these ideas with our molality guide to understand the mass-based standard state.

Nernstian response

Electrometric pH measurement rests on the Nernst equation for hydrogen-ion-sensitive electrodes: 

E = E⁰ + (RT/F) · ln(a_H⁺)

At 25 °C, the theoretical slope is −59.16 mV per pH unit. Departures from this slope indicate electrode aging, junction effects, or temperature mismatch. Validate slopes and conversions with the pH from concentration calculator whenever you translate laboratory readings into reporting formats.

Related quantities

  • pOH: pOH = −log10(aOH⁻), related via pH + pOH = pKw.
  • pKa: Acid dissociation constants adopt the same logarithmic form, enabling linearized treatment of equilibria.

Primary and Operational Realizations

Primary methods

Harned cells (without liquid junction) allow assignment of primary pH values to buffer solutions by measuring emf of the cell Pt | H₂(g) | HCl(m) | AgCl(s) | Ag. From emf and thermodynamic data, aH⁺ is deduced with low uncertainty. National metrology institutes maintain sets of primary buffers (e.g., phosphate, phthalate, carbonate systems) with certified pH as a function of temperature.

Routine measurement

Glass combination electrodes (indicator + reference) are calibrated with at least two buffer standards bracketing the sample’s pH. Good practice includes temperature equilibration, slope verification, and junction maintenance. ISFET pH sensors offer robust alternatives in harsh environments.

Measurement Influences and Uncertainty

Temperature

pH depends on temperature both through the Nernst slope and through the intrinsic temperature dependence of chemical equilibria (e.g., pKw(T)). Report the measurement temperature and consider automatic temperature compensation carefully—ATC corrects the electrode slope but does not “correct” the chemistry of the sample.

Ionic strength and junction potentials

High ionic strength affects activity coefficients and can introduce liquid-junction potentials. Use buffers matched in ionic strength to the sample when feasible, or adopt ionic-strength adjustment buffers. Tie these adjustments back to the concentration framework when documenting sample composition.

Electrode performance

Alkaline error (sodium interference at high pH), acid error (non-ideal response at very low pH), glass hydration layer thickness, and reference electrode contamination contribute to drift and bias. Routine checks of slope (ideally 95–105 % of theoretical) and offset are essential.

Applications

Environmental and water quality

pH governs speciation (e.g., ammonia/ammonium, carbonate equilibria), metal solubility, corrosion potential, and disinfection efficacy. Regulatory frameworks specify pH ranges for potable, wastewater, and natural waters.

Biochemistry and medicine

Enzyme kinetics, protein stability, and cell culture viability are strongly pH-dependent; buffers are formulated to maintain pH within narrow windows under physiological ionic strength and temperature. Translate those buffer recipes into concentration limits with the blood glucose converter when patient communications require mass-based framing alongside pH control.

Industrial processes and materials

Electrodeposition, etching, dyeing, fermentation, and polymerization rely on controlled pH. Corrosion science uses pH in potential-pH (Pourbaix) diagrams to delineate immunity, passivation, and corrosion regions. Monitor fermentation shifts with the kombucha fermentation time calculator to keep artisanal processes aligned with metrological guidance.

Food and agriculture

pH influences microbial safety, fermentation endpoints, and organoleptic properties; soil pH controls nutrient availability and amendment strategies.

Best Practice and Reporting

  • Identify the pH scale and buffer standards used; specify temperature and ionic strength (or salinity) of both buffers and sample when relevant.
  • Calibrate with two or more buffers bracketing the sample; verify electrode slope and offset.
  • Allow thermal equilibration; avoid cross-contamination and junction clogging.
  • Quote measurement uncertainty where decisions depend on thresholds (e.g., pharmaceutical specifications).

Why It Matters

pH is a cornerstone quantity linking thermodynamics, electrochemistry, and practical analytics. ISO 80000-9 places pH within a rigorous framework of symbols and definitions, enabling traceable, reproducible acidity measurements from bioreactors to oceans. Its logarithmic nature condenses a vast range of proton activities into a manageable scale while maintaining direct ties to fundamental chemistry.

Related resources on CalcSimpler

Continue building your chemical metrology knowledge with these linked explainers.

  • Amount-of-Substance Concentration, c (mol·m⁻³)

    Use volume-based composition data to connect measurable concentrations with hydrogen activities.

    Read more

  • Molality, b (mol·kg⁻¹)

    Review the mass-based reference scale that underpins standard states for activity coefficients.

    Read more

  • ISO 80000-9: Quantities and Units of Physical Chemistry

    See how ISO formalises logarithmic quantities, concentration terms, and activity notation.

    Read more

Featured calculators

Experiment with these calculators to reinforce pH concepts.

  • pH from Concentration Calculator

    Apply the pH = −log10[H⁺] relationship to laboratory datasets instantly.

    Launch calculator

  • Kombucha Fermentation Time Calculator

    Monitor fermentation schedules with daily pH checks that follow best practices here.

    Launch calculator

  • Blood Glucose mmol/L to mg/dL

    Compare how clinical concentration reporting aligns with molality- and pH-based assessments.

    Launch calculator