https://doi.org/10.1351/goldbook.P04524
The quantity pH is defined in terms of the activity of hydrogen(1+) ions (hydrogen ions) in solution: pH=lg[a(H+)]=lg[m(H+)γm(H+)/m] where a(H+) is the activity of hydrogen ion (hydrogen 1+) in aqueous solution, H+(aq), γm(H+) is the
activity coefficient
of H+(aq) (molality basis) at molality m(H+), and m=1 molkg1 is the standard molality.
Notes:
  1. pH cannot be measured independently because calculation of the activity involves the activity
    coefficient
    of a single ion. Thus it can be regarded only as a notional definition.
  2. The establishment of
    primary pH standards
    requires the application of the concept of 'primary method of measurement', assuring full
    traceability
    of the results of all measurements and their uncertainties. Any limitation in the theory of determination of experimental variables must be included in the estimated uncertainty of the method.
  3. The primary method for measurement of pH involves the use of a cell without transference, known as the Harned cell:
    Pt(s) | H2(g) | Buffer S, Cl(aq) | AgCl(s) | Ag(s)
    The equation for this cell can be rearranged to give: lg[a(H+)γ(Cl)]=EE(RTln10)/F+lg[m(Cl)/m] where E is the potential difference of the cell and E is the known standard potential of the AgCl | Ag electrode. Measurements of E as a function of m(Cl) are made and the quantity a(H+)γ(Cl) (called the
    acidity function
    ) is found by extrapolation to m(Cl)/m=0. The value of γ(Cl) is calculated using the
    Bates–Guggenheim convention
    based on
    Debye
    –Hückel theory. Then lg[a(H+)] is calculated and identified as pH(PS), where PS signifies
    primary standard
    . The uncertainties in the two estimates are typically 0.001 in lg[a(H+)γ(Cl)] and 0.003 in pH. Materials for
    primary standard
    buffers must also meet the appropriate requirements for reference materials, including chemical purity and stability, and applicability of the
    Bates–Guggenheim convention
    for the estimation of lg[γ(Cl)]. This convention requires that the
    ionic strength
    be 0.1molkg1.
    Primary standard
    buffers should also lead to small
    liquid junction
    potentials when used in cells with liquid junctions. Secondary standards, pH(SS), are also available, but carry a greater uncertainty in measured values.
  4. Practical pH measurements generally use cells with liquid junctions in which, consequently,
    liquid junction
    potentials, Ej, are present. Measurements of pH are not normally performed using the Pt|H2 electrode, but rather the glass (or other H+- selective) electrode, whose response factor (dE/dpH) usually deviates from the Nernst slope. The associated uncertainties are significantly larger than those associated with fundamental measurements using the Harned cell. Nonetheless, incorporation of the uncertainties for the primary method, and for all subsequent measurements, permits the uncertainties for all procedures to be linked to the primary standards by an unbroken chain of comparisons.
  5. Reference values for standards in D2O and aqueous-organic solvent mixtures exist.
Sources:
Green Book, 3rd ed., p. 75 [Terms] [Book]
PAC, 1996, 68, 957. (Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)) on page 986 [Terms] [Paper]
PAC, 1997, 69, 1007. (Reference value standards and primary standards for pH measurements in D2O and aqueousorganic solvent mixtures: New accessions and assessments (Technical Report)) on page 1007 [Terms] [Paper]
See also:
PAC, 1984, 56, 567. (Physicochemical quantities and units in clinical chemistry with special emphasis on activities and activity coefficients (Recommendations 1983)) on page 569 [Terms] [Paper]
PAC, 1990, 62, 2167. (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2205 [Terms] [Paper]
PAC, 2002, 74, 2169. (Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002)) on page 2169 [Terms] [Paper]