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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: $\text{pH} = -\text{lg}[a(\text{H}^{+})] = -\text{lg}[\text{m}(\text{H}^{+})\gamma_{\text{m}}(\text{H}^{+})/m^{\unicode{x29B5} }]$ where $$a(\text{H}^{+})$$ is the activity of hydrogen ion (hydrogen 1+) in aqueous solution, $$\text{H}^{+}\text{(aq)}$$, $$\gamma_{\text{m}}(\text{H}^{+})$$ is the @[email protected] of $$\text{H}^{+}\text{(aq)}$$ (molality basis) at molality $$m(\text{H}^{+})$$, and $$m^{\unicode{x29B5}} = 1\ \text{mol kg}^{-1}$$ is the standard molality.
Notes:
1. pH cannot be measured independently because calculation of the activity involves the activity @[email protected] of a single ion. Thus it can be regarded only as a notional definition.
2. The establishment of @[email protected] requires the application of the concept of 'primary method of measurement', assuring full @[email protected] 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: $-\text{lg}[a(\text{H}^{+})\gamma(\text{Cl}^{-})] = \frac{E - E^{\unicode{x29B5} }}{(R\:T\:\text{ln}10)/F}+ \text{lg}[m(\text{Cl}^{-})/m^{\unicode{x29B5}}]$ where $$E$$ is the potential difference of the cell and $$E^{\unicode{x29B5}}$$ is the known standard potential of the AgCl | Ag electrode. Measurements of $$E^{\unicode{x29B5}}$$ as a function of $$m(\text{Cl}^{-})$$ are made and the quantity $$a(\text{H}^{+})\gamma(\text{Cl}^{-})$$ (called the @[email protected]) is found by extrapolation to $$m(\text{Cl}^{-})/m^{\unicode{x29B5}} = 0$$. The value of $$\gamma(\text{Cl}^{-})$$ is calculated using the @[email protected] based on @[email protected]–Hückel theory. Then $$\text{lg}[a(\text{H}^{+})]$$ is calculated and identified as $$\text{pH(PS)}$$, where $$\text{PS}$$ signifies @[email protected] The uncertainties in the two estimates are typically $$0.001$$ in $$\text{lg}[a(\text{H}^{+})\gamma(\text{Cl}^{-})]$$ and $$0.003$$ in pH. Materials for @[email protected] buffers must also meet the appropriate requirements for reference materials, including chemical purity and stability, and applicability of the @[email protected] for the estimation of $$-\text{lg}[\gamma(\text{Cl}^{-})]$$. This convention requires that the @[email protected] be $$\leq 0.1\ \text{mol kg}^{-1}$$. @[email protected] buffers should also lead to small @[email protected] potentials when used in cells with liquid junctions. Secondary standards, $$\text{pH(SS)}$$, are also available, but carry a greater uncertainty in measured values.
4. Practical pH measurements generally use cells with liquid junctions in which, consequently, @[email protected] potentials, $$E_{\text{j}}$$, 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 ($$\text{d}E/\text{dpH}$$) 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]