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3.9.5 pH Values
The concept of pH is unique amongst the commonly encountered physicochemical quantities, in that its definition,
involves a single ion quantity, the activity of the hydrogen ion, which is immeasurable by any thermodynamically valid method and requires a convention for its evaluation. In terms of molality, eqn (1) may be rewritten
where m0 is an arbitrary constant representing the standard state condition and equal to 1 mol kg−1, mH is the molality of hydrogen ion and γH is the single ion activity coefficient of the hydrogen ion. Arising from the non-experimental determinability of single ion activities, the definition and determination of pH depend on the assignment of pH values to standard solutions together with the determination of pH difference by a cell with liquid junction.
The electromotive force, emf, E(X) of the cell with liquid junction:
is measured, and likewise that E(S) of the cell:
The temperature of both cells (I and II) must be equal and uniform throughout, and the hydrogen gas pressures identical. The two bridge solutions are any molality of KCl not less than 3.5 mol kg−1 (4.2 mol dm−3) provided they are the same. The reference electrode may be silver/silver chloride or calomel.
The pH of the solution X, pH(X) is then related to the assigned pH of the solution S, pH(S), by the definition:
where R is the gas constant, T the thermodynamic
temperature, F the Faraday constant. The quantity
A Working Party of IUPAC, after extensive considerations over five years, recently produced a report (1) which sets pH firmly within the International System of Units (SI). A summary of these important developments is given below.
Since pH is a single ion quantity, it is not determinable in terms of a fundamental (or base) unit of any measurement system, and there is therefore difficulty in providing a proper basis for the traceability of pH measurements. A satisfactory approach is now available in that pH determinations can be incorporated into the International System (SI), provided they can be traced to measurements made using a method that fulfils the definition of a 'primary method of measurement'.
The essential feature of a primary method is that it must operate according to a well-defined measurement equation in which all of the variables can be determined experimentally in terms of SI units. Any limitation in the determination of the experimental variables, or in the theory, must be included within the estimated uncertainty of the method if traceability to the SI is to be established. If a convention were used without an estimate of its uncertainty, true traceability to SI would not be established. The electrochemical cell without liquid junction, known as the Harned cell,
fulfils the definition of a primary method for the measurement of a quantity called the acidity function, p(aHγCl), which is related to pH, and subsequently to the pH, of carefully chosen buffer solutions.
pH values have been assigned by the Harned cell without transference method (III) to seven buffer solutions which meet certain criteria of reproducibility of preparation and properties. These solutions are called primary pH standards (PS). When two PS solutions are used in cells II, the experimental value of the slope will not be exactly in accord with the slope factor value, and, moreover, the experimental value could change if additional primary standard solutions were to be used. Hence the pH value determined for an unknown solution can be slightly dependent (± 0.02) on the choice of primary standard. Details of solution compositions, and pH(PS) values assigned, are given in the table below.
Typical Values of pH(PS) for Primary Standards at 0 - 50 °C
Secondary standards (SS) are also defined, and values are also assigned by means of the Harned cell (III). These secondary standards do not for some reason of detail fulfil the criteria for primary standards in terms of reliable chemical quality.
Calibration Procedures: choice of standard reference solution
Some useful data for standard buffers are given in the table below
Summary of Useful Properties of some Primary and Secondary Standard Buffer Substances and Solutions
1. If pH is not required to better than ±0.05 any standard
reference solution can be selected.
1. R.P. Buck, S. Rondinini, A.K. Covington, F.G.K. Baucke, C.M.A. Brett, M.F. Camoes, M.J.T. Milton, T.Mussini, R. Naumann,, K.W. Pratt, P. Spitzer, and G.S. Wilson Pure Appl. Chem. 2002, 74, 2105.
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