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"HEPES = AT-2-hydroxyethylpiperazine-JV'-2-ethanesulfonic acid. 'MOPSO = 3-(iV-morpholino)-2-hydroxypropanesulfonic acid. TRIS = tris(hydroxymethyl)aminomethane. Source: Ref. 2, and NIST, private communication.

"HEPES = AT-2-hydroxyethylpiperazine-JV'-2-ethanesulfonic acid. 'MOPSO = 3-(iV-morpholino)-2-hydroxypropanesulfonic acid. TRIS = tris(hydroxymethyl)aminomethane. Source: Ref. 2, and NIST, private communication.

quently should minimize the residual liquid-junction potential. The International Union of Pure and Applied Chemistry recommends the NIST primary standards plus a series of operational standards, measured versus the phthalate reference value standard in a cell with a well-defined liquid junction, for the definition of the pH scale (9). However, this recommendation is currently under review, although significant change in the present scale is not anticipated other than its extension to higher ionic strength solutions.

Accuracy and Interpretation of Measured pH Values

The acidity function p(aHycl), which is the experimental basis for the assignment of pH(S), is reproducible within about 0.003 pH unit from 10 to 40°C. If the ionic strength is known and £0.1, the assignment of numerical values to the activity coefficient of chloride ion does not add to the uncertainty. However, errors in the standard potential of the cell, in the composition of the buffer materials, and in the preparation of the solutions may raise the uncertainty to 0.005 pH unit.

The reproducibility of the practical scale that has been defined using the seven primary standards includes the possible inconsistencies introduced in the standardization of the instrument with seven different standards of different composition and concentration. These inconsistencies are the result of variations in the liquid-junction potential when one solution is replaced by another and are unavoidable. The accuracy of the practical scale from 10 to 40°C therefore appears to be in the range from 0.008 to 0.01 pH unit.

Variations in the liquid-junction potential may be increased when the standard solutions are replaced by test solutions that do not closely match the standards with respect to the composition and concentrations of solutes, or to the solvent composition, for example, nonaqueous and mixed solvents. Under these circumstances, the pH remains a reproducible number, but it may have little or no meaning in terms of the conventional hydrogen-ion activity of the medium. The use of experimental pH numbers as a measure of the extent of acid-base reactions or to obtain thermodynamic equilibrium constants is justified only when the pH of the medium is between 2.5 and 11.5 and when the mixture is an aqueous solution of simple solutes in total concentration of approximately £0.2 M.

Sources of Error

Although subject to fewer interferences and other types of error than most potentiometric ionic-activity sensors, that is, ion-selective electrodes (qv), pH electrodes must be used with an awareness of their particular response characteristics as well as the potential sources of error that may affect the other components of the measurement system, especially the reference electrode (see also "pH Measurement System Electrodes"). Several common causes of measurement problems are electrode interferences and/or fouling of the pH sensor, sample matrix effects, reference electrode instability, and improper calibration of the measurement system (10).

In general, the potential of an electrochemical cell, £„,11, is the sum of three potential terms:

where Epii and Ele{ are the potentials of the pH and reference electrodes, respectively, and Ey is the ubiquitous liquid-junction potential. After substitution of the Nernst equation for the pH electrode potential term in equation 9,

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