REPORT FOR ANALYSTS and the like. I t is possible, however, to define arbitrarily the single ionic ac tivity coefficient and to establish in this way a conventional scale of aH that serves quite well. Perhaps the most logical procedure is to ascribe to the activity coefficient of a univalent ion the well-understood properties of the mean activity coefficient of a uni-univalent electrolyte in a similarly constituted medium. This approach was chosen as a basis for the establishment of the National Bureau of Standards pH stand
ards. These NBS reference materials, now six in number, enable pH measure ments to be standardized from 0° to 95° C. and over the pH range 1.6 to 12.4 at 25° C. In the procedure for the assignment of standard values (1), an alkali chloride is added in known concentration to the buffer solution, and the e.m.f. between hydrogen and silver-silver chloride electrodes in a cell without liquid junc tion is obtained. Standard potentials and fundamental constants being
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known, the e.m.f. is an unambiguous measure of — log(/H/ciCH), a quantity that has been termed pwH for con venience. The effect of the chloride on pwH is eliminated by a suitable ex trapolation, and /ci is made to disappear by introduction of the conventional definition of the single ionic activity coefficient. The result is a pH stand ard value, or pH s . Inasmuch as /H/CI is equivalent to / ^ , where / ^ is the mean activity coefficient of hydrochloric acid in the buffer solution, p H s has" in reality the dimensions of —log f^ca, but it is often convenient to regard f^ca as the conventional hydrogen ion activity. The specific properties of the ions of strong electrolytes of a single charge type are different and, hence, so also are the mean activity coefficients of these electrolytes, even at rather low values of the ionic strength (μ). For example, the value of a, the "ion-size parameter" in the Debye-Huckel equation at 25° C , - l o g / ±
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0.328α\/μ), may vary from 3 to 6 for different strong uni-univalent electro lytes below 0.2M. Hence, a single con vention cannot yield exactly compar able pHs or pH values for differently constituted standards and unknowns, even under the most favorable circum stances. As μ decreases, the differences in / ± evidently also decrease. Ac cordingly, the NBS procedure selects standards of ionic strength 0.1 or less, where the assigned uncertainty of ±0.01 unit in p H s will allow a con siderable variation in the parameter a. A similar restriction to the application of measured pH \'alues to chemical equilibria is inescapable. Here again it is impracticable, or even impossible, to recognize specific differences of a secondary character, among the con stituents of the solution. Differences of electric charge are, however, of primary ' influence on the activity coefficients, and allowance must be made for them. If / ± is the conventional definition of the activity coefficient of a single uni valent ion, the activity coefficients, /,·, of other ionic and molecular species of valence zf may be expressed by log /,· = 2 2 ilog/ ± . This expression is con sistent with the ionic strength principle and with the valence relations of the Debye-Huckel limiting law. The manner in which measured pH values are employed in chemical equilib ria, when the favorable circumstances of the measurement justify this step, is now clear. The equilibrium is first formulated in its exact (thermodynamic) form, and the following substitutions are made: (1) — log fnCa is replaced by the experimental pH value; (2) the activity coefficients of the other species are expressed in terms of / ± ; and (3)
