c14 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come
230 ELECTROCHEMICAL CELLShas a Nernst equation ofEcell=Ecalomel− 0 .0257 ln H+(aq)because all of the activities other than H+(aq) are 1.0 or are included inEcalomel.This
leads to−ln H+(aq)=Ecell−Ecalomel
0. 0257or, as is more commonly written,pH≡−log H+(aq)=Ecell−Ecalomel
0. 0592These results will not be accurate to an indefinite number of significant figures
because the activity coefficient is not exactly 1.0 in real solutions. Cell potentials can
be measured to four or more significant figures, but pH values should be regarded with
a prudent degree of skepticism. Conversely, departure of pH values from expectation
can be used to estimate activity coefficients.14.12 THE GLASS ELECTRODE
We still have the problem of a bulky, somewhat dangerous hydrogen half-cell to de-
termine pH in the field. For practical work, the glass electrode is used instead. Within
certain limits, the potential between opposite sides of a very thin glass membrane
varies in a linear way with hydrogen ion concentration. This is used in to determine
pH, but the nature of the hydrogen ion sensitivity is not rigorously understood beyond
knowing that there is an interchange between the aqueous hydrogen ions and the Na+
ions in the glass on one side of the membrane that is different from the interchange
on the other. Consequently, pH measurements have only relative significance. We
measure pH by the potential relative to that due to a standard buffer solution for
which we take the pH to be known. Glass electrodes can be made that are quite
small, and the hand-held pH meter is common in many branches of laboratory and
field chemistry. Other types of membranes lead to various electrodes sensitive to ions
other than H+(aq)—for example, Ca+(aq).PROBLEMS AND EXAMPLES
Example 14.1 pH from the Hydrogen Half-Cell
The pH meter with a glass electrode is by no means the only way of determining pH.
Suppose we reverse the method of Section 14.8 and use the half-cell potential of the