Concise Physical Chemistry

c14 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

228 ELECTROCHEMICAL CELLS

m1/2

0.00 0.01 0.02 0.03 0.04 0.05 0.06

E'

(volts)

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

FIGURE 14.2 Extrapolation toE◦= 0 .2223 for the standard hydrogen–silver–silver chlo-

ride Cell. (Standard value: 0.22239; data from Klotz and Rosenberg, 2008.) At higher concen-

trations the experimental points fall away from the linear function.

14.9 SOLUBILITY AND STABILITY PRODUCTS

In general chemistry we memorized the solubility product constant of silver chloride,

Ksp=[Ag+][Cl−]= 10 −^10 , which implies that the concentration of silver ion in a

solution of AgCl in pure water is [Ag+]= 10 −^5. How do you make an accurate

measurement of the concentration of an ion that is 0.00001 molar (or molal)? The

question becomes even more daunting for the case of copper phosphate,Ksp= 10 −^37.

Because the Nernst equation relates the cell potential to thelogarithmof the

concentration, very small metal ion concentrations such as those in saturated solutions

of sparingly soluble salts and stable complexes can be measured. For example, we can

set up a cell consisting of a silver–silver ion half-cell in opposition to a silver–silver

iodide half-cell which is analogous to the silver–silver chloride half-cell discussed in

the previous section. The cell diagram and cell reactions are

Ag(s); AgI(s); I−(aq)||Ag+(aq); Ag(s)

Ag+(aq)+I−(aq)→←AgI(s)

The equilibrium constant for the cell reaction is

Keq=

aAgI

aAg+aI−

=

1

Ksp