Measurement of ion concentrations with electrodes is used in a wide range of applications. Suppose you are interested in removing silver ions from exhausted electroplating solutions by precipitating the silver as silver chloride. To test the efficiency of your process, you decide to build an electrochemical cell to measure Ag⁺ concentrations. Each electrode compartment of your galvanic cell contains a silver electrode and 10.0 mL of 0.10 m AgNO₃(aq); they are connected by a salt bridge. You now add 10.0 mL of 0.10 m NaCl(aq) to the left-hand electrode compartment. Almost all the silver precipitates as silver chloride, but a little remains in solution as a saturated solution of AgCl. The measured cell potential is E_cell = 10.42 V. What is the concentration of Ag⁺ in the saturated solution?

ANTICIPATE Because silver chloride is very insoluble, you should expect a very low concentration.

PLAN Use the Nernst equation, Eq. 2, to find the concentration of Ag⁺ in the compartment with the precipitate. The standard cell potential is 0 (in their standard states the half-cells are identical). At 25.00°C, RT/F = 0.025 693 V.