Challenge Problem: At one time, the standard hydrogen electrode was used for measuring pH....

Challenge Problem: At one time, the standard hydrogen electrode was used for measuring pH.

(a) Sketch a diagram of an electrochemical cell that could be used to measure pH and label all parts of the diagram. Use the SHE for both half-cells.

(b) Derive an equation that gives the potential of the cell in terms of the hydronium ion concentration [H3O1] in both half-cells.

(c) One half-cell should contain a solution of known hydronium ion concentration, and the other should contain the unknown solution. Solve the equation in (b) for the pH of the solution in the unknown half-cell.

(d) Modify your resulting equation to account for activity coefficients and express the result in terms of paH = -log aH, the negative logarithm of the hydronium ion activity.

(e) Describe the circumstances under which you would expect the cell to provide accurate measurements of paH.

(f) Could your cell be used to make practical absolute measurements of paH or would you have to calibrate your cell with solutions of known paH? Explain your answer in detail.

(g) How (or where) could you obtain solutions of known paH?

(h) Discuss the practical problems that you might encounter in using your cell for making pH measurements.

(i) Klopsteg5 discusses how to make hydrogen electrode measurements. In Figure 2 of his paper, he suggests using a slide rule, a segment of which is shown here, to convert hydronium ion concentrations to pH and vice versa.