A pH meter employs a voltaic cell for which the cell potential is very sensitive

Question

A pH meter employs a voltaic cell for which the cell potential is very sensitive to pH. A simple (but impractical) pH meter can be constructed by using two hydrogen electrodes: one standard hydrogen electrode and a hydrogen electrode (with 1 atm pressure of H2 gas) dipped into the solution of unknown pH. The two half-cells are connected by a salt bridge or porous glass disk.

a)Write the half-cell reactions for the cell.

1) No reaction.

2) H+(aq,1M)+H2O(l)H3O+(aq), H2(g)2H+(aq,1M)+2e.

3) 2H2O(l)+2e2OH(aq)+H2(g), H2(g)2H+(aq,1M)+2e.

4) 2H+(aq,1M)+2eH2(g), H2(g)2H+(aq,1M)+2e.

b) Calculate the standard Ecell.

c)What is the pH of the solution in the half-cell that has the standard hydrogen electrode?

d)What is the Ecell when the pH of the unknown solution is 6.0?

Explanation / Answer

a. This is a concentration cell.

In the lower H+ concentration   half cell   the reaction is    H2(g)2H+(aq,1M)+2e.

In the higher H+ concentration   half cell   the reaction is 2H+(aq,1M)+2eH2(g)

Answer a.4.    In fact the measurement is made with a high impedance voltmeter (the current is very close to 0), thus the measurement is not modifying in a significant way, the cell concentrations.

b. In a concentration cell, Eo is always =0.

c. [H+] = 1 M in standard condition, thus pH = 0

d. E = - 0.0592 V · log (1M/1x10-6M) =

          - 0.0592 V · 6 = -0.3552 V vs NHE

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