Question

Use the Nernst equation to derive an equation relating the voltage of the cell (E_cell) consisting of a glass electrode and a silver/silver chloride reference electrode, to the pH of a solution. Define all variables in the equation.

Answer 1

The short hand notation of the glass electrode with Ag/AgCl reference cell is

Ag(s) | AgCl(s) |Cl-(aq)|H+unk| HCl(0.1M)| AgCl(sat'd)| Ag(s)

FOr the silver/silver chloride section

E = 0.222 - 0.0591/1 log [Cl-]/1

Since in the [Cl-] is 1 M then log [Cl-]/1 = log 1 = 0

So E = 0.222

For the glass electrode

E = K + 0.0591 log a1/a2

where K is a constant

and in this standard cell

a2 =0.1 M

SO E = K + 0.0591 log a1/0.1

SO the E = K' + 0.0591 log a1

a1 is the activity of hydrogen where pH = -log aH+

So E = K' + 0.0591 x pH

SO we can see from this equation E is related to the pH

So voltage is related to the pH