Question 25.10: Another commonly used electrode that is used to measure pH i......
Another commonly used electrode that is used to measure pH is described by the cell diagram Cl^–(aq)|Hg_{2}Cl_2(s)|Hg(l) and the corresponding (reduction) half reaction
Hg_{2}Cl_{2}(s) + 2\ e^– → 2\ Hg(l) + 2\ Cl^−(aq) \qquad E^{\circ}_{red} = 0.268\ VThis electrode is called a calomel electrode because Hg_{2}Cl_{2}(s) used to be called calomel. The cell diagram of the complete cell is
If the cell voltage is measured to be 0.432 V at 25.0°C, calculate the corresponding pH.
The equation for the overall cell reaction is
H_2(g) + Hg_2Cl_2(s) → 2\ H^+(aq) + 2\ Cl^−(aq) + 2\ Hg(l )and the standard cell voltage is given by
E^{\circ}_{cell}= E^{\circ}_{red}[Hg_2Cl_2|Hg] + E^{\circ}_{ox}[H_2|H^+] = +0.268\ VThe thermodynamic reaction quotient for the above equation under the stated conditions is
Q =\frac{([H^+]/M)^2([Cl^–]/M)^2}{P_{H_{2}}/bar} = ([H^+]/M)^2Substituting this into the Nernst equation (Equation 25.13) gives
E_{cell} =E^{\circ}_{cell} – \left(\frac{0.02570\ V}{ν_e} \right) ln\ Q \qquad (at\ 25.0^{\circ}C) (25.13)
E_{cell} = 0.268\ V – (0.02570\ V)ln([H^+]/M)Again, using the conversion ln x = 2.303 log x, we have
E_{cell} = 0.268\ V – (0.02570\ V)\log([H^+]/M)or
pH = –\log([H^+]/M) =\frac{E_{cell} – 0.268\ V}{0.0592\ V} (25.24)
Given that E_{cell} = 0.432\ V, we see that the pH is
pH =\frac{0.432\ V – 0.268\ V}{0.0592\ V} = 2.77