Saturated calomel electrode

In cell notation the electrode is written as:

${\displaystyle {\text{Cl}}^{-}(4\text{M})|{\text{Hg}}_2^{}{\text{Cl}}_2^{}(\text{s})|\text{Hg}(\text{l})|\text{Pt}}$

Theory of electrolysis

Solubility product

The electrode is based on the redox reactions

${\displaystyle {\text{Hg}}_2^{2+}+2{\text{e}}^{-}\stackrel{-\rightharpoonup }{\leftharpoondown -}2\text{Hg}(\text{l}),\text{with}{E}_{{\text{Hg}}_2^{2+}/\text{Hg}}^0=+0.80\text{V}}$

${\displaystyle {\text{Hg}}_2^{}{\text{Cl}}_2^{}+2{\text{e}}^{-}\stackrel{-\rightharpoonup }{\leftharpoondown -}2\text{Hg}(\text{l})+2{\text{Cl}}^{-},\text{with}{E}_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/\text{Hg},{\text{Cl}}^{-}}^0=+0.27\text{V}}$

The half reactions can be balanced to the following reaction

${\displaystyle {\text{Hg}}_2^{2+}+2{\text{Cl}}^{-}+2\text{Hg}(\text{l})\stackrel{-\rightharpoonup }{\leftharpoondown -}{\text{Hg}}_2^{}{\text{Cl}}_2^{}(\text{s})+2\text{Hg}(\text{l}),\text{with}{E}_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/{\text{Hg}}_2^{2+},{\text{Cl}}^{-}}^0=+0.53\text{V}}$.

Which can be simplified to the precipitation reaction, with the equilibrium constant of the solubility product.

${\displaystyle {\text{Hg}}_2^{2+}+2{\text{Cl}}^{-}\stackrel{-\rightharpoonup }{\leftharpoondown -}{\text{Hg}}_2^{}{\text{Cl}}_2^{}(\text{s}),K_{sp}=a_{{\text{Hg}}_2^{2+}}{a}_{{\text{Cl}}^{-}}^2=[{\text{Hg}}_2^{2+}]\cdot [{\text{Cl}}^{-}{]}^2}$

The Nernst equations for these half reactions are:

${\displaystyle \{\begin{array}{lll}{E}_{\frac{1}{2}\text{cathode}}& =E_{{\text{Hg}}_2^{2+}/\text{Hg}}^0-\frac{RT}{2F}\ln \frac{1}{a_{{\text{Hg}}_2^{2+}}}& \text{in which}{E}_{{\text{Hg}}_2^{2+}/\text{Hg}}^0=+0.80\text{V}.\\ E_{\frac{1}{2}\text{anode}}& =E_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/\text{Hg},{\text{Cl}}^{-}}^0-\frac{RT}{2F}\ln a_{{\text{Cl}}^{-}}^2& \text{in which}{E}_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/\text{Hg},{\text{Cl}}^{-}}^0=+0.27\text{V}.\end{array}}$

The Nernst equation for the balanced reaction is:

${\displaystyle \begin{array}{cc}{E}_{\text{cell}}& =E_{\frac{1}{2}\text{cathode}}-E_{\frac{1}{2}\text{anode}}\\ & =E_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/{\text{Hg}}_2^{2+},{\text{Cl}}^{-}}^0-\frac{RT}{2F}\ln \frac{1}{[{\text{Hg}}_2^{2+}]\cdot {[\text{Cl}-]}^2}\\ & =E_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/{\text{Hg}}_2^{2+},{\text{Cl}}^{-}}^0-\frac{RT}{2F}\ln \frac{1}{K_{sp}}\text{in which}{E}_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/{\text{Hg}}_2^{2+},{\text{Cl}}^{-}}^0=+0.53\text{V}\end{array}}$

where E⁰ is the standard electrode potential for the reaction and a_Hg is the activity for the mercury cation.

At equilibrium,

${\displaystyle \mathrm{\Delta }G=-nFE=0\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}}$, or equivalently ${\displaystyle E_{\text{cell}}=0\mathrm{V}}$.

This equality allows us to find the solubility product.

${\displaystyle E_{\text{cell}}=E_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/{\text{Hg}}_2^{2+},{\text{Cl}}^{-}}^0-\frac{RT}{2F}\ln \frac{1}{[{\text{Hg}}_2^{2+}]\cdot {[\text{Cl}-]}^2}=+0.53+\frac{RT}{2F}\ln K_{sp}=0\text{V}}$

${\displaystyle \begin{array}{cc}\ln K_{sp}& =-0.53\cdot \frac{2F}{RT}\\ K_{sp}& =e^{-0.53\cdot \frac{2F}{RT}}\\ & =[{\text{Hg}}_2^{2+}]\cdot [{\text{Cl}}^{-}{]}^2=1.184\times {10}^{-18}\end{array}}$

Due to the high concentration of chloride ions, the concentration of mercury ions (${\displaystyle [{\text{Hg}}_2^{2+}]}$) is low. This reduces risk of mercury poisoning for users and other mercury problems.

SCE potential

${\displaystyle {\text{Hg}}_2^{}{\text{Cl}}_2^{}+2{\text{e}}^{-}\stackrel{-\rightharpoonup }{\leftharpoondown -}2\text{Hg}(\text{l})+2{\text{Cl}}^{-},\text{with}{E}_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/\text{Hg},{\text{Cl}}^{-}}^0=+0.27\text{V}}$

${\displaystyle \begin{array}{cc}{E}_{\frac{1}{2}\text{SCE}}& =E_{{\text{Hg}}_2^{}{\text{Cl}}_2^{}/\text{Hg},{\text{Cl}}^{-}}^0-\frac{RT}{2F}\ln a_{{\text{Cl}}^{-}}^2\\ & =+0.27-\frac{RT}{F}\ln [{\text{Cl}}^{-}].\end{array}}$

The only variable in this equation is the activity (or concentration) of the chloride anion. But since the inner solution is saturated with potassium chloride, this activity is fixed by the solubility of potassium chloride, which is: ⁠342 g/L/74.5513 g/mol⁠ = 4.587 M @ 20 °C. This gives the SCE a potential of +0.248 V vs. SHE at 20 °C and +0.244 V vs. SHE at 25 °C, but slightly higher when the chloride solution is less than saturated. For example, a 3.5M KCl electrolyte solution has an increased reference potential of +0.250 V vs. SHE at 25°C while a 1 M solution has a +0.283 V potential at the same temperature.