Reversible hydrogen electrode

A reversible hydrogen electrode (RHE) is a reference electrode, more specifically a subtype of the standard hydrogen electrodes, for electrochemical processes. Unlike the standard hydrogen electrode, its measured potential does change with the pH, so it can be directly used in the electrolyte.

The name refers to the fact that the electrode is directly immersed in the actual electrolyte solution and not separated by a salt bridge. The hydrogen ion concentration is therefore not 1 mol/L, or 1 mol/kg, but corresponds to that of the electrolyte solution. In this way, it is possible to achieve a stable potential with a changing pH value. The potential of the RHE correlates to the pH value: : E = 0.000 - 0.059\times\mathrm{pH}

In general, for a hydrogen electrode in which the reduction of the hydronium ions () occurs:

: {2H3O+} + {2e^-} {H2} + {2H2O}

or, more often commonly written simply with denoting :

: {2H+} + {2e^-} {H2}

with, : K = \frac {p{\ce{H2}}} {\ce{(aH+)^2}}

the equilibrium potential E depends on the hydrogen pressure pH2 and the activity aH+ as follows:

: E = E^{\ominus} - \frac{RT}{zF} \ln K

: E = E^{\ominus} - \frac{RT}{2F} \ln \frac {p{\ce{H2}}} {\ce{(aH+)^2}}

: E = E^{\ominus} - \frac{RT}{F} \left( \tfrac12\ln p{\ce{H2}} - \ln \ce{(aH+)} \right)

: E = E^{\ominus} + \frac{RT}{F} \left( \ln a\ce{H+} - \tfrac12\ln p\ce{H2} \right)

Here, E^{\ominus} is the standard reduction potential (by convention equal to zero), R is the universal gas constant, T the absolute temperature, and F is the Faraday constant.

An overpotential occurs in the electrolysis of water. This means that the required cell voltage is higher than the equilibrium potential because of kinetic limitations. The potential increases with increasing current density at the electrodes. The measurement of equilibrium potentials is therefore possible without power.