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 × p H {\displaystyle E=0.000-0.059\times \mathrm {pH} }
In general, for a hydrogen electrode in which the reduction of the hydronium ions (H3O+) occurs:
2 H 3 O + + 2 e − ↽ − − ⇀ H 2 + 2 H 2 O {\displaystyle {\ce {{2H3O+}+{2e^{-}}<=>{H2}+{2H2O}}}}
or, more often commonly written simply with H+ denoting H3O+:
2 H + + 2 e − ↽ − − ⇀ H 2 {\displaystyle {\ce {{2H+}+{2e^{-}}<=>{H2}}}}
with,
K = p H 2 ( aH + ) 2 {\displaystyle 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 ⊖ − R T z F ln K {\displaystyle E=E^{\ominus }-{\frac {RT}{zF}}\ln K}
E = E ⊖ − R T 2 F ln p H 2 ( aH + ) 2 {\displaystyle E=E^{\ominus }-{\frac {RT}{2F}}\ln {\frac {p{{\ce {H2}}}}{{\ce {(aH+)^2}}}}}
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