Standard hydrogen electrode
reference redox electrode used under standard conditions
In electrochemistry, the standard hydrogen electrode (abbreviated SHE), is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential (E°) is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.
Nernst equation for SHE
The hydrogen electrode is based on the redox half cell corresponding to the reduction of two hydrated protons, 2 H+(aq), into one gaseous hydrogen molecule, H2(g).
General equation for a reduction reaction:
(oxidant)
ox
+
z
e
−
↽
−
−
⇀
(reductant)
red
{\displaystyle {\underset {\text{ox}}{\text{(oxidant)}}}+z{\ce {e- <=>}}\ {\underset {\text{red}}{\text{(reductant)}}}}
The reaction quotient (Qr) of the half-reaction is the ratio between the chemical activities (a) of the reduced form (the reductant, ared) and the oxidized form (the oxidant, aox).
Q
r
=
a
red
a
ox
{\displaystyle Q_{r}={\frac {a_{\text{red}}}{a_{\text{ox}}}}}
Considering the 2 H+ / H2 redox couple:
2
H
(
aq
)
+
+
2
e
−
↽
−
−
⇀
H
2
(
g
)
{\displaystyle {\ce {2H_{(aq)}+ + 2e- <=> H2_{(g)}}}}
at chemical equilibrium, the ratio Qr of the reaction products by the reagents is equal to the equilibrium constant K of the half-reaction:
K
=
a
red
a
ox
=
a
H
2
a
H
+
2
=
p
H
2
/
p
0
a
H
+
2
=
x
H
2
p
/
p
0
a
H
+
2
{\displaystyle K={\frac {a_{\text{red}}}{a_{\text{ox}}}}={\frac {a_{\mathrm {H_{2}} }}{a_{\mathrm {H^{+}} }^{2}}}={\frac {p_{\mathrm {H_{2}} }/p^{0}}{a_{\mathrm {H^{+}} }^{2}}}={\frac {x_{\mathrm {H_{2}} }p/p^{0}}{a_{\mathrm {H^{+}} }^{2}}}}
where
a
red
{\displaystyle a_{\text{red}}}
and
a
ox
{\displaystyle a_{\text{ox}}}
correspond to the chemical activities of the reduced and oxidized species involved in the redox reaction
a
H
+
{\displaystyle a_{\mathrm {H^{+}} }}
represents the activity of H+.
a
H
2
{\displaystyle a_{\mathrm {H_{2}} }}
denotes the chemical activity of gaseous hydrogen (H2), which is approximated here by its fugacity
p
H
2
.
{\displaystyle p_{\mathrm {H_{2}} }.}
p
H
2
{\displaystyle p_{\mathrm {H_{2}} }}
denotes the partial pressure of gaseous hydrogen, expressed without unit;
p
H
2
=
x
H
2
⋅
p
,
{\displaystyle p_{\mathrm {H_{2}} }=x_{\mathrm {H_{2}} }\cdot p,}
where
x
H
2
{\displaystyle x_{\mathrm {H_{2}} }}
is the H2 mole fraction
p
{\displaystyle p}
is the total gas pressure in the system
p0 is the standard pressure (1 bar = 105 pascal) introduced here simply to overcome the pressure unit and to obtain an equilibrium constant without unit.
More details on managing gas fugacity to get rid of the pressure unit in thermodynamic calculations can be found at thermodynamic activity#Gases. The followed approach is the same as for chemical activity and molar concentration of solutes in solution.
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