Standard hydrogen electrode

In electrochemistry, the standard hydrogen electrode, is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential 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, into one gaseous hydrogen molecule,
General equation for a reduction reaction:
The reaction quotient of the half-reaction is the ratio between the chemical activities of the reduced form and the oxidized form.
Considering the redox couple:
at chemical equilibrium, the ratio of the reaction products by the reagents is equal to the equilibrium constant of the half-reaction:
where

and correspond to the chemical activities of the reduced and oxidized species involved in the redox reaction
represents the activity of.
denotes the chemical activity of gaseous hydrogen, which is approximated here by its fugacity
denotes the partial pressure of gaseous hydrogen, expressed without unit; where
* is the mole fraction
* is the total gas pressure in the system
is the standard pressure 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. In the SHE, pure hydrogen gas at the standard pressure of is engaged in the system. Meanwhile the general SHE equation can also be applied to other thermodynamic systems with different mole fraction or total pressure of hydrogen.
This redox reaction occurs at a platinized platinum electrode.
The electrode is immersed in the acidic solution and pure hydrogen gas is bubbled over its surface. The concentration of both the reduced and oxidised forms of hydrogen are maintained at unity. That implies that the pressure of hydrogen gas is 1 bar and the activity coefficient of hydrogen ions in the solution is unity. The activity of hydrogen ions is their effective concentration, which is equal to the formal concentration times the activity coefficient. These unit-less activity coefficients are close to 1.00 for very dilute water solutions, but usually lower for more concentrated solutions.
As the general form of the Nernst equation at equilibrium is the following:
and as by definition in the case of the SHE,
The Nernst equation for the SHE becomes:
Simply neglecting the pressure unit present in, this last equation can often be directly written as:
And by solving the numerical values for the term
the practical formula commonly used in the calculations of this Nernst equation is:
As under standard conditions the equation simplifies to:
This last equation describes the straight line with a negative slope of −0.0591 volt/ pH unit delimiting the lower stability region of water in a Pourbaix diagram where gaseous hydrogen is evolving because of water decomposition.
where:

is the activity of the hydrogen ions in aqueous solution,

with:

* is the activity coefficient of hydrogen ions in aqueous solution
* is the molar concentration of hydrogen ions in aqueous solution
* is the standard concentration used to overcome concentration unit
is the partial pressure of the hydrogen gas, in bar
is the universal gas constant: J⋅K⁻¹⋅mol⁻¹
is the absolute temperature, in kelvin
is the Faraday constant, equal to
is the standard pressure:
SHE vs NHE vs RHE

During the early development of electrochemistry, researchers used the normal hydrogen electrode as their standard for zero potential. This was convenient because it could actually be constructed by " a platinum electrode into a solution of 1 N strong acid and hydrogen gas through the solution at about 1 atm pressure". However, this electrode/solution interface was later changed. What replaced it was a theoretical electrode/solution interface, where the concentration of H⁺ was 1 M, but the H⁺ ions were assumed to have no interaction with other ions. To differentiate this new standard from the previous one, it was given the name 'standard hydrogen electrode'.
In summary,

Choice of platinum

The choice of platinum for the hydrogen electrode is due to several factors:

inertness of platinum
the capability of platinum to catalyze the reaction of proton reduction
a high intrinsic exchange current density for proton reduction on platinum
excellent reproducibility of the potential

The surface of platinum is platinized to:

Increase total surface area. This improves reaction kinetics and maximum possible current
Use a surface material that adsorbs hydrogen well at its interface. This also improves reaction kinetics

Other metals can be used for fabricating electrodes with a similar function such as the palladium-hydrogen electrode.

Interference

Because of the high adsorption activity of the platinized platinum electrode, it's very important to protect electrode surface and solution from the presence of organic substances as well as from atmospheric oxygen. Inorganic ions that can be reduced to a lower valency state at the electrode also have to be avoided. A number of organic substances are also reduced by hydrogen on a platinum surface, and these also have to be avoided.
Cations that can be reduced and deposited on the platinum can be source of interference: silver, mercury, copper, lead, cadmium and thallium.
Substances that can inactivate the catalytic sites include arsenic, sulfides and other sulfur compounds, colloidal substances, alkaloids, and material found in biological systems.

Isotopic effect

The standard redox potential of the deuterium couple is slightly different from that of the proton couple. Various values in this range have been obtained: −0.0061 V, −0.00431 V, −0.0074 V.
Also difference occurs when hydrogen deuteride is used instead of hydrogen in the electrode.

Experimental setup

The scheme of the standard hydrogen electrode:

platinized platinum electrode
hydrogen gas
solution of the acid with activity of H⁺ = 1 mol dm⁻³
gas bubbler for preventing oxygen interference
reservoir through which the second half-element of the galvanic cell should be attached. The connection can be direct, through a narrow tube to reduce mixing, or through a salt bridge, depending on the other electrode and solution. This creates an ionically conductive path to the working electrode of interest.