The Hydrogen Reference Electrode

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Often we see an electrode potential reported versus the hydrogen electrode. The hydrogen electrode may be abbreviated SHE, NHE, or RHE. This page should help clarify the differences between these acronyms.

The Hydrogen Electrode

The hydrogen electrode is easy to build. All that is required is to bubble hydrogen through an acid solution of known pH so that it is saturated with hydrogen.  An (ideal) noble metal electrode is placed into the solution. Platinized platinum is generally used to insure a large electrochemical surface area and rapid equilibrium conditions. The pressure of the hydrogen must also be known. Fairly detailed construction details are given ( Ref 1, Ref 2 ) in several texts.

The potential is given by the Nernst equation:

2 H⁺ + 2e^- --> H₂

E = E^o - RT/2F ln P(H₂) / a(H⁺)²
= E^o -(RT/F)*pH -RT/2F ln P(H₂) 

P(H₂) is the partial pressure of H₂ in atmospheres. a(H⁺) is the activity of hydrogen ion. E^o for this half-reaction is defined to be 0.0V at all temperatures. The potential of this reference is only 0.0V if the partial pressure (actually, fugacity) of H₂ and the activity of H⁺ are both unity.

SHE - Thermodynamically sound! But . . .

The Standard Hydrogen Electrode (SHE) is officially the 0.0V thermodynamic reference point for all potential measurements at all temperatures. It is easy to define, but not convenient to implement rigorously.

How much acid do you need to make a solution with a=1?  Compton & Sanders ( 3 ) suggest [H⁺] = 1.18M, but that number will be different for sulfuric and hydrochloric acids since the activity coefficients are different.

Things are not much better when you think about the partial pressure of hydrogen. The vapor pressure of water is about 25 mm Hg at room temperature. So, even if the barometric pressure is 760 mm Hg, the partial pressure of water saturated hydrogen is only 735 mm Hg!

Using 1M H⁺ and using a total pressure of one atmosphere each only contribute about 5mV error.  The errors are in opposite directions, so they tend to cancel.

NHE - A Synonym?

The SHE is also sometimes called the NHE, for Normal Hydrogen Electrode. "Normal" makes me think of the NCE, "Normal Calomel Electrode," which is filled with 1N KCl. I suspect that many have made that association.  Luckily, the potential difference between 1M ( or 1N ) HCl and HCl @ a=1 is small.

In the tables on this web site, I have used NHE because that is the way the majority of the references cited have listed the potentials.

RHE - A Practical Reference!

The Reversible Hydrogen Electrode (RHE) is a fairly practical and reproducible electrode "standard."  The term refers to a hydrogen electrode immersed in the electrolyte solution actually used. I would assume that the total pressure (not partial pressure of hydrogen) is one atmosphere. This electrode is the favorite of those who study hydrogen UPD on Pt electrodes in H₂SO₄. No extraneous ions are introduced, and the hydrogen has to be there anyway!

A Reversible Hydrogen Electrode is available commercially from Gaskatel.  This clever design fills the inside of the electrode body with hydrogen. They use a carbon supported platinum catalyst as a gas diffusion electrode that is in contact with the fixed pressure hydrogen atmosphere on the inside and the solution on the outside. Contact the manufacturer for more details.

More About Reference Electrodes

REFERENCES
(1) "Electrochemistry for Chemists", Sawyer, Sobkowiak, & Roberts, Wiley-Interscience, 1995.
(2) "Principles and Prevention of Corrosion",  DA Jones, Prentice-Hall, 1995.
(3) "Electrode Potentials", Compton & Sanders, Oxford Univ. Press, 1996.

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