The Handbook of Electrochemistry ISBN: 978-0-444-51958-0 has a good chapter on Reference electrodes which answers this. Also check out http://www.reference-electrode.info/Hydrogenelectrode.html for a brief and complete answer to your question.
They are often used interchangeably in publications, but the difference is:
SHE = Standard Hydrogen Electrode. This is a theoretical concept, defining the scale of electrode potential as 0.00000 V; It is the potential of a 1/2H2 H+ electrode at a fugacity of 1 bar (100kPa), 1N (1 molar activity, ie pH=0) of H+, at all temperatures.
The difficulty with this definition is that the pressure and concentration are not equal to fugacity and activity, so the Normal Hydrogen Electrode (NHE) is used, defined as 1 M H+ concentration and 1 atm pressure. I've read somewhere that the difference between 1 atm and 1 bar (101325 Pa and 100000 Pa) makes 0.17 mV difference to the potential of the NHE.
The RHE is Reversible Hydrogen Electrode, which is a practical hydrogen electrode whose potential depends on the pH of the solution it is used in and the pressure of Hydrogen.
The Handbook of Electrochemistry ISBN: 978-0-444-51958-0 has a good chapter on Reference electrodes which answers this. Also check out http://www.reference-electrode.info/Hydrogenelectrode.html for a brief and complete answer to your question.
They are often used interchangeably in publications, but the difference is:
SHE = Standard Hydrogen Electrode. This is a theoretical concept, defining the scale of electrode potential as 0.00000 V; It is the potential of a 1/2H2 H+ electrode at a fugacity of 1 bar (100kPa), 1N (1 molar activity, ie pH=0) of H+, at all temperatures.
The difficulty with this definition is that the pressure and concentration are not equal to fugacity and activity, so the Normal Hydrogen Electrode (NHE) is used, defined as 1 M H+ concentration and 1 atm pressure. I've read somewhere that the difference between 1 atm and 1 bar (101325 Pa and 100000 Pa) makes 0.17 mV difference to the potential of the NHE.
The RHE is Reversible Hydrogen Electrode, which is a practical hydrogen electrode whose potential depends on the pH of the solution it is used in and the pressure of Hydrogen.