# In a voltaic cell with standard hydrogen electrode is the measure half cell always the cathode?

I am a bit confused. My openstax textbook states:

"When the half-cell X is under standard-state conditions, its potential is the standard electrode potential, E°X. Since the definition of cell potential requires the half-cells function as cathodes, these potentials are sometimes called standard reduction potentials."

I would greatly appreciate if someone can explain to me why the half cell has to be a cathode if the measured reduction table has both positive and negative values.

• Formal negative reduction potential (Positive reaction Gibbs energy as $\Delta G^{\circ}_r = -nFE^{\circ}$) for being cathode means positive oxidation potential (negative reaction Gibbs energy) for being actually anode, as the latter is the direction of spontaneity. Reaction H2 + 2 Na+ -> 2 H+ + 2 Na has highly positive reaction Gibbs energy and highly negative formal reduction potential. Commented Apr 21, 2023 at 5:43
• Sorry I am not quite understanding. So its the cathode even though it had less "electron wanting desire" because hydrogen is the lowest? Commented Apr 21, 2023 at 5:46
• It is formal cathode, but actually anode, as the Gibbs energy change and related potential are formally evaluated in this case in the direction opposite to spontaneity. If we used absolute values of reduction potentials instead, it would bring huge mess. Commented Apr 21, 2023 at 5:48
• So whether if an electrode is a cathode or anode it will always be a "formal" cathode. However, when you calculate the E° the value would either be neg or positive. If its an actual "anode" the electrode would be having electrons flowing out from that end and the cell will have a negative E°? Commented Apr 21, 2023 at 5:52
• The half cell reduction potential can be seen as the relative external potential (wrt SHE), that has to be set on the considered half cell to keep the half-cell at the edge between being a cathode and being an anode. The halfcell is an anode if Eext > E and vice versa. This addresses just TD, but not kinetic aspects. Many potentials are due frozen kinetics purely formal. Commented Apr 21, 2023 at 7:16

In aqueous solution the potential of the standard hydrogen electrode is defined as 0. volts. The standard conditions are: all activities, fugacities, molarities equal to one [1.]. By DEFINITION in a cell Oxidation is at the Anode and Reduction is at the Cathode. Now comes the dilemma How do we write a standard redox equation?

Na +1/2H3O+ = Na+ + 1/2H2 + H2O; E = ~+2.8V oxidation at the anode. Or

Na+ +1/2H2 + H2O = Na + H3O+ E = ~-2.8V reduction at the cathode!

Way back when, the Europeans liked the first and the Americans liked the second. As usual they fought it out and decided on the second [It was preferred that Sodium ions did not react with water than that Sodium did react explosively with water.] but you can still reverse everything when necessary.

Physicists are still confused because they consider electric current as the flow of +charge not as [we know it] the flow of electrons.

Sodium reacts violently with water. It is oxidized. the oxidation potential is positive [+]. Sodium ion is reduced with difficulty in water. The reduction potential is negative [-].

Finally, it is the nature of aqueous solution that the potentials for H2 are "central". Some species [Na+, Ca++ etc.] are reduced with difficulty and have negative reduction potentials. Others such as O2, F2, Cl2, MnO4- etc. are reduced easily and have positive reduction potentials. There is a large range in between. Of course, if one prefers to work with oxidation potentials everything is reversed.

• You have it the other way round: Europeans preferred the reduction potential (Ostwald school of thought), not the Americans (Gibbs and Latimer school) and it was not simply not a matter of reversing the sign. It is the actual electrostatic sign of the electrode with respect to the hydrogen electrode and this is why all the reduction potentials have been adopted. So the European convention won not the American :-)
– ACR
Commented Apr 22, 2023 at 17:19
• Thanks! I was working from memory of my Quant analysis course, the potential table was oxidation, and a long ago discussion. The way the equation is written has no effect on what is happening at the electrode. Commented Apr 22, 2023 at 23:36