Interpreting Electrode Potentials

[etotheipi]

My teacher insists that the reverse reaction has a negated electrode potential (oxidation potential?).

This doesn’t make sense to me, since I am under the impression that the electrode potential is a property of the half cell at equilibrium and not of either of the reactions in a particular direction. That is, the potential difference E(cell) should be simply the difference of the electrode potentials when the reactions in each cell are in equilibrium.

What is the logic behind assigning different electrode potentials to different directions of the reaction? Isn’t the underlying physics just the difference between the raw potentials of each electrode?

 

[mjc123]

From Wikipedia article "Electrode potential":

"Historically, two conventions for sign for the electrode potential have formed:

1. convention "Nernst–Lewis–Latimer" (sometimes referred to as "American"),
2. convention "Gibbs–Ostwald–Stockholm" (sometimes referred to as "European").

In 1953 in Stockholm IUPAC recognized that either of the conventions is permissible; however, it unanimously recommended that only the magnitude expressed according to the convention (2) be called "the electrode potential". To avoid possible ambiguities, the electrode potential thus defined can also be referred to as Gibbs–Stockholm electrode potential. In both conventions, the standard hydrogen electrode is defined to have a potential of 0 V. Both conventions also agree on the sign of E for a half-cell reaction when it is written as a reduction.
The main difference between the two conventions is that upon reversing the direction of a half-cell reaction as written, according to convention (1) the sign of E also switches, whereas in convention (2) it does not. The logic behind switching the sign of E is to maintain the correct sign relationship with the Gibbs free energy change, given by ΔG = -nFE where n is the number of electrons involved and F is the Faraday constant. It is assumed that the half-reaction is balanced by the appropriate SHE half-reaction. Since ΔG switches sign when a reaction is written in reverse, so to, proponents of convention (1) argue, should the sign of E. Proponents of convention (2) argue that it is more convenient to consider oxidants and reductants on the same scale."

 

[etotheipi]

The logic behind switching the sign of E is to maintain the correct sign relationship with the Gibbs free energy change

So suppose the two half reactions are

$A^{n+} + ne^{-} \rightarrow A$, with $\Delta G_{1}$ and $E_{1}$
and $B \rightarrow B^{n+} + ne^{-}$, with $\Delta G_{2}$ and $E_{2}$

On adding the half equations, we obtain
$A^{n+} + B \rightarrow A + B^{n+}$, with $\Delta G_{cell} = \Delta G_{1} + \Delta G_{2}$ since Gibbs free energies are definitely additive.

If we accept that $\Delta G = -nFE$ is valid for half equations (I'm not sure if it is), then the argument that $E_{cell} = E_{1} + E_{2}$ could be made (since $-nFE_{cell} = -nFE_{1} -nFE_{2}$). In this case, $E_{2}$ would need to be an oxidation potential.

The Gibbs-Ostwald-Stockholm convention still makes more sense to me, since it seems more intuitive to measure the differences in potential from the same scale, however evidently we cannot add the equations in the same manner.

Is this to say that we can only use $\Delta G = -nFE$ for a half equation if we use convention 1? Or does $\Delta G = -nFE$ not apply to any half equations at all?

Since I'd always thought $\Delta G = -nFE$ was derived by considering the work done by electric field for charges moving from one electrode to the other, I don't see why it would apply to half equations. But that begs the question of what "maintain[ing] the correct sign relationship with the Gibbs free energy change" was referring to!

 

[mjc123]

I suppose it's a matter of convention. We can only measure a potential difference across two electrodes, or ΔG for a whole reaction, so the meaning of these quantities is somewhat arbitrary when applied to a half-reaction (for instance, it begs the question of the physical state of the electrons). If we define E° ≡ 0V for the SHE, and define E° for any other electrode as the potential of the cell in which it is coupled to the SHE, then we can define ΔG° = 0 for SHE and ΔG° = -nFE° for the other electrode. Then Es and ΔGs are additive in the same way; but you can only do this if you use convention 1.

 

[etotheipi]

If we define E° ≡ 0V for the SHE, and define E° for any other electrode as the potential of the cell in which it is coupled to the SHE, then we can define ΔG° = 0 for SHE and ΔG° = -nFE° for the other electrode. Then Es and ΔGs are additive in the same way; but you can only do this if you use convention 1.

Hi @mjc123 , sorry to reopen an old thread but I just thought up another question about this part.

You say that if we define ΔG° = -nFE° for a half equation, then the E's become additive, though in fact doesn't ΔG° = -nFE° only hold for a cell as a whole (since we derive it by considering charge moving from one terminal to the other)?

Another thing is that if ΔG° = -nFE° were true for a half equation, then if we double the half equation ΔG° like all thermodynamic state variables should also double. But E° does not! So the relationship cannot be true.

So in that case isn't convention (1) slightly arbitrary? Sorry to bother you further!

 

[mjc123]

Easy one first, if we double the half-equation we double n.

ΔG° = -nFE° may be derived as you say for a whole cell. That's why I say we choose (as a matter of convention) to define ΔG° = -nFE° for a half reaction (rather than saying it's thermodynamically true).

 

[etotheipi]

@mjc123 On a slightly unrelated note, is an “electrode potential” an electric potential or a potential difference?

Some sources write it is the difference between the potentials between the electrode and the electrolyte (evidently also shifted by a constant that equals the absolute electrode potential of the SHE electrode).

But then why do we call it a potential?

Thanks a bunch for your help

 

[mjc123]

Think about a number of identical cells connected in series. Do the cathodes all have the same potential? Do they have the same potential difference (relative to the electrolyte in the same cell)?

 

[etotheipi]

This is actually how I came to the conclusion that the electrode potential must be a potential difference. Since if we connected a number of cells with e.g one half cell hydrogen and one half cell zinc, then the potentials of successive hydrogen electrodes would increment by around 2.7 every cell.

So I decided that the electrode potential is the difference between the electrode and electrolyte, plus a constant which equals the absolute electrode potential of hydrogen (as a “shift” term).

It’s just a little odd since, also, the potential difference across a cell is named the “cell potential”, when it would be much more accurate to call it a cell potential difference!

 

[mjc123]

the potentials of successive hydrogen electrodes would increment by around 2.7 every cell.

Do you mean 0.76V?

 

[etotheipi]

I can't thank you enough for your help @mjc123; I came across the following IUPAC related recommendation which seems to say that the electrode potential is not the aforementioned potential difference,

http://users.unimi.it/ECEA/IUPAC Trasatti Absolute Potential.pdf

This is apparently because we disregard the Galvani potential between the metals.

It seems that it is instead defined as the electric potential of the electrode relative to the electric potential of the hydrogen electrode - in the same cell.

And then the so-called absolute electrode potential is the electric potential of the chosen electrode relative to vacuo, just outside the cell being considered.

Am I getting this mixed up, it's all very confusing. I'm really sorry to bother you again!

 

[etotheipi]

I found this from Bagotsky which might be useful,

In the past, the relation $φ^{(M2,E)} - φ^{(M1,E)}$, involving the individual Galvani potentials between the electrodes and the electrolyte, had been examined under this aspect. However, this relation disregards the Galvani potential between the metals; moreover, it is not useful, insofar as it contains parameters that cannot be determined.

A parameter that is convenient for said purpose is the electrode potential E; it must not be confused with the concept of a potential difference between the electrode and the electrolyte. By convention the term electrode potential E is used to denote the OCV of a galvanic cell that consists of the given electrode (the one that is studied) and a reference electrode selected arbitrarily. Thus, the potential of this electrode is compared with that of a reference electrode that is identical for all electrodes being studied. In accordance with this definition, the electrode potential of the reference electrode itself is (conventionally) regarded as zero.

Though it seems to imply that an electrode potential is just an electric potential of that electrode relative to the electrode of the standard hydrogen half cell.

 

[mjc123]

Yes. In practice, the electrode potential is the potential of the electrode relative to the SHE in a cell. What is meant by the electrode potential of a single electrode on its own is pretty irrelevant to practical electrochemistry. We can't measure it, and we certainly don't know that it has the value 0 for the SHE. We simply assign that electrode a value of 0 in order to assign values to other electrodes. What matters for a cell is the difference between the two electrode potentials.

Why do you need to know all this anyway? Just curiosity?

 

[etotheipi]

Yes. In practice, the electrode potential is the potential of the electrode relative to the SHE in a cell. What is meant by the electrode potential of a single electrode on its own is pretty irrelevant to practical electrochemistry. We can't measure it, and we certainly don't know that it has the value 0 for the SHE. We simply assign that electrode a value of 0 in order to assign values to other electrodes. What matters for a cell is the difference between the two electrode potentials.

Why do you need to know all this anyway? Just curiosity?

Yes it’s mainly out of curiosity, the topic isn’t really covered in any depth in my course so I’m having a lot of trouble with the “chemistry to physics mapping” so that I can relate electrochemistry to general circuit theory.

And the term that seems to be most ambiguous is that of “electrode potential”, since in addition to the functional (and not really very intuitive) IUPAC definition, many sources give different interpretations.

I think now I’m happy to say the electrode potential is the electric potential relative to the potential of a SHE in the same cell, and not the electrode/electrolyte potential difference.

As opposed to the absolute electric potential with the reference at infinity, as i lots of electrostatics!

Of course, none of this really matters too much, but I quite like to have a sort of consistent picture of things!

 

[etotheipi]

@mjc123 One last thing, I promise I won't bother you any more!

I know you said that the electrode potential of a single electrode is pretty much irrelevant, however suppose we did consider the absolute electrode potential of an electrode (as I hear is sometimes done in some semi-conductor research).

The absolute electrode potential of the SHE - which I take to be the electric potential of the electrode relative to vacuum at infinite distance - measured by Trasatti is given as such,

$E^{⦵}_{{H^+}/H_2, abs} = 4.44 \pm 0.02 V$

If I set up two half cells in series, as such:

then which SHE is this value referring to? It can't be both, since there's 0.76 V between them! Something seems really fishy about this...

Edit

Having read over the paper a few more times, I believe the reference relative to which he eventually decided to measure absolute electrode potentials is "a point in a vacuum close to the surface of the the solution (the point where contact potentials are measured". So I am assuming for each individual half cell, the reference is just above the surface of the solution for each - hence resolving my question? Would you say that this is correct?

He did mention the option of choosing to place the reference at infinity, however concluded that it wasn't as meaningful a measure as the aforementioned reference!

 

[mjc123]

which SHE is this value referring to?

Neither. It refers to an isolated single electrode. Connecting them to other electrodes affects the potential.
Consider e.g. a small conducting sphere of radius r with a charge of +Q. In isolation, the potential at the surface is kQ/r. Now consider arranging 4 spheres in a line, with a distance d between each, as follows:
+Q...-Q...+Q...-Q
Will the two positive spheres have the same potential as each other, or as the isolated sphere?

I am assuming for each individual half cell, the reference is just above the surface of the solution for each

I think that is right - each individual electrode has its own reference. If you have a common reference (e.g. the RH Zn electrode) the two SHE electrodes will have different potentials.

 

[etotheipi]

Just to summarise, I came back to this a few weeks later and thought I'd add this just in case it helps anyone in the future, regarding the American and European conventions for electrode potentials.

• Everyone agrees on the value of a standard electrode potential of a couple, as well as the reduction potentials and the oxidation potentials of different species (these are clearly defined quantities!). The last two are related via implicit negation (i.e. $V_{a} - V_{b}$ vs $V_{b} - V_{a}$).
• Everyone agrees that $\mathcal{E_{cell}} = \mathcal{E}^{\mathbb{r}}_{cat}-\mathcal{E}^{\mathbb{r}}_{an} = \mathcal{E}^{\mathbb{r}}_{cat} + \mathcal{E}^{\mathbb{ox}}_{an}$

But...

• The difference arises simply by how electrode potentials are assigned to written half reactions. This is already a slightly sticky point, since the $\mathcal{E}$'s written next to half equations are actually associated with the electrodes in the redox couples and shouldn't be conflated with the chemical concept of the underlying reaction!
• The only difference is that in the European convention, reduction potentials are written next to all half equations no matter the direction, whilst in the American convention, reduction potentials are written next to reductions and oxidation potentials are written next to oxidations.

The European convention has the benefit that $\mathcal{E}$ gives the electric potential of the electrode, which is indeed invariant no matter which reaction direction is occurring at that electrode. The American convention has the benefit that it is perhaps easier to use, e.g. for calculations with many half equations where the commutativity of addition is a useful tool!

The confusion crops up due to conflating the concept of the chemical reaction with the potential written next to it. Unlike quantities like $\Delta H$, $\Delta G$ etc., $\mathcal{E}^o$ is related to the the potential of the electrode formed by the redox couple. We do not get a certain amount of $\mathcal{E}^o$ per mole of reaction!