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Electrochemistry calculations (redox potentials and cells)

Dear Reader,

I was recently teaching some electrochemistry to some students, now before we get going it is important to note that the conventions on writing electrode potentials changed years ago. So if thou gets one’s ye olde text book out or ye olde almanack of chemie be ready for some possible problems.

For example in the 1950s paper on plutonium redox chemistry by Sherman W. Rabideau and  Joe F. Lemon, Journal of the American Chemical Society, 1951, 73, 2895-2899 the redox couple for Pu(IV)/Pu(III) is listed as being -0.953 volts vs the standard hydrogen electrode. Now in modern text books it is listed as about + 0.95 volts. This modern use is an example of the “European” convention while the example I gave as an example of the “American” convention. I would say that both are equally valid but if you want to do a redox calculation be careful that you do not mix unwittingly mix data from both conventions up.

I have not seen the american convention being used much in modern text books, but please be aware that it does exist.

OK Health warning over lets get on with some chemistry. Now as a brain teaser (or brain expanded) I asked my students to consider the question of will a solution of iron(II) tend to reduce a solution of plutonium(IV) to plutonium(III) thus forming iron(III) in the process.

Now the redox couple of iron(II) / iron (III) is +0.77 volts (European convention). So we can calculate the cell voltage for our cell under “standard” conditions (1 mole per litre of everything, at 25 ºC and 1 bar).

We can combine the following two half equations

Fe2+ → Fe3+ + e

e + Pu4+ → Pu3+

To give us

Fe2++ Pu4+ → Fe3+ + Pu3+

The emf of the cell will be under standard conditions equal to 0.18 volts, but which thing will be reduced and what will be oxidized. The plutonium couple is higher (more positive) than the iron one in our European type text. So the plutonium will tend to oxidize the iron to form plutonium(III).

We get the emf of the cell from the difference between the two redox couples. All redox couples are expressed relative to hydrogen gas / hydrogen ions in 1 M acid. This choice of standard is simply a convention. Like the Greenwich meridian we need some arbitrary point to call zero. Hydrogen is a good choice as it features in so many reactions.

From the value of the emf of our cell we can get the ΔG of the reaction, to do this we use the following equation.

ΔG = -nFE

n is the number of electrons which are transferred in the cell reaction (1) and F is Faraday’s constant (charge on a mole of electrons) which is equal to 96485 C. Using this we can get a value for the Gibbs free energy of the reaction. Keep in mind that a cell with a positive emf is a cell which is able to do work, thus ΔG for the reaction in the cell must be negative.

This works out as -17367.3 joules per mole.

We can now get the equilibrium constant for this reaction, when a cell has a emf of zero then it has reached equilibrium. Now we need to use a different equation.

ΔG = ΔGº + RT Ln Q

In our case

Q = aPu3+ aFe3+ / aPu4+ aFe2+

Now in the ideal world (nice place I wish I lived there) the activity coefficient is equal to one, the closest we get to an ideal world is a dilute solution. So for nice and dilute solutions we can write

Q = [Pu3+] [Fe3+] / [Pu4+] [Fe2+]

If ΔG = 0 (zero) then

ΔGº = -RT ln ([Pu3+] [Fe3+] / [Pu4+] [Fe2+])

Rearrange to

-ΔGº / RT = ln ([Pu3+] [Fe3+] / [Pu4+] [Fe2+])

exp (-ΔGº / RT) = ([Pu3+] [Fe3+] / [Pu4+] [Fe2+])

Now do the maths

exp (7) = ([Pu3+] [Fe3+] / [Pu4+] [Fe2+]) = k

Now k = 1107

we can rewrite the equations to give us

ΔGº = -RT ln k

Now it should be clear to my readers that a solution of iron(II) will reduce tetravalent plutonium into trivalent plutonium. You might be interested to read that the classic method of adjusting the oxidation state of plutonium from +4 to +3 in the PUREX process is to use ferrous sulfamate.

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Reference electrodes

OK yesterday was an interesting day the electric power went off during a thunderstorm at about 13:15 which brings me onto the topic of electrochemistry; I tried to write as long as the electrochemical cells in my laptop allow me to.

I was recently at a nuclear research centre where fuel is placed inside a research reactor to allow a range of different reactors to be simulated both under their normal conditions and under accident conditions. One of the things which I saw was the mention of a Fe/Fe3O4 reference electrode.

Before we go any further you need to know what a reference electrode is, it can be thought of as a stake driven into the ground and a landmark. This allows to locations of other things to be measured relative to the stake.

The classic reference electrode is the normal hydrogen electrode, this is the primary standard but it is a real dinosaur.

H2 → 2H+ + 2e

It requires a supply of good clean hydrogen (fire risk) and it is not easy to use. The potential is controlled by the proton concentration in the half cell and the partial pressure of the hydrogen. Much of the time people want to use electrodes which are more simple to use.

A classic which is an old friend of mine is the saturated calomel electrode; please note it is not a caramel electrode! Calomel is mercury(I) chloride (Hg2Cl2) which is a white solid with a low solubility. The electrode operates using the following equation.

2Hg + 2Cl→ Hg2Cl2 + 2e

The electrode consists of some mercury metal covered with some calomel which is then immersed in saturated potassium chloride solution. Hence as a result it is banned in Sweden, I can recall as a first year undergraduate at Imperial College making my own SCE in a teaching lab.

The potential of this electrode is largely controlled by the solubility product of calomel and the potassium chloride concentration.

Needless to say chemists have come up with some alternative electrodes which do not contain mercury and are suitable for aqueous media. One of these is the silver / silver chloride electrode which is used by many electrochemists.

A typical Ag/AgCl electrode consists of a silver wire with a coating of silver chloride which is immersed in a chloride solution. It operates by the following equation.

Ag + Cl→  AgCl + e-

Some other reference electrodes exist such as the copper / copper sulphate electrode which is quite popular for corrosion studies. This one is a copper wire which is immersed in copper sulphate solution. This forms part of the classic Daniel cell. I will let you write out the mechanism for this electrode.

When I saw description of a iron/iron oxide reference electrode which is designed for use under BWR conditions. This reference electrode is intended for use under the rather extreme conditions found in a boiling water reactor. It will be hot and unlike a PWR it will not be possible to maintain a constant concentration of hydrogen. The lack of hydrogen rules out the use of a platinum reference electrode.

I have not been able to find details of the construction of the iron/iron oxide electrode but I have found from the literature details of a copper/cuprous oxide electrode. This electrode is a mixture of copper powder and copper(I) oxide inside a yttrium stabilised zirconia (YSZ) tube.

The half cell will be Cu | Cu2O | ZrO2 | H2O

The reaction in the reference electrode will be

2 Cu + O2-→ Cu2O + 2e-

The YSZ is an oxide conductor, oxide anions are mobile in this solid. So the overall set of equations for the electrode will be

2 Cu + O2-→  Cu2O + 2e- on the central wire

H2O → 2H+ + O2- and HO → H+ + O2- on the surface of the YSZ tube

If we combine the equations we can get a single equation.

2 Cu + H2O + O2- → Cu2O + 2e + 2H+ + O2-

Remove the items which appear on both sides of the arrow.

2 Cu + H2O → Cu2O + 2e + 2H+

As the overall electrode equation has protons in it then the electrode potential will change as a function of pH, this is a disadvantage over electrodes such as the SCE. But on the other hand the SCE is dependant on the chloride concentration inside it.

PS. The power came back on about 1 hour and 15 minutes after it went off.

Polyaniline

Polyaniline changes colour when its redox state is changed, I have seen it happen and it is very pretty.

Regarding polyaniline here is a paper on the subject of this wonderful substance

http://physics.msuiit.edu.ph/spvm/papers/2002/jacosalem.pdf

Chairs

Dear Reader,

Here is something interesting, it is a pair of chairs which change colour. The artist does not say how he did it but I think one possible way would be to use an electrochromic dye such as polyaniline.

http://www.tofsen.se/articles/34/two-chairs-changing-appearance-in-9-was-6-if

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