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Two_Fishes
science forum beginner

Joined: 17 Jan 2006
Posts: 24

Posted: Mon Apr 17, 2006 3:55 am    Post subject: Differing electrode potentials in tables

Could somebody explain to me why the CRC Handbook shows different
standard electrode potentials for half-reactions done stepwise and all
at once? For example, chlorate to chloride (alkaline) is given as 0.6v,
approximately. Chlorate to chlorite to hypochlorite to chloride adds up
to 1.8 volts. Another example, Fe+3 to Fe is -0.3v direct, but Fe+3 to
Fe+2 is +0.77v and Fe+2 to Fe is -0.44, which totals +0.33v. Surely
both go through the Fe+2 stage.
Lasse Murtomäki
science forum beginner

Joined: 17 Jun 2005
Posts: 35

 Posted: Tue Apr 18, 2006 1:55 pm    Post subject: Re: Differing electrode potentials in tables Look at the stoichiometry. For the reaction Fe(3+) + 3 e- = Fe we can write E_1 = E_1^0 + RT/(3F)*log[Fe(3+)] Accordingly: Fe(3+) + e- = Fe(2+) E_2 = E_2^0 + RT/F*log{[Fe(3+)]/[Fe(2+)]} Fe(2+) + 2 e- = Fe E_3 = E_3^0 + RT/(2F)*log[Fe(2+)] If you sum two latter reactions: E_2 + E_3 = E_2^0 + E_3^0 + RT/F*log{[Fe(3+)]/[Fe(2+)]^½} which is not equal to E1. But 1/3*(E_2 + 2*E_3) = E_1 1/3*(0.77 - 2*0.44) = -0.036666666... You have a misprint: for the first reaction E_1^0 = -0.036 V, I checked CRC. Thanks for a very interesting question!
Oscar Lanzi III
science forum Guru Wannabe

Joined: 30 Apr 2005
Posts: 176

Posted: Wed Apr 19, 2006 1:37 am    Post subject: Re: Differing electrode potentials in tables

You don't add up voltages. You add up free energies. The free energy
associated with a half-reaction is the voltage times the charge
transferred, with the sign reversed (thus positive voltage --> negative
free energy.) The charge transferred is proportional to the number of
electrons you see in the reaction. Thus Fe(2+) + 2e(-) = Fe involves
twice as much charge transfer as Fe(3+) + 1e(-) = Fe(2+). The constant
of proportionality in this relation is the accumulated charge of one
mole of electrons, called Faraday's Constant and usually labeled F and
evaluated as 96,487 Coulombs. Thus our product relation fro free energy
is usually written

deltaG = -n*F*E.

So if we are given voltages for the above two half-reactions and want to
compute the overall voltage for Fe(3+) + 3e(-) = Fe, we multiply the
Fe(2+)/Fe reaction by 2F and the Fe(3+)/Fe(2+) reaction by just F to get
the right free energy terms to add up. Then we see that the overall
free energy corresponds to a three-electron transfer, so we have to
divide by 3F to get back to a voltage. What we ultimately get is a
weighted average of voltages instead of just a sum.

--OL
Two_Fishes
science forum beginner

Joined: 17 Jan 2006
Posts: 24

 Posted: Wed Apr 19, 2006 2:56 pm    Post subject: Re: Differing electrode potentials in tables Thanks for the explanations! So you take the average, weighted by the number of electrons, to get the half-cell voltage. Then you add the two half-cells together to get the cell voltage. Then you multiply the voltage by Faraday's constant and divide by the molecular weight per mole of electrons to get the theoretical energy density of an electromotive cell (which is what I was trying to compute.) Boron - Air (acidic) B + 3H2O = H3BO3 + 3H+ + 3e- 2.5 v 3.6 g/e O2 + 4H+ + 4e- = 4H2O 1.229v 8 g/e 3.729v, 8615 W-hr/kg Borohydride - Air (alkaline) BH4- + 8OH- = H2BO3- + 5H2O + 8e- 1.24v 4.75 g/e O2 + 2H2O + 4e- = 4OH- 0.401v 8 g/e 1.641 v, 3449 W-hr/kg I'll see if I can get these to work. Would be nice, wouldn't it?
Two_Fishes
science forum beginner

Joined: 17 Jan 2006
Posts: 24

 Posted: Thu Apr 20, 2006 6:58 pm    Post subject: Re: Differing electrode potentials in tables Now it seems I can't even read the Handbook correctly. It is pretty small type. My apologies to anybody who was offended by the wrong figures. Boron - Air (acidic) B + 3H2O = H3BO3 + 3H+ + 3e- 0.73 v 3.6 g/e O2 + 4H+ + 4e- = 4H2O 1.229v 8 g/e 1.959v, 4526 W-hr/kg Boron - Air (alkaline) B + 4OH- = H2BO3- + H2O + 3e- 2.5 v 3.6 g/e O2 + 2H2O + 4e- = 4OH- 0.401v 8 g/e 2.901v, 6702 W-hr/kg Boron - Sodium Chlorate B + 4OH- = H2BO3- + H2O + 3e- 2.5 v 3.6 g/e ClO3- + 3H2O + 6e- = Cl- + 6OH- 0.62 v 17.74 g/e 3.12v, 3918 W-hr/kg The discharged state is Sodium Borate and Sodium Chloride; if the cell can be recharged from those materials it would be inexpensive.

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