[Big-Daddy]

How far will VO₂⁺ be reduced by Zn  Zn²⁺ + 2e^- reaction (E°=-0.76 V for the reduction, E°=0.76 V for the oxidation), given that I have calculated E° for these reactions to be:

E°(VO₂⁺ + 2H⁺ + e^-  VO²⁺ + H₂O) = 1.00 V
E°(VO₂⁺ + 4H⁺ + 2e^-  V³⁺ + 2H₂O) = 0.68 V
E°(VO₂⁺ + 4H⁺ + 3e^-  V²⁺ + 2H₂O) = 0.3683333 V
E°(VO₂⁺ + 4H⁺ + 5e^-  V + 2H₂O) = -0.231 V

It is tempting to hypothesize that the last reaction with positive E° will be the last that occurs, i.e. it will be reduced to +2 oxidation state but no further - but this appears to have no dependence on E°(oxidation) of the reducing agent, which can't be right. So how do we work out?

[Big-Daddy]

The original source of this problem is International Chemistry Olympiad 2008 Preparatory Problem 13, http://www.icho.hu/files/prep_problems_icho40.pdf , if someone wants to check that I've done E° calculations right.

I considered calculating ΔG° for the overall redox reaction, but I don't think it is fair to say that the most negative ΔG° will show how far VO₂⁺ is reduced, because then we could just multiply one of the (less) negative (but still negative) reactions by some large number through all its stoichiometric coefficients and say "now this reaction has most negative ΔG°".

[Rutherford]

Convert the voltages to Gibbs' energy and calculate the Gibbs' energy of the overall reactions for each case and see whether the reaction is spontaneous.

[Big-Daddy]

Convert the voltages to Gibbs' energy and calculate the Gibbs' energy of the overall reactions for each case and see whether the reaction is spontaneous.

Well we can't use ΔG since we don't have enough information about concentrations, but we can use ΔG°. My results are


ΔG°(2VO₂⁺ + 4H⁺ + Zn 2VO²⁺ + 2H₂O + Zn²⁺) = -339.6 kJ/mol
ΔG°(VO₂⁺ + 4H⁺ + Zn V³⁺ + 2H₂O + Zn²⁺) = -277.9 kJ/mol
ΔG°(2VO₂⁺ + 8H⁺ + 3Zn 2V²⁺ + 4H₂O + 3Zn²⁺) = -653.2 kJ/mol
ΔG°(2VO₂⁺ + 8H⁺ + 5Zn 2V + 4H₂O + 5Zn²⁺) = -510.4 kJ/mol

So you'd think then that VO₂⁺ is reduced all the way to V, since every reaction on the line has (strongly) negative ΔG°. But this isn't the correct answer... instead it stops at V²⁺. Most negative ΔG° argument, refer to my post above?

[Rutherford]

No, calculate the Gibbs' energy for zinc oxidation and then calculate the Gibbs energy for the overall reaction in each of the four cases (just as using Hess law).

[Big-Daddy]

No, calculate the Gibbs' energy for zinc oxidation and then calculate the Gibbs energy for the overall reaction in each of the four cases (just as using Hess law).

Didn't I just calculate the (standard) Gibbs' energy for the overall reaction in each of the four cases?

[Rutherford]

Oops. Sorry, didn't see. Most negative ΔG° argument is correct, you can prove it. Calculate the Gibbs energy for V²⁺ to V reduction. It should be positive, so as the V²⁺ production has the most negative Gibbs energy, and V²⁺ isn't reduced further to V, it can be concluded that VO₂⁺ will be mostly reduced to V²⁺.

[Big-Daddy]

Oops. Sorry, didn't see. Most negative ΔG° argument is correct, you can prove it. Calculate the Gibbs energy for V²⁺ to V reduction. It should be positive, so as the V²⁺ production has the most negative Gibbs energy, and V²⁺ isn't reduced further to V, it can be concluded that VO₂⁺ will be mostly reduced to V²⁺.

I see the logic. One point - if we consider VO₂⁺ to V³⁺ reduction, do we have to use ΔG°(2VO₂⁺ + 8H⁺ + 2Zn 2V³⁺ + 4H₂O + 2Zn²⁺) = -277.9*2 = -555.8 kJ/mol to consider it fairly alongside the others? So if, e.g. the ΔG° for the reduction by Zn to V²⁺ was -520 kJ/mol rather than -653 kJ/mol, then we'd get reduction to V³⁺ and no further?

[Rutherford]

Yes.

[Big-Daddy]

Ok. Now let's say we make it more complicated and use Cu metal instead of Zn. Cu can be oxidized to +1 or +2 oxidation states or not at all (http://hyperphysics.phy-astr.gsu.edu/hbase/tables/electpot.html). Would you still know how to solve it? (by solve it, I mean find the main reaction of the system)

I think mastering Latimer diagrams would be good for this year's IChO.

[Rutherford]

Then you would have 8 reactions plus 4 more to compare the copper(I) oxidation to copper(II) in each case.

[Big-Daddy]

Why plus 4 more? We are starting with Cu, so isn't it true that either Cu remains Cu (no reaction occurs, the VO₂⁺ does not get to form a redox equilibrium at all), or it gets oxidized to Cu⁺ (by one of the 4 reductions), or it gets oxidized to Cu²⁺ (by one of the 4 reductions)?

So then, in this case, the most negative ΔG° approach is still going to be for the main reaction (which shows how far Cu gets oxidized and VO₂⁺ gets reduced)?

Note: if Cu remains Cu, we could call this a null reaction with K=1 and ΔG°=0, meaning that if all the possible reactions in our system had ΔG°>0, the null reaction would 'occur' and nothing will happen.

[Rutherford]

Maybe Cu⁺ is even easier oxidized to Cu²⁺ than Cu. I am not sure exactly if it is, but this should be checked.

[Big-Daddy]

Maybe Cu⁺ is even easier oxidized to Cu²⁺ than Cu. I am not sure exactly if it is, but this should be checked.

From general knowledge I know that Cu⁺ tends to disproportionate to Cu²⁺ and Cu. But I would think that all these possibilities are included when you calculate ΔG° for all 8 reactions you mentioned before? I do not think "the main reaction" in this question could start with Cu⁺ because there is no Cu⁺ initially present. And if there was, it would just disproportionate.

So if we have a set of the reactions that can happen starting from the initial reactants present (here, seems to be 8 - starting from Cu and VO₂⁺) are you sure most negative ΔG° is the right way to find the main reaction?

[Rutherford]

I don't see why not. I didn't say that the main reaction would start with Cu(I). If Cu(I) disproportionates easily, then in the overall reaction Cu(II) would be produced even if you previously get the most negative Gibbs energy for an overall reaction with Cu(I) being produced (by checking the 8 reactions).