[plu]

Hello.  Again, I find myself stuck with a simple analytical problem     I am given a table of reduction potentials for various vanadium half-reactions relating to the speciation of vanadium in aqueous solutions and I am asked to find the most stable vanadium-containing species at pH 4 with all other conditions being standard.  I calculated the potential of the hydrogen half-cell to be -0.236 at pH 4.  To identify the most stable vanadium species, would I simply look for the half-reaction that has a value closest to -0.236?

The next question I am given asks to determine the pH range over which a 1 molar solution of VO₂⁺ would be stable if all other conditions are standard.  The reduction potential of VO₂⁺ is 0.991.  I calculated the pH that would be required to make the hydrogen half-cell potential 0.991 and found this to be 0.218.  However, the question gives a hint that the required pH range is from acidic to slightly basic.  I've checked my calculations over and they are all correct.  I am thinking that my mistake here is a conceptual one.  What conceptual mistake have I made?

[Borek]

I am given a table of reduction potentials for various vanadium half-reactions relating to the speciation of vanadium in aqueous solutions

Can you show it?

[plu]

Here is the chart:
2 H⁺ + 2 e–  ->  H₂                                  E_o = 0.000 V
V²⁺ + 2 e–  ->  V                                      E_o = –1.175 V (1)
V³⁺ + e–  ->  V²⁺                                    E_o = –0.255 V (2)
VO²⁺ + 2 H⁺ + e–  ->  V³⁺ + H₂O                 E_o = 0.337 V (3)
VO₂⁺ + 2 H⁺ + e–  ->  VO²⁺ + H₂O               E_o = 0.991 V (4)
V₂O₅ + 6 H⁺ + 2 e–  ->  2 VO²⁺ + 3 H₂O       E_o = 0.957 V (5)
V₂O₅ + 10 H⁺ + 10 e–  ->  2 V + 5 H₂O         E_o = –0.242 V (6)

[Borek]

At first sight - stable will be all compounds with halfreaction potential higher than that calculated for H⁺/H₂.

However, note that some of the reactions include H⁺ - thus their potentials are pH dependent, I suppose that can be the missing point in your calculations.

[plu]

Sorry to resurrect an old post but I recently looked over this problem again and realized that I still can't find a solution!  Would there be anybody out there that can give me some insight on this problem?  The question is posed as such: "Given the above half-reaction potentials, find the pH range under which a 1 molar solution of VO₂⁺ is stable.  All other conditions are standard."  Kind thanks

[wereworm73]

Looks hard, but I'll take a stab at it.


H₂ --> 2 H⁺ + 2 e^-
2 VO₂⁺ + 4 H⁺ + 2 e^- --> 2 VO²⁺ + 2 H₂O


E = E^o - 0.05916/2 (log [VO²⁺]²/[VO₂⁺]²[H⁺]⁴)

0 = 0.991 - 0.05916/2 (log 1/[H⁺]⁴)

Solving for [H⁺], I get 4.212 x 10^-9 M  (pH= 8.376)

I'm not 100% sure if that's correct, but it is slightly basic like the hint says.