Chemistry Problem

Question

Consider a battery made of the following.
Ni(s)|Ni2+(aq)||VO+2 (aq),H+(aq),VO2+(aq)|Pt(s) The concentrations of some of the species are given below.
[VO2+] = 0.1M [VO+2 ] = 0.1M [Ni2+] = 0.02M
If you want the cell potential to be exactly Ecell = 1.00 V, what must the pH be of the cell? Hint: Find [H+] so that Ecell = 1.00 V.

Answer 1

Your notation is a little confusing because of the VO2+ and the VO+2, so I'll rewrite it as VO₂⁺ and VO²⁺

Oxidation half reaction:  Ni(s) ===> Ni²⁺(aq) + 2e-

Reduction half reaction:  VO₂⁺(aq 0.1M) + 2H⁺(aq. ? M) + e- ===> VO²⁺(aq 0.1M) + H₂O(l)

Multiply reduction reaction by 2 to equalize electrons and add the two half reactions to get:

Ni(s) + 2VO₂⁺_(0.1M) + 4H⁺(xM) ===> 2VO²⁺_(0.1M) + 2H₂O(l)

 

Now, the cell potential will depend on the temperature, and one also needs to know the standard potentials at 1M concentrations and 298K.  You can then use the Nernst equation as shown below:

E_cell = Eº_cell - RT/nF (lnQ) where Eºcell is the standard cell potential; R=8.314 J/kmol; T is temp in K (assumed to be 298); n = moles of electrons transferred = 2; F = the Faraday = 96,500 C/mole electrons and Q is the reaction quotient.

Q = [VO²⁺]²/[VO₂⁺]²[H⁺]⁴ = (0.1)²/(0.1)²(x)⁴

Find the Eº_cell by subtracting the standard reduction potential at the anode from that at the cathode (ox - red) and substitute that into the Nernst equation for Eº_cell.  Substitute 1.00 for E_cell and solve for x, which is the [H⁺].  Take the negative log of [H⁺] to obtain the pH.