[Thermofox]

PROBLEM

A Nickel-iron battery is composed by a Fe anode and a NiO cathode, in solution with the electrolyte KOH. The battery has a standard cell potential of Δε_cell°= 0.400 V and operates through the following half reactions, at T= 25°C:

Fe + 2OH^-  Fe(OH)₂ + 2e^-

NiO + H₂O + e^-  Ni(OH)₂ + OH^-

Determine,

• ΔG° of the reaction and K_eq.
• E.M.F. when [KOH]= 5.00 M

ATTEMPT

For the first point I know that ΔG°= -nΔε_cell°F. From the half reactions I notice that n=2
=> ΔG°= -(2)(0.400 J/C)(96485 C/mol)= -7.72 10⁴ J/mol.
From this I can then determine K_eq.=[itex]e^{(\frac {-\Delta G°}{RT})}[/itex] = [itex]e^{(\frac {(7.72)(10^{4} J/mol)}{(8.31 J/(mol K))(298 K)})}[/itex]= 31.2.

For the second point E.M.F. should ≡ Δε_cell = [itex]\Deltaε_{cell}° + \frac {RT}{nF}\ln Q[/itex]. What I don't understand is how to determine Q. I know that Q is the reaction quotient so I thought of analyzing the total reaction of the battery:

Fe + 2OH^- + 2NiO + 2H₂O + 2e^- Fe(OH)₂ + 2e^- + 2Ni(OH)₂ + 2OH^-

But now if I simplify, I obtain: Fe + 2NiO + 2H₂O  Fe(OH)₂ + 2Ni(OH)₂ and consequently log(Q)= 0 since Q= 1 because under the conditions of the problem all reactants and products have an activity of 1.

[Borek]

I am not saying that's the answer, but at first sight the most obvious conclusion is that Δε_cell just doesn't depend on KOH concentration.

[Thermofox]

I am not saying that's the answer, but at first sight the most obvious conclusion is that Δε_cell just doesn't depend on KOH concentration.

If Δε_cell doesn't depend on [KOH], then Δε_cell=Δε_cell°. Since nothing that has an impact on Δε_cell is changing from standard conditions, right?

[Hunter2]

There is also a mistake in the equation with nickel.
NiO and Ni(OH)2 has same oxidation number for Ni +2.
The stoichiometry is also wrong

NiO + H2O + e- → Ni(OH)2 + OH-

The right half reaction is

NiO(OH) +  H2O +  e−  → Ni(OH)2   +  OH−

https://en.m.wikipedia.org/wiki/Nickel%E2%80%93iron_battery

[Thermofox]

There is also a mistake in the equation with nickel.
NiO and Ni(OH)2 has same oxidation number for Ni +2.
The stoichiometry is also wrong

NiO + H2O + e- → Ni(OH)2 + OH-

The right half reaction is

NiO(OH) +  H2O +  e−  → Ni(OH)2   +  OH−

https://en.m.wikipedia.org/wiki/Nickel%E2%80%93iron_battery

In the problem that I was given there was written that first half reaction, so I mindlessly pasted it here. But now I realize that it even isn't a half reaction. Still the doubt I had persists. Does Δε_cell depend on [KOH]? If I add the 2 equations together, OH^- cancels out, even with the correct half reaction.

[Hunter2]

OH- is only spectator ion.

The reaction simplyfied is
Ni3+ + e- => Ni2+ and
Fe => Fe2+ + 2e-

Combined
2 Ni3+ + Fe => 2 Ni2+ + Fe2+

This has to put in the Nernst equation.

[Thermofox]

OH- is only spectator ion.

The reaction simplyfied is
Ni3+ + e- => Ni2+ and
Fe => Fe2+ + 2e-

Combined
2 Ni3+ + Fe => 2 Ni2+ + Fe2+

This has to put in the Nernst equation.

Then Q= ([Ni²⁺]² [Fe²⁺])/([Ni³⁺]²). And that is how I can use the information that the problem gives me, [KOH]= 5.00M; To determine the concentrations of the reactants and products I can use the half reactions and [KOH]= 5.00M.

[Borek]

If the reacting compound is NiO(OH) there is no such thing as Ni³⁺ in the solution. Or, more precisely, it can exist only in equilibrium with OH^- and H₂O

NiO(OH) + H₂O Ni³⁺ + 3OH^-

but then to do any calculations you would need to know K for this reaction. Perhaps K_sp for Ni(OH)₃ will do.

Actually the same goes for Fe²⁺/Fe(OH)₂, but in this case finding Ksp is trivial.

[Hunter2]

I think in this battery beside KOH, we don't have much ions in solution, the reaction takes place on the surface of the electrodes, NiO, Ni(OH)2, NiOOH, Fe(OH)2 and Fe itself is not much dissolved in solution. Probably the Hydroxide built some complex with Ni or Fe to get some solubility.

https://www.google.com/search?q=iron%20nickel%20battery&ie=utf-8&oe=utf-8&client=firefox-b-m#vhid=E84Hb9XnnXZdMM&vssid=l

[Thermofox]

but then to do any calculations you would need to know K for this reaction. Perhaps K_sp for Ni(OH)₃ will do.

I've searched the K_sp for Ni(OH)₃ to no avail, but I've found that K_sp for Ni(OH)₂=2,8x10^-16​. Generally, for all other hydroxides, the one with OH₃ has a considerably higher K_sp than the one with OH₂. So, I think it safe to assume that Ni(OH)₃ won't dissolve in water in a considerable amount.

[Borek]

I think it safe to assume that Ni(OH)₃ won't dissolve in water in a considerable amount.

That's not what is important here.

You can calculate standard potential of a more complicated electrode like Ag/AgCl assuming you know potential for Ag/Ag⁺ and Ksp of AgCl. Same for even less soluble salts like AgBr or AgI.

If you have Ni electrode covered with NiO(OH) you could be able to calculate its potential from Ni/Ni³⁺ potential and Ksp of Ni(OH)₃ (which is in a way equivalent to Ni(OH)₃). I am not surprised Ksp for Ni(OH)₃ isn't listed, but it is the closest thing I can think of that could be used here).