[Fzang]

I have an element, consisting of Zn/Pb electrodes:

(L) Zn l ZnSO₄(aq) ll ZnSO₄ l PbSO₄(s) l Pb(s) (R)

The cell process is

PbSO₄(s) + Zn(s) -> Pb(s) + Zn₂₊(aq) + SO₄^2-(aq)

One of the first problems is to calculate the standard potential. From standard Gibbs energies I get E° = 0.3906 V

Now comes the tricky part:
In the element, at 25 °C and with molality b = 0.0005 mol/kg ZnSO₄ in each of the two separated electrolyte solutions at the electrode, is added
b = 0.0005 mol/kg Na₂SO₄(s) at the left electrode L, and
b = 0.0005 mol/kg ZnCl₂(s) at the right electrode R.

Calculate the change in the electromotive force E caused by the addition of above, if electrolyte solutions are treated as ideal solutions.

I have to calculate the new equilibrium constant with the solutes in mind, and then convert it into an electromotive force, and finally find the difference between the new E and E°. I'm a bit unsure about getting the equilibrium constant, though.

Can anyone give me a push in the right direction?

[Borek]

I would start with Nernst equation, no need for ΔG nor equilibrium constants.

[Fzang]

So,

E = E° - RT/zF lnQ

where Q would be b(Zn²⁺)b(SO₄^2-), since the rest are solids.

But what numbers do I plug in? This "add to left/right cell" is confusing me a bit. Do I simply look at the numbers and realize that I have 0.005 mol/kg of both ions, and add another 0.005 mol/kg of both ions, totalling 0.010 mol/kg = b(Zn²⁺) = b(SO₄^2-)?

[Borek]

Start determining half reactions and write Nernst equation for each. Initially you can even ignore PbSO₄ presence, it can be incorporated later.

Please note - element doesn't necessarily mean what you think it does, recheck with dictionary.

[Fzang]

My assignment does have 'element' written all over it, though.






anyway, the half cell reactions are,
Zn²⁺ + 2 e^- -> Zn(s) , reduction of Zn
PbSO₄ + 2 e^- -> Pb(s) + SO₄^2- , reduction of Pb

And I'd use the Nernst equation for half cells, to find reduction potential:
(assuming the activity coefficient is 1)
But now I'm back at the molality issue as I wrote before. Do I have 0.010 mol/kg in place of Zn²⁺?

Zn/Zn²⁺ = 1/?

[geterdun]

"assuming the activity coefficient is 1." 

Go back to your definition of Q and the connection with molality Debye-Hückel that bad boy.

[Fzang]

Afraid I'm not sure I follow.

[geterdun]

For clarification, you are not solving for an equilibrium constant, K_eq. You are solving for your reaction quotient, Q. If you were at equilibrium, E_cell would be zero and E˚would suffice.

You have your Nernst. You have your E˚. You have your molalities and your rxn cell. Now how do you get Q? Well, the definition of Q is , where your v_j is your species-specific stoichiometric coefficient. Once you have your Q, then break down each component and analyze.

The D-H limiting law: Any one of these forms is usable, but the last is most practical, where A = 1.172 mol^-1/2kg^1/2 or A = 0.509 mol^-1/2kg^1/2 if you are using log.

Definition of ionic strength: . I is a unitless entity because b_i is really b_i/b_standard. This is important because it defines your b, rather than assuming the conditions.

If you don't recognize these equations, then you need to read your text. I know Atkins has numerous chapter problems almost identical to your problem here and I have no doubt McQuarrie (the big red beast) treats this quite thoroughly. Assuming you have an English text. Don't know of any Norwegian pchem/achem texts. Like I said before, go back to your definition of Q and how it connects with molality.

Now if you have been told to assume that activity coeffs for all species = 1.0, then meh. That would be quite simple to figure out by using your definition of Q.