[galvanichell]

Hello,

I'm trying to learn galvanic cell calculations and am having some trouble understanding this material. If a galvanic cell is made of half cells with standard reduction potentials Co2+(aq) + 2e- -> Co(s) -0.28 volt and Cr3+(aq) + 3e- -> Cr(s) -0.74 volt and then you have actual concentrations given by the molarity of Co2+ (aq) = 0.00100M and Cr3+ = 0.100 M how do you calculate the free energy change for it?

From what I have been able to find so far you use G=-nFEcell. So I balanced the equation like this:

3Co2+(aq) + 2Cr -> 2Cr3+(aq) + 3Co(s)

thus, n = 6

Now I need to find Ecell in relation to the actual molarities. How do I do this? Any help would be appreciated. Thank you.

[renge ishyo]

First you have to find E_cell using the Nernst equation (which takes into account the differences in concentration between the two ions). You can calculate E⁰ using the data given in the question. Then use:

E_cell = E⁰ - (0.0257/(n)) ln ([Cr⁺³]²/[CO⁺²]³)

Where n is equal to the number of electrons in your balanced chemical equation. Once you have E_cell you can calculate  :delta: G_r = -nF(E_cell).

[galvanichell]

Thank you for the reply. So basically I would do these types of equations like this:

1) Balance equation to determine electrons:

3Co₂+(aq) + 2Cr -> 2Cr₃+(aq) + 3Co(s) thus, n = 6

2) Determine the potential for the cell:
E^O = -0.28 - (-0.740) = 0.46 v

3) Find Ecell:
E = 0.46 - (0.0257/6)ln([0.1]²/[0.001]³) = 0.39 v

4) Find Free Energy:
G=-(6)(96485)(0.39) = -225774 J = -226 kJ

Ok that clear that up. Thanks for the help. I understand it now.