[Big-Daddy]

Calculate the pH of the cathode compartment for the following reaction given E_cell = 3.01 V when [Cr³⁺] = 0.15 M, [Al³⁺] = 0.30 M, and [Cr₂O₇^2-] = 0.55 M.

 2 Al(s) + Cr₂O₇^2-(aq) + 14 H⁺(aq) → 2 Al³⁺(aq) + 2 Cr³⁺(aq) + 7 H₂O(l)

I'm only just starting with electrochemistry problems and I'm not sure what to do. First of all I don't know how to work out how many electrons are being transferred in the formal cell reaction as above.

Other than that, I know that

[tex]E = E° - \frac{R \cdot T}{F} \cdot log_e(Q)[/tex]

We can evaluate Q with the exception of [H⁺], which is just what we want. T I must assume is 298.15 K. However, how do we find E° - right now there are 2 variables, E° and [H⁺]. And what does it mean by pH in the "cathode compartment" - this is just the value of [H⁺] which contributes to Q, right?

[Corribus]

The first thing I always do is write out balanced half-reactions for the reduction and oxidation.  Then you can easily identify which corresponds to your anode and your cathode, how many electrons are transferred, and etc.

Balancing half-reactions can be a little trickier than balancing normal chemical reactions.  You should seek out a good general chemistry textbook that explains how to do this, if you aren't sure.

[Big-Daddy]

Balancing half-reactions can be a little trickier than balancing normal chemical reactions.  You should seek out a good general chemistry textbook that explains how to do this, if you aren't sure.

I'm fine with balancing half-reactions, but how do I figure out what the components are in each of them? Is it just Al -> Al³⁺ and dichromate -> Cr³⁺, and then balance? I've got that done, don't worry.

That's going to help, because we can figure out what the expression for Q should be if we do it like that. To find [H⁺] it seems to me we must first find Q, which requires us to know E°. We aren't told E°. We need some way to circumvent this issue? Or do you think we have to just look up the E° values for the cathode and anode respectively and then have E°(cell)=E°(cathode)-E°(anode)?