[vagabondita]

Given: A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25 ∘C. The initial concentrations of Pb2+ and Cu2+ are 5.10×10−2 M and 1.60 M , respectively.  Initial cell potential is 0.51V

Question: What are the concentrations of Pb2+ and Cu2+ when the cell potential falls to 0.360 V ?
Enter your answers numerically separated by a comma. Express your answer using two significant figures.

I checked my calculations and my answer should be correct.  I got [Pb2+], [Cu2+] = 1.6, 0.04.   But Masteringchemistry.com kept saying that my answer is wrong!   I don't get it, please help.

[Borek]

Show how you got these numbers.

[mjc123]

And the second number is not to two significant figures. That might be all that is wrong.

[orthoformate]

 Using the formula E=(RT/nF)ln(Q) for the 0.51V value:

0.51V=0.013Ln(Q)

39=ln(Q)

e^39=Q

Q=8.65x10^18

This doesn't match the concentration ratio given in the problem. Does anyone know where I have made a mistake?

Thanks!

[Borek]

Using the formula E=(RT/nF)ln(Q)

Doesn't look correct for me. Where is E₀?

[orthoformate]

ah ok, the formula is E=(RT/nF)ln(K/Q) which rearranges to

E=(RT/nF)ln(K)-(RT/nF)ln(Q)

This means that if T is constant than the relationship is essentially:

E=ln(K/Q)

Where is this derived from?

[Borek]

ah ok, the formula is E=(RT/nF)ln(K/Q)

No, that's not a correct formula for the Nernst equation.

[PhotoElectroMaterials]

I wonder how this problem can be solved.
From the given data we can get only the value of Q, for the final potential. 
To my knowledge, it is possible to get individual concentrations only if we have to choose from one of the given choices.
Someone please explain.
E=0.47 +((0.059/2)x log Q) is the Nernst equation for this. 

[mjc123]

You don't need E°, you have two voltages and one set of concentrations, so you can work out the other set.
E₁ = E° + RT/nF ln([Cu²⁺]₁/[Pb²⁺]₁)
E₂ = E° + RT/nF ln([Cu²⁺]₂/[Pb²⁺]₂)
so E₂ - E₁ = ?
If [Pb²⁺]₂ = [Pb²⁺]₁ + X, what is [Cu²⁺]₂?

[orthoformate]

ah ok, the formula is E=(RT/nF)ln(K/Q)

No, that's not a correct formula for the Nernst equation.

So the Nernst equation is:

E=E°-(RT/nF)ln(Q)

So since (RT/nF) is a constant i'll just denote it τ; (RT/nF)=τ

E=τln(K)-τln(Q)

E=τln(K/Q)

E=(RT/nF)ln(K/Q)

Does anyone know why this is incorrect? I am studying for the chemistry GRE and I am feeling uneasy about physical chemistry!