Electrochemistry homework help problem

[zorro]

Homework Statement

Tl⁺/Tl couple can be prepared by saturating 0.100 M KBr with TlBr and alowing Tl⁺ ions from the insoluble bromide to equilibrate. This couple was observed to have a potential of -0.443V w.r.t Pb²⁺/Pb couple in which Pb²⁺ was 1 M. K_sp of TlBr is ?

Given: E^o_Pb²⁺/Pb = -0.126V and E^o_Tl⁺/Tl= -0.336V

The Attempt at a Solution

I have a problem understanding the question. Can somebody explain me?

 

[Borek]

You have a cell made of two half cells - one is Pb/Pb²⁺, the other Tl/Tl⁺. You are given everything but [Tl⁺], and that's the only thing you need to calculate to find Ksp of TlBr.

 

[zorro]

The potential -0.443V given in the question confuses me. It simply means that the cell reaction is not spontaneous. Which one is cathode and which one is anode?

We have E_cell = -0.443V and E^o_cell = -0.21 (if we assume Tl⁺/Tl is the cathode)

Is this right?

 

[Borek]

To be honest - I am not sure which way it goes off the top of my head, but if you take the sign wrong, you will get absurd results.

You will need E0 for Pb/Pb²⁺ as well.

 

[zorro]

Cathode- Tl⁺ + e ----> Tl
Anode- Pb------> Pb²⁺ + 2e

E_cell = E^o_cell - 0.059/2*log[Pb²⁺/[Tl⁺]²]

We have Pb²⁺=1M
What is the use of 0.1M KBr?

E0 for Pb/Pb²⁺ is given in the question.

 

[Borek]

What is the use of 0.1M KBr?

Have you read the question?

 

[zorro]

I read it but did not understand fully.
Br^- concentration is 0.1M

Let us assume that Tl+ produced from TlBr is x moles
Ksp = x(0.1+x)

How to find 'x'?

 

[Borek]

Br^- concentration is 0.1M

Right.

Let us assume that Tl+ produced from TlBr is x moles
Ksp = x(0.1+x)

How to find 'x'?

From the cell potential. It will be so low you can easily ignore x in 0.1+x part.

 

[zorro]

From the cell potential. It will be so low you can easily ignore x in 0.1+x part.

Plugging the values in the equation in my post #5, I got x as 1.124 x 10^-4
So Ksp = 1.124 x 10^-5. This is not the correct answer.

 

[epenguin]

Thallium chemistry.

Prof. is showing off?

 

[zorro]

Thallium chemistry.

Prof. is showing off?

@Borek- where is the mistake?

 

[Borek]

Your Ksp looks OK to me, unless you are expected to take ionic strength of the solution into account.

 

[zorro]

I just have the answer for it.
3.6 x 10^-6
There is a big difference.
I think the answer given is incorrect.

 

[Borek]

No my fault. I know answer calculated is different from the Ksp value from tables, but as far as I can tell data given yields 1.12e-5.