Analytical Chemistry- Ksp problem help

1. Oct 4, 2012

hskrnt8590

1. The problem statement, all variables and given/known data

Find the concentration of Pb2+ in 0.0010 M KI with PbI2. Include activity coefficients in your solubility-product expression. The Ksp of PbI2 is 9.8*10^-9

2. Relevant equations

Ksp= [Pb2+]$\gamma$Pb2+[I-]2$\gamma$2I-

Assume that [I-]=0.0010 M. The ionic strength of 0.0010 M Ki can be calculated, then used to find the activity coefficients from a table.

3. The attempt at a solution
-The ionic strength is 0.0010 M.
-Based on that ionic strength the activity coefficients are 0.868 for lead and 0.965 for iodide
9.8*10^-9=[x](.868)[.001+2x]^2(.965)^2
solve for x=.0011345

2. Oct 4, 2012

Staff: Mentor

I don't see anything obviously wrong about your calculations (apart from the fact real calculations should take several iterations - knowing x you should immediately see ionic strength is much higher than the one used as a starting point).

What formula do you use for calculation of activity coefficients?

3. Oct 4, 2012

hskrnt8590

The debeye huckel equation: log($\gamma$)=(-0.51z^2$\sqrt{}I$)/(1+[(a$\sqrt{}I$)/305]

Where: gamma is the activity coefficient. z is the charge of the ion. I is the ionic strength of the solution. a is the ion size parameter, which is 450 for lead and 300 for iodide.

4. Oct 4, 2012

Staff: Mentor

OK, I checked ignoring ion size, that's why my numbers were slightly different.

So the only thing left are iterations...

5. Oct 4, 2012

hskrnt8590

I have an iterations calculator now set up through excel, but I am still continuing to get it wrong. I got .00157 this time. Can anyone help?

6. Oct 4, 2012

Staff: Mentor

How do you know it is wrong?

Can you list all concentrations, ionic strength and activity coefficients that you got?

7. Oct 4, 2012

hskrnt8590

It is an online assignment and it says it is wrong. I have tried it two different times now and got the answer of .0012432355 both times and it is wrong.

Concentration of iodide = .003508607
ionic strength = .00474
activity of iodide = .92706917508

8. Oct 5, 2012

Staff: Mentor

Have you checked if the results are self consistent?

Ksp = 0.0012432*0.74557*(0.0035086*0.92707)2 = 9.81*10-9

so this part looks OK, but

I = (4*.0012432+1*0.0035086)/2 = 0.0042407

is different from what you listed. Could be just a typo.

I did calculations using a specialized program and it shows very similar results (it uses slightly simplified method of calculation of activity coefficients, one that assumes radius of an ion over 305 is always 1, hence the differences).

(don't pay attention to the solid concentration, it is just a way of entering information about the solid presence). Activity coefficients are not shown in this view, but they were calculated to be 0.9270 and 0.7384.

Perhaps your result is correct, you are just fighting some significant figures issue?

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