Analytical Chemistry- Ksp problem help

[hskrnt8590]

Homework Statement

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

Homework Equations

Ksp= [Pb2+]$\gamma$_Pb2+[I-]²$\gamma$²_I-

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.

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=[lead](.868)[iodide]^2(.965)^2
9.8*10^-9=[x](.868)[.001+2x]^2(.965)^2
solve for x=.0011345

That is wrong and I have no idea why. Could anyone please help me.

 

[Borek]

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?

 

[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.

 

[Borek]

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

So the only thing left are iterations...

 

[hskrnt8590]

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

So the only thing left are iterations...

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?

 

[Borek]

How do you know it is wrong?

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

 

[hskrnt8590]

How do you know it is wrong?

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

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 lead = .0012432355
Concentration of iodide = .003508607
ionic strength = .00474
activity of lead = .74557681557
activity of iodide = .92706917508

 

[Borek]

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?