Question

Finding cconcentration from Ksp, advanced topics in chemistry.

Find the concentration of I- in 0.0010 M AgNO3 saturated with AgI. In clude aciticity coefficients in your solubility-product expresion. The Kap od AgI is 8.3 x10 -17.

Ans is not:

1.03 x10 -13

9.44 x10 -9

8.3 x 10-14

8.135 x 10 -14

1.028 x10 -13

1.028 x 10 -14

Answer 1

Since this involving the activity coefficients you would have to find the ionic strength then the activity coefficient to solve this problem.
Also note this involves the common ion effect so the answer is going to be really small.
First you get the ionic strength of 0.0010M AgNO3 using this formula...
I=1/2Sum[cz^2) where c is the concentration of the ion times z= the charge squared.
you does this separately for the Ag+ and NO3- then add the values then multiply by 1/2.
Then use the debye-huckel equation, (i suggest you look it up) the a or alpha represents the size of the ion,
in this case Ag+, just do it for Ag+ to get is activity coefficient, which should be around 0.75,
now you need the activity coefficient, look that up also but it should be 0.755

Setup your equlibrium equation AgI <-->Ag+ + I- and do ICE.

Now setup your Ksp=[Ag+]y[I-]y y=activity coefficient corresponding to their ion and solve for x which is your [I-]

it should be 8.3E-17= (x)0.75(0.0010+x)0.755, the second x dont worry about since x is small in this case, so then its now
8.3x10-17= (x)0.75(0.0010)0.755 and just solve for x. And you done