Question

Find the concentration of I– in 0.050 M AgNO3 saturated with AgI. Include activity coefficients in your solubility-product expression. The Ksp of AgI is 8.3× 10–17. A table of activity coefficients at various ionic strengths can be found here.

Answer 1

Since this involving the activity coefficients you would have to find the ionic strength then the activity coefficients 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 0.050 M AgNO₃ using this formula ..... I = 1/2 [CZ²] . where C is the concentration of the ion times z= the charge squared. you does this separatley for the Ag⁺ and NO₃^_ then add the values then multiply by 1/2. Then use the debye- huckel equation, 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

set up your equilibrium equation AgI Ag⁺ + I^- and do ICE.

Now setup your K_sp = [Ag⁺]y[I^-]y

y= activity coefficient corresponding to their ion and solve for x which is your [I^-]

it should be 8.3 10^-17 = (X) 0.75 (0.050 + X)0.75, the second X dont worry about since x is small in this case, so then its now

8.3 10^-17 = (X) 0.750 (0.050) 0.755 and just solve for X. And you done