Please help me solve this chemistry question

Question

Find the concentration of I− in 0.010M AgNO3 saturated with AgI. Include activity coefficients in the solubility-product expression. The 𝐾sp of AgI Is 8.3×10−17.

use this table for activity coefficients

 Refer to the table of activity coefficients at various ionic strengths as needed.

Answer 1

To find the concentration of I- in a saturated solution of AgI, we can use the solubility product expression:

Ksp = [Ag+][I-]

where Ksp is the solubility product constant, [Ag+] is the concentration of Ag+ ions in the solution, and [I-] is the concentration of I- ions in the solution.

Given that the Ksp of AgI is 8.3×10^(-17), we can set up an ICE (Initial, Change, Equilibrium) table to find the concentrations of Ag+ and I- ions in the saturated solution when AgNO3 is added.

Initial: [Ag+] = 0.010 M (from the AgNO3)

[I-] = 0 M (there is no I- initially)

Change: When AgNO3 is added, it will dissociate into Ag+ and NO3- ions, but AgNO3 does not contain any I- ions, so there is no change in the concentration of I- initially.

Equilibrium: [Ag+] = 0.010 M [I-] = ? (we need to find this)

Now, we can use the Ksp expression and the information from the equilibrium step:

Ksp = [Ag+][I-]

8.3×10^(-17) = (0.010 M)[I-]

Now, solve for [I-]: [I-] = (8.3×10^(-17)) / (0.010 M) [I-] = 8.3×10^(-15) M

So, the concentration of I- ions in the saturated solution of AgI is 8.3×10^(-15) M when considering the activity coefficients.