Chemistry Problem

Question

A solution is 0.10 M Ba(NO3)2 and also 0.10 M AgNO3. Solid KIO3 is added slowly. (a) Calculate the concentration of iodate ion needed to saturate the solution with Ba(IO3)2(s) and with AgIO3(s). (b) Which compound precipitates first? Why? (c) Once the solution is saturated with the first compound to precipitate, more potassium iodate is added. Calculate the concentration remaining in solution of the first cation to precipitate when the solution is just saturated with the second compound. (d) What percent of the first cation to precipitate remains in solution at that point? Can potassium iodate be used to successfully separate barium and silver ions?

Answer 1

To solve this problem, we'll follow the steps outlined:

(a) To calculate the concentration of iodate ion needed to saturate the solution with Ba(IO3)2(s) and AgIO3(s), we need to determine the solubility products (Ksp) of the respective compounds.

The solubility product expression for Ba(IO3)2 is: Ksp = [Ba2+][IO3^-]^2

The solubility product expression for AgIO3 is: Ksp = [Ag+][IO3^-]

Since the concentration of Ba(NO3)2 and AgNO3 is both 0.10 M, the initial concentration of Ba2+ and Ag+ is 0.10 M.

For Ba(IO3)2, Ksp = [Ba2+][IO3^-]^2 Let's assume the concentration of IO3^- needed to saturate the solution is x M. Therefore, [Ba2+] = x M and [IO3^-] = x M. Substituting these values into the solubility product expression: Ksp = (x)(x)^2 = x^3

For AgIO3, Ksp = [Ag+][IO3^-] Let's assume the concentration of IO3^- needed to saturate the solution is y M. Therefore, [Ag+] = y M and [IO3^-] = y M. Substituting these values into the solubility product expression: Ksp = (y)(y) = y^2

(b) To determine which compound precipitates first, we compare the solubility product expressions and their respective Ksp values. The compound with the smaller Ksp value will precipitate first. In this case, since Ksp(Ba(IO3)2) = x^3 and Ksp(AgIO3) = y^2, the compound with the smaller Ksp value will precipitate first.

(c) Once the solution is saturated with the first compound to precipitate, the concentration of the remaining cation (Ba2+ or Ag+) can be calculated. Assuming AgIO3 precipitates first, we need to find the concentration of Ag+ when the solution is just saturated with Ba(IO3)2.

Using the Ksp expression for AgIO3: Ksp = [Ag+][IO3^-] Substituting [IO3^-] = x M (concentration of IO3^- in saturated solution of Ba(IO3)2): y^2 = (Ag+)(x)

Solving for [Ag+], we get: [Ag+] = y^2/x

(d) The percent of the first cation (Ag+) remaining in solution at this point can be calculated using the formula: Percent remaining = ([Ag+] initial - [Ag+] saturated) / [Ag+] initial * 100

Substituting the values we found in part (c), we can calculate the percent remaining.

Based on the results obtained in parts (a) to (d), we can determine if potassium iodate can successfully separate barium and silver ions by comparing the solubility products and the percent remaining.