Question

Determine the minimum concentration of the precipitating agent on the right to cause precipitation of the cation from the solution on the left.

a. 9.0x10^-2 M CaI2 ; K2SO4
b. 2.0x10^-3 M AgNO3 ; RbCl

Answer 1

2.67 x 10^-4 M & 8.85 x 10^-8 M

Step-by-step explanation:

The minimum concentration of the precipitating agent required to cause precipitation of the cation from the solution can be determined using the solubility product constant (Ksp) of the salt that would be formed. The Ksp is an equilibrium constant that represents the maximum amount of solid that can dissolve in water to form a saturated solution.

For part a, calcium iodide (CaI2) and potassium sulfate (K2SO4) are mixed. The reaction that occurs is:

CaI2(aq) + K2SO4(aq) → CaSO4(s) + 2KI(aq)

The solubility product constant for calcium sulfate (CaSO4) is 2.4 x 10^-5. Let x represent the minimum concentration of K2SO4 required to cause precipitation. The concentration of Ca2+ ions in solution is 9.0 x 10^-2 M. The Ksp expression for CaSO4 is:

Ksp = [Ca2+][SO42-]

Substituting the known values gives:

(2.4 x 10^-5) = (9.0 x 10^-2)(x)

Solving for x gives:

x = (2.4 x 10^-5)/(9.0 x 10^-2)

x = 2.67 x 10^-4 M

So, the minimum concentration of K2SO4 required to cause precipitation of CaSO4 is 2.67 x 10^-4 M.

For part b, silver nitrate (AgNO3) and rubidium chloride (RbCl) are mixed. The reaction that occurs is:

AgNO3(aq) + RbCl(aq) → AgCl(s) + RbNO3(aq)

The solubility product constant for silver chloride (AgCl) is 1.77 x 10^-10. Let y represent the minimum concentration of RbCl required to cause precipitation. The concentration of Ag+ ions in solution is 2.0 x 10^-3 M. The Ksp expression for AgCl is:

Ksp = [Ag+][Cl-]

Substituting the known values gives:

(1.77 x 10^-10) = (2.0 x 10^-3)(y)

Solving for y gives:

y = (1.77 x 10^-10)/(2.0 x 10^-3)

y = 8.85 x 10^-8 M

So, the minimum concentration of RbCl required to cause precipitation of AgCl is 8.85 x 10^-8 M.

Answer 2

a. The chemical equation for the reaction between CaI2 and K2SO4 is:

CaI2 + K2SO4 → 2 KI + CaSO4

The solubility product constant (Ksp) for CaSO4 is 2.4 x 10^-5 at 25°C.

Using the Ksp expression for CaSO4, we can write:

Ksp = [Ca2+][SO42-]

Let x be the concentration of Ca2+ ions in the solution. Then, the concentration of SO42- ions will also be x, since the reaction is 1:1. Substituting into the Ksp expression, we get:

Ksp = x^2

Solving for x, we get:

x = sqrt(Ksp) = sqrt(2.4 x 10^-5) = 0.0049 M

Therefore, the minimum concentration of CaI2 needed to cause precipitation is 0.0049 M.

b. The chemical equation for the reaction between AgNO3 and RbCl is:

AgNO3 + RbCl → AgCl + RbNO3

The solubility product constant (Ksp) for AgCl is 1.8 x 10^-10 at 25°C.

Using the Ksp expression for AgCl, we can write:

Ksp = [Ag+][Cl-]

Let x be the concentration of Ag+ ions in the solution. Then, the concentration of Cl- ions will also be x, since the reaction is 1:1. Substituting into the Ksp expression, we get:

Ksp = x^2

Solving for x, we get:

x = sqrt(Ksp) = sqrt(1.8 x 10^-10) = 1.34 x 10^-5 M

Therefore, the minimum concentration of AgNO3 needed to cause precipitation is 1.34 x 10^-5 M.