Concentration of all solute species

Question

Calculate the concentration of all solute species in each of the following solutions of salts

in contact with a solution containing a common ion.

Show that changes in the initial concentrations of the common ions can be neglected.

a) AgCl (s) in 0.025 M NaCl

AgCl (s) Ksp = 1.6 x 10^–10

b) CaF₂ (s) Ksp = 4.0 x 10^–11 in 0.00133 M KF

c) Ag₂SO₄ (s) Ksp = 1.12 x 10^–5 in 0.500 L of a solution containing 19.50 g of K₂SO₄

Answer 1

(a) AgCl (s) in 0.025 M NaCl; AgCl (s) Ksp = 1.6 x 10^–10

AgCl(s) <==> Ag⁺(aq) + Cl^-(aq)

Ksp = [Ag⁺][Cl^-]

[Ag⁺] = x

[Cl^-] = 0.025 M + x since Ksp is so small (10^-10) we can assume Cl^- contributed by AgCl is small

1.6x10^-10 = (x)(0.025)

x = [Ag⁺] = 6.4x10^-9

Summary

[Ag⁺] = 6.4x10^-9 M

[Cl^-] = 0.025 M

[Na⁺] = 0.025 M

[AgCl] = negligible

The initial concentration of the common ion Cl^- would be ~ 6.4x10^-9 M which is so small relative to the added common ion from NaCl (0.025 M) it can be neglected in the calculations.

(b) CaF₂ (s) Ksp = 4.0 x 10^–11 in 0.00133 M KF

CaF₂(s) <==> Ca²⁺(aq) + 2F^-(aq)

Ksp = [Ca²⁺][F^-]²

[Ca²⁺] = x

[F^-] = 0.00133 M and since Ksp is so small (10^-11) we can assume F^- contributed by CaF₂ is small

4.0x10^-11 = (x)(0.00133)²

x = [Ca²⁺] = 2.26x10^-5 M

Summary

[Ca²⁺] = 2.26x10^-5 M

[F^-] = 0.00133 M = 1.33x10^-3 M

[K⁺] = 0.00133 M = 1.33x10^-3 M

[CaF₂] = negligible

The initial concentration of the common ion F^- would be ~ 2.26x10^-5 M which is so small relative to the added common ion from KF (0.00133 M) it can be neglected in the calculations.

(c) Ag₂SO₄ (s) Ksp = 1.12 x 10^–5 in 0.500 L of a solution containing 19.50 g of K₂SO₄

molar mass K₂SO₄ = 174 g/mole

moles K₂SO₄ present = 19.50 g x 1 mol / 174 g = 0.112 moles K₂SO₄

[K₂SO₄] = 0.112 mol/0.500 L = 0.224 M

Ag₂SO₄(s) <==> 2Ag⁺(aq) + SO₄^2-(aq)

Ksp = [Ag⁺]²[SO₄^2-]

[Ag⁺] = 2x

[SO₄^2-] = 0.224 M and since Ksp is relatively small (10^-5) we can assume SO₄^2- contributed by Ag₂SO₄ is small

1.12x10^-5 = (2x)²(0.224)

4x² = 5x10^-5

x = [Ag⁺] = 3.54x10^-3 M

Summary

[Ag⁺] = 3.54x10^-3 M

[SO₄^2-] = 0.224 M

[K⁺] = 0.448 M (there are 2 K⁺ for each SO₄^2-)

[Ag₂SO₄] = negligible

The initial concentration of the common ion SO₄^2- would be ~ 1/2 x 7.07x10^-3 M = 3.54x10^-3 M which is small relative to the added common ion from K2SO4 (0.224 M) it can be neglected in the calculations.