Question

The Ksp of AgCl is 1.8 × 10–10. How do you know that mixing equal amounts of 0.04M solution of AgNO3 and 0.002M solution of NaCl will lead to the formation of a precipitate?
a. [Ag+]×[Cl–] = Ksp AgCl


b. [Ag+]×[Cl–] < Ksp AgCl


c. [Ag+]×[Cl–] > Ksp AgCl

Answer 1

Answer:

• option c. [Ag⁺] × [Cl⁻] > Ksp AgCl,

Explanation:

Ksp is the product solubility constant.

The solubility equation for AgCl is:

• AgCl ⇄ Ag⁺ + Cl⁻

The Ksp expression is:

• Ksp = [Ag⁺] [Cl⁻]

Since Ksp = 1.8 ×  10⁻¹⁰, at equilibrium  [Ag⁺] [Cl⁻] = 1.8 ×  10⁻¹⁰.

When AgNO₃ dissolves in water it completely ionizes into Ag⁺ and NO₃⁻.

When NaCl dissolves in water it completely inoizes into Na⁺ and Cl⁻.

Uisng the molarity formula, M = n / V, you get n = M × V.

So, a volume V of a 0.04 M solution of AgNO₃ will yield 0.04V moles of Ag⁺ and the same volume V of a 0.002 M solution of NaCl will yield 0.02V moles of Cl⁻⁻

So the concentrations will be:

• [Ag⁺] = 0.04V / (2V) = 0.02 M

• [Cl⁻] = 0.002V / (2V) = 0.001 M

And the product of the two concentrations will be:

• 0.02 × 0.0001 = 0.00002 = 2.0 ×  10⁻⁵

That product is much greater than 1.8 ×  10⁻¹⁰ meaning that the concentrations are higher than the equilibrium concentrations and the mixture will lead to the formation of a precipitate.

The option c., [Ag⁺] × [Cl⁻] > Ksp AgCl, describes that situation.