equilibrium summary

Question

Will a precipitate form when 65.0 mL of 0.0200 M Ag₂SO₄ is mixed with 50.0 mL of 0.00500 M K₂CO₃? The K_sp for silver carbonate is 8.00 x 10^-12.

Answer 1

To answer this question, we will calculate the value of Q (reaction quotient) and compare it to the given value of Ksp. If Q > Ksp, then a precipitate will form.

Ag₂SO₄ + K₂CO₃ ==> Ag₂CO₃(s) + K₂SO₄(aq)

moles Ag⁺ = 65.0 ml Ag₂SO₄ x 1 L / 1000 ml x 0.0200 mol/L x 2 mol Ag⁺/mol Ag₂SO₄ = 0.0026 mols Ag⁺

moles CO₃^2- = 50.0 ml K₂CO₃ x 1 L / 1000 ml x 0.00500 mol /L x 1 mol CO₃^2-/mol = 0.00025 mols CO₃^2-

Final volume = 65.0 ml + 50.0 ml = 115 mls = 0.115 L

Final concentrations:

[Ag⁺] = 0.0026 mol / 0.115 L = 0.0226 M

[CO₃^2-] = 0.00025 mol / 0.115 L = 0.00217 M

Q = [Ag⁺]²[CO₃²⁺] = (0.0226)²(0.00217) = 1.1x10^-5 and compare this to Ksp of 8.00x10^-12

Q > Ksp so a precipitate will form