The value of Ksp for Ag₂CO₃ in the saturated solution will be 8.39 × 10⁻¹².
A saturated solution is the one in which the maximum amount of solute that a solvent can dissolve in it has been dissolved. If more solute is tried to be dissolved than the crystals of the solute will be present in the solution as they won't dissolve.
According to the solution,
[Ag⁺] = 2.56 × 10⁻⁴ M
In saturated solution,
Ag₂CO₃ + H₂O ⇒ 2Ag⁺ + CO₃²⁻
Ksp = [Ag⁺]² [CO₃²⁻]
[CO₃²⁻] = 1/2 [Ag⁺]
[Ag⁺] = 2.56 × 10⁻⁴ M
Therefore, [CO₃²⁻] = 1.28 × 10⁻⁴ M
Hence, Ksp = (2.56 × 10⁻⁴ M)² × (1.28 × 10⁻⁴ M)
Therefore, Ksp = 8.39 × 10⁻¹²
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