The solubility of AgSCN in pure water is x times its solubility in a 0.001 M KSCN solution. The value of x is: (Given : K_ sp of AgSCN = 10⁻¹² )

Step-by-step solution

Let the solubility of AgSCN in pure water be s₁ . For pure water: AgSCN (s) Ag ^+(aq) + SCN ^-(aq) K_ sp = s₁^2 s₁ = 10⁻¹² = 10⁻⁶ M Let the solubility of AgSCN in 0.001 M KSCN be s₂ . Due to the common ion effect, [ SCN ^-] = s₂ + 0.001 10⁻³ M (since s₂ is very small compared to 10⁻³ ). K_ sp = [ Ag ^+][ SCN ^-] = s₂ 10⁻³ s₂ = 10⁻¹² 10⁻³ = 10⁻⁹ M Given that s₁ = x s₂ x = s₁ s₂ = 10⁻⁶ 10⁻⁹ = 10^3 Answer: 10^3