The solubility of AgCl in an aqueous NaCl solution is 10⁻³ times its solubility in pure water. What is the concentration of NaCl in the solution? (Given : Solubility product of AgCl = 10⁻¹⁰ )

Step-by-step solution

Let the solubility of AgCl in pure water be s₀ . K_ sp = s₀^2 s₀ = 10⁻¹⁰ = 10⁻⁵ M The solubility of AgCl in the NaCl solution ( s ) is given as 10⁻³ times its solubility in pure water. s = 10⁻³ s₀ = 10⁻³ 10⁻⁵ = 10⁻⁸ M In the NaCl solution, the chloride ion concentration is mainly due to NaCl (common ion effect). Let the concentration of NaCl be C . K_ sp = [ Ag^+ ][ Cl^- ] = s C 10⁻¹⁰ = 10⁻⁸ C C = 10⁻¹⁰ 10⁻⁸ = 10⁻² M Answer: 10⁻² M