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JEE MainChemistryIonic Equilibrium

An aqueous solution contains 0.1 M of Cl ^- ions and 0.1 M of Br ^- ions. Solid AgNO ₃ is gradually added to this solution without changing its volume. Given that K_ sp ( AgCl ) = 1.0 10⁻¹⁰ and K_ sp ( AgBr ) = 5.0 10⁻¹³ , what is the concentration of Br ^- ions remaining in the solution exactly when AgCl just begins to precipitate?

Options

  1. A5.0 10⁻⁴ M
  2. B1.0 10⁻⁹ M
  3. C5.0 10⁻¹² M
  4. D2.0 10⁻³ M

Correct answer

A. 5.0 10⁻⁴ M

Step-by-step solution

For precipitation of a salt to begin, the ionic product must just exceed its solubility product K_ sp . The concentration of Ag ^+ required to start precipitating AgCl is: [ Ag ^+] = K_ sp ( AgCl ) [ Cl ^-] = 1.0 10⁻¹⁰ 0.1 = 1.0 10⁻⁹ M The concentration of Ag ^+ required to start precipitating AgBr is: [ Ag ^+] = K_ sp ( AgBr ) [ Br ^-] = 5.0 10⁻¹³ 0.1 = 5.0 10⁻¹² M Since a lower concentration of Ag ^+ is needed for AgBr , it will precipitate first. As more AgNO ₃ is added, AgBr continues to precipitate, and the co

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