Calculate the solubility of silver chloride in a solution that is 0.100 M in NH₃.

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the dissolution of silver chloride (AgCl) in ammonia (NH3). AgCl(s) + 2NH3(aq) ⇌ [Ag(NH3)2]+(aq) + Cl-(aq)
2. Step 2: Write the expression for the solubility product constant (Ksp) for AgCl and the formation constant (Kf) for the complex ion [Ag(NH3)2]+. Ksp = [Ag+][Cl-] and Kf = [[Ag(NH3)2]+]/([Ag+][NH3]^2)
3. Step 3: Since the Ag+ ions are completely consumed by the reaction with NH3, we can say that the concentration of Ag+ ions is equal to the solubility of AgCl. Therefore, we can substitute [Ag+] in the Kf expression with the solubility of AgCl (let's denote it as 's').
4. Step 4: We know the concentration of NH3 is 0.100 M. Substitute this value and the expression for [Ag+] from step 3 into the Kf expression. Solve the equation for 's' (the solubility of AgCl).
5. Step 5: The value of 's' obtained in step 4 is the solubility of AgCl in a 0.100 M NH3 solution. Remember to check if the value of 's' makes sense in the context of the problem (it should be a positive value less than or equal to the initial concentration of NH3).

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For silver chloride (AgCl), Ksp can be expressed as Ksp = [Ag+][Cl-]. Understanding Ksp is essential for calculating the solubility of AgCl in different solutions.

Common Ion Effect

The common ion effect refers to the decrease in solubility of an ionic compound when a common ion is added to the solution. In this case, the presence of NH3 can affect the solubility of AgCl by shifting the equilibrium. This is important because NH3 can form a complex with Ag+, reducing the concentration of free Ag+ ions and thus influencing the solubility of AgCl.

Complex Ion Formation

Complex ion formation occurs when a metal ion binds with one or more ligands, resulting in a complex that can alter the solubility of the metal's salts. In the context of this question, NH3 acts as a ligand that can form a complex with Ag+, which increases the solubility of AgCl in the presence of NH3. Understanding this concept is crucial for accurately calculating the solubility of silver chloride in the given solution.