In quantitative analysis, Ag+, Hg2+, and Pb2+ are seperated from other cations by the addition of HCl. Calculate the concentration of Cl-ions required to just begin the precipitation of (a) AgCl, (b) Hg2Cl2, (c) PbCl2 in a solution hav-ing metal-ion concentrations of 0.030 M. What fraction of the Pb2+ remains in solution when the Ag+ just begins to precipitate?

Verified step by step guidance

1. Identify the solubility product constants (K_sp) for AgCl, Hg2Cl2, and PbCl2 from a reliable source.
2. Use the expression for the solubility product (K_sp) to set up the equation for each salt: (a) K_sp(AgCl) = [Ag^+][Cl^-], (b) K_sp(Hg2Cl2) = [Hg2^2+][Cl^-]^2, (c) K_sp(PbCl2) = [Pb^2+][Cl^-]^2.
3. Substitute the given metal-ion concentration (0.030 M) into each equation to solve for the concentration of Cl^- required to begin precipitation: (a) [Cl^-] = K_sp(AgCl) / [Ag^+], (b) [Cl^-] = sqrt(K_sp(Hg2Cl2) / [Hg2^2+]), (c) [Cl^-] = sqrt(K_sp(PbCl2) / [Pb^2+]).
4. To find the fraction of Pb^2+ remaining in solution when Ag^+ just begins to precipitate, calculate the concentration of Cl^- at this point using the K_sp of AgCl, then use this Cl^- concentration in the K_sp expression for PbCl2 to find the remaining [Pb^2+].
5. Calculate the fraction of Pb^2+ remaining by dividing the remaining [Pb^2+] by the initial concentration (0.030 M).

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a numerical value that represents the equilibrium between a solid and its ions in a saturated solution. It is specific to a particular compound and temperature. For example, the Ksp of AgCl indicates the concentration of Ag+ and Cl- ions at which AgCl begins to precipitate. Understanding Ksp is essential for calculating the concentration of ions needed to initiate precipitation.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react to form an insoluble compound, which then separates from the solution as a solid. In this context, the addition of HCl leads to the formation of insoluble chlorides like AgCl, Hg2Cl2, and PbCl2. Recognizing the conditions under which these precipitates form is crucial for determining the concentrations of Cl- ions required for each metal ion.

Fraction Remaining in Solution

The fraction of a metal ion remaining in solution after precipitation can be calculated using the initial concentration and the amount that precipitates. When Ag+ begins to precipitate, it affects the equilibrium of the other metal ions present. Understanding how to calculate this fraction involves applying the principles of stoichiometry and equilibrium to determine how much Pb2+ remains in solution when Ag+ starts to form AgCl.