A 1.00-L solution saturated at 25 C with lead(II) iodide contains 0.54 g of PbI2. Calculate the solubility-product constant for this salt at 25 C.

Verified step by step guidance

1. Determine the molar mass of lead(II) iodide (PbI2). The atomic masses are: Pb = 207.2 g/mol, I = 126.9 g/mol. Calculate the molar mass by adding the mass of one Pb atom and two I atoms.
2. Calculate the number of moles of PbI2 dissolved in the solution using the mass of PbI2 given and its molar mass. Use the formula: moles = mass / molar mass.
3. Write the dissolution equation for PbI2: PbI2(s) ⇌ Pb^2+(aq) + 2I^-(aq).
4. Using the stoichiometry of the dissolution equation, determine the concentrations of Pb^2+ and I^- in the solution. Since the dissolution produces one mole of Pb^2+ and two moles of I^- for each mole of PbI2, the concentration of I^- will be twice that of Pb^2+.
5. Calculate the solubility product constant (Ksp) for PbI2 at 25 C using the formula: Ksp = [Pb^2+][I^-]^2, where [Pb^2+] and [I^-] are the concentrations calculated in the previous step.

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 lead(II) iodide (PbI2), Ksp can be expressed as Ksp = [Pb^2+][I^-]^2, where [Pb^2+] and [I^-] are the molar concentrations of lead and iodide ions, respectively.

Molar Mass and Molarity

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molarity of a solution, which is the concentration of a solute in a given volume of solution, you divide the number of moles of solute by the volume of the solution in liters. In this case, knowing the molar mass of PbI2 allows us to convert the mass of the solute into moles, which is essential for determining the concentrations of the ions in the saturated solution.

Saturation and Equilibrium

A saturated solution is one in which the maximum amount of solute has been dissolved at a given temperature, leading to a dynamic equilibrium between the dissolved ions and the undissolved solute. At this point, the rate of dissolution of the solid equals the rate of precipitation. Understanding this concept is crucial for calculating Ksp, as it reflects the concentrations of ions present when the solution is saturated with PbI2.