(b) If 0.0490 g of AgIO3 dissolves per liter of solution, calculate the solubility-product constant.

Verified step by step guidance

1. Identify the dissolution equation for silver iodate (AgIO3). When AgIO3 dissolves, it dissociates into silver ions (Ag+) and iodate ions (IO3-). The equation can be written as: \( AgIO3(s) \rightarrow Ag^+(aq) + IO3^-(aq) \).
2. Determine the molar mass of AgIO3 to convert grams per liter to moles per liter. The molar mass of AgIO3 is calculated by adding the atomic masses of silver (Ag), iodine (I), and three oxygen (O) atoms.
3. Convert the mass of AgIO3 given (0.0490 g) into moles using the molar mass calculated in the previous step. This will give you the concentration of AgIO3 in moles per liter, which is also the concentration of Ag+ and IO3- since each formula unit of AgIO3 produces one ion of each.
4. Write the expression for the solubility product constant (Ksp) of AgIO3. The Ksp expression for AgIO3 is given by: \( K_{sp} = [Ag^+][IO3^-] \), where [Ag+] and [IO3-] are the molar concentrations of the respective ions in a saturated solution.
5. Substitute the concentrations of Ag+ and IO3- obtained from the dissolution of AgIO3 into the Ksp expression to calculate the solubility-product constant.

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 a compound like AgIO3, Ksp can be calculated from the concentrations of Ag+ and IO3- ions in a saturated solution.

Dissociation of Ionic Compounds

When ionic compounds dissolve in water, they dissociate into their constituent ions. For AgIO3, it dissociates into Ag+ and IO3- ions. Understanding this dissociation is crucial for calculating Ksp, as the concentrations of these ions directly influence the solubility product constant.

Molar Mass and Concentration Calculations

To calculate Ksp, it is essential to determine the molar mass of the compound and the concentration of ions in solution. The molar mass of AgIO3 is needed to convert the given mass (0.0490 g) into moles, which can then be used to find the molarity of the solution. This concentration is vital for accurately calculating the Ksp value.