Problem 11 - Chemistry: Atoms First

Question

The Handbook of Chemistry and Physics (http://openstaxcollege.org///16Handbook) gives solubilities of the following compounds in grams per \(100 \mathrm{mL}\) of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each. (a) \(\mathrm{BaSeO}_{4}, 0.0118 \mathrm{g} / 100 \mathrm{mL}\) (b) \(\mathrm{Ba}\left(\mathrm{BrO}_{3}\right)_{2} \cdot \mathrm{H}_{2} \mathrm{O}, 0.30 \mathrm{g} / 100 \mathrm{mL}\) (c) \(\mathrm{NH}_{4} \mathrm{MgAsO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}, 0.038 \mathrm{g} / 100 \mathrm{mL}\) (d) \(\mathrm{La}_{2}\left(\mathrm{MoO}_{4}\right)_{3}, 0.00179 \mathrm{g} / 100 \mathrm{mL}\)

Step-by-Step Solution

Answer

The Ksp values are calculated by first converting solubility from grams to moles, then determining the ion concentrations for each compound, and finally applying the solubility product expression for each respective compound.

Step 1 - Converting solubility from grams to moles for BaSeO4

The molar mass of BaSeO4 is calculated from the sum of the atomic masses of its constituent atoms. This gives a molar mass of 217.39 g/mol (137.33 for Ba, 78.96 for Se, and 16*4 for four O atoms). To convert the solubility from grams to moles, divide the solubility by molar mass: 0.0118 g / 217.39 g/mol.

Step 2 - Determining the ion concentration for BaSeO4

BaSeO4 dissociates into Ba2+ and SeO42- in a 1:1 ratio. The concentration of ions can be found by dividing the moles of BaSeO4 by the volume of the solution in liters (0.1 L for 100 mL).

Step 3 - Calculating the solubility product Ksp for BaSeO4

The solubility product Ksp for BaSeO4 can be calculated using the product of the concentrations of the ions, each raised to the power of its stoichiometric coefficient in the balanced dissolution equation, which for BaSeO4 is: Ksp = [Ba2+][SeO42-].

Step 4 - Repeating the process for Ba(BrO3)2.H2O

Calculate the number of moles for Ba(BrO3)2.H2O using its molar mass (437.74 g/mol), find the concentration of ions Ba2+ and BrO3- (ratio 1:2) in the solution, and then calculate the Ksp with the formula: Ksp = [Ba2+][BrO3-]^2.

Step 5 - Repeating the process for NH4MgAsO4.6H2O

Determine the molar mass of NH4MgAsO4.6H2O (329.86 g/mol), convert solubility to moles, find the concentration of ions NH4+, Mg2+, and AsO42- in the solution, and calculate the Ksp based on the balanced dissolution reaction.

Step 6 - Repeating the process for La2(MoO4)3

Find the molar mass of La2(MoO4)3 (1071.86 g/mol), convert the solubility to moles, calculate the concentration of La3+ and MoO42- ions, and use these to compute the Ksp with the formula: Ksp = [La3+]^2[MoO42-]^3.

Key Concepts

Solubility Calculations

Understanding solubility calculations is essential for predicting the extent to which a compound will dissolve in a solvent. The solubility of a substance is often given in grams per 100 mL of solvent, as seen in the exercise. To calculate the solubility product constant (Ksp), these values must be converted to molar solubility, which is the number of moles of the solute dissolved per liter of solution.

Converting grams to moles requires the use of the molar mass of the compound, which can be found by adding the atomic masses of its constituent elements. For instance, the molar mass of barium selenate (BaSeO4) is obtained by summing the atomic masses of barium, selenium, and oxygen. Once the moles of the solute are determined, the concentration of ions in the solution can be found. This is a crucial step because the Ksp is calculated using the concentrations of the ions produced when the compound dissolves.

The dissolution of BaSeO4, according to the balanced equation, produces Ba2+ and SeO42- ions in a 1:1 ratio. Thus, the solubility product for BaSeO4 can be calculated by multiplying the concentrations of these ions. Similar steps are followed for other compounds mentioned in the exercise.

Molar Mass Determination

Determining the molar mass of a compound is a fundamental step in chemistry that involves summing the atomic masses of each element present in the compound based on its chemical formula. It is significant in many areas of chemistry including stoichiometry, preparation of solutions, and solubility calculations. The molar mass serves as a conversion factor between grams and moles—a measure of the number of particles in a given substance.

For the compound Ba(BrO3)2.H2O, the molar mass is calculated by adding together the atomic masses of barium, bromine, oxygen, and hydrogen. The atomic mass of each element is typically found on the periodic table and must be multiplied by the number of atoms of that element in the compound. After determining the molar mass, we can then convert the solubility from grams per 100 mL into moles per liter, setting the stage for the calculation of the solubility product constant.

Dissolution Equations

Dissolution equations express the process by which a solid compound disassociates into its constituent ions in a solution. Each equation represents a balanced chemical reaction that takes place when the solid is introduced to the solvent. These equations are critical to calculating the solubility product constant, as they provide the stoichiometry of the ions involved.

For example, the dissolution of NH4MgAsO4.6H2O in water can be represented by an equation showing that it disassociates into NH4+, Mg2+, and AsO42- ions. The coefficients in the dissolution equation dictate the ratio in which ions are produced and therefore how to calculate the concentration of each ion in the solution. When these ionic concentrations, determined from the molar solubility, are substituted into the expression for Ksp, they must be raised to the power of their respective coefficients to find the solubility product. This relationship is crucial and allows chemists to predict the solubility behavior of compounds under various conditions.