Question

Complete the following table for aqueous solutions of aluminum nitrate. $$ \begin{array}{cccc} \hline & \text { Mass of Solute } & \text { Volume of Solution } & \text { Molarity } \\ \hline \text { (a) } & 1.672 \mathrm{~g} & 145.0 \mathrm{~mL} & \\ \text { (b) } & 2.544 \mathrm{~g} & \- & 1.688 \mathrm{M} \\ \text { (c) } & & 894 \mathrm{~mL} & 0.729 \mathrm{M} \end{array} $$

Short answer

Answer: The molarity of the solution in part (c) is 0.0286 M.

Step-by-step solution

Part (a) - Mass of solute

To calculate the mass of solute for part (a), we first need to find the moles of solute. Using the molarity formula: molarity = moles of solute/liters of solution, we can determine the moles of solute by multiplying molarity by liters of solution: Moles of solute = molarity × volume of solution = 0.08415 M × 1.37 L = 0.11529 mol Now, we need to find the molar mass of barium perchlorate (Ba(ClO4)2). The molar mass is calculated by adding up the atomic masses of barium, chlorine, and oxygen: Molar mass of Ba(ClO4)2 = Ba + 2×(Cl + 4×O) = 137.33 g/mol + 2×(35.45 g/mol + 4×16.00 g/mol) = 336.23 g/mol Finally, by multiplying the moles of solute by the molar mass, we can find the mass of solute: Mass of solute = moles of solute × molar mass of Ba(ClO4)2 = 0.11529 mol × 336.23 g/mol = 38.75 g

Part (b) - Volume of solution

To calculate the volume of solution for part (b), we first need to find the moles of solute. We can use the mass of solute and the molar mass of Ba(ClO4)2 to determine the moles of solute: Moles of solute = mass of solute ÷ molar mass = 12.01 g ÷ 336.23 g/mol = 0.03574 mol Now, using the molarity formula, we can find the volume of solution by dividing the moles of solute by the molarity: Volume of solution = moles of solute ÷ molarity = 0.03574 mol ÷ 0.0579 M = 0.617 L

Part (c) - Molarity

To calculate the molarity for part (c), we first need to find the moles of solute. We can use the mass of solute and the molar mass of Ba(ClO4)2 to determine the moles of solute: Moles of solute = mass of solute ÷ molar mass = 26.44 g ÷ 336.23 g/mol = 0.07863 mol Next, using the molarity formula, we can find the molarity by dividing the moles of solute by the volume of solution: Molarity = moles of solute ÷ volume of solution = 0.07863 mol ÷ 2.75 L = 0.0286 M The completed table is: $$ \begin{array}{lccc} \hline & \text { Mass of Solute } & \text { Volume of Solution } & \text { Molarity } \\\ \hline \text { (a) } & 38.75 \mathrm{~g} & 1.370 \mathrm{~L} & 0.08415 \mathrm{M} \\\ \text { (b) } & 12.01 \mathrm{~g} & 0.617 \mathrm{~L} & 0.0579 \mathrm{M} \\\ \text { (c) } & 26.44 \mathrm{~g} & 2.750 \mathrm{~L} & 0.0286 \mathrm{M} \\\ \hline \end{array} $$

Key concepts

Aqueous Solutions

When studying chemistry, one often deals with aqueous solutions, which are mixtures where water acts as the solvent. In such solutions, various compounds like salts, acids, or bases dissolve, breaking into ions or molecules, which become evenly dispersed within the water. This process is crucial for a wide range of reactions in both laboratories and biological systems.

Understanding the behavior of chemicals within aqueous solutions is key, particularly when determining concentrations. Concentration describes how much solute (a dissolved substance) is present in a given volume of solution. One common unit of concentration is molarity, represented by the symbol M and defined as moles of solute per liter of solution.

Moles of Solute

The term moles of solute refers to the amount of substance dissolved in a solution, measured in moles. A mole is a standard unit in chemistry and represents a specific number of particles, akin to a dozen representing twelve items. One mole of any substance contains exactly 6.022×10²³ entities (Avogadro's number).

To calculate the moles of solute in an aqueous solution, divide the mass of the solute by its molar mass. This information, coupled with the solution's volume, allows you to determine its molarity. When establishing the molarity of an aqueous solution, knowing the moles of solute is essential. For example, a method commonly used involves using the molarity formula: \( \text{Molarity} = \frac{\text{Moles of solute}}{\text{Liters of solution}} \). This allows you to bridge the gap between the physical mass of a substance and its concentration in a solution.

Molar Mass

Understanding molar mass is crucial for many calculations in chemistry, including those involving molarity. The molar mass is the weight of one mole of a substance and is typically expressed in grams per mole (g/mol). It reflects the sum of the atomic masses of all atoms making up a molecule, taking into account the number of each type of atom.

For example, to find the molar mass of a compound like aluminum nitrate (Al(NO₃)₃), you would sum the molar masses of aluminum, nitrogen, and oxygen, while considering their respective quantities within the compound. This value can be used alongside the mass of the solute to calculate the moles of solute present in a solution, which is a fundamental step in determining molarity. In our exercise, the correct molar mass calculation enables students to progress to finding the mass of solute needed to achieve a specific molarity in a solution, illustrating the interconnected nature of these concepts.