Question

What is the weight percent of \(23.4 \mathrm{g}\) of \(\mathrm{CaF}_{2}\) if dissolved in 10.5 mol of water? (a) \(0.028\); (b)\( 1.59\);(c) \(11.0\); (d) \(12.4 ;\) (e) none of these.

Short answer

The weight percent of \(23.4 g\) of \(CaF_{2}\) if dissolved in 10.5 mol of water is approximately 11.01%. So, the closest answer choice is (c) 11.0. If none of the options were close enough, then (e) 'none of these' would be chosen.

Step-by-step solution

Identify Given Information

Extract the given values from the problem - the mass of the solute (Calcium Fluoride - \(CaF_{2}\)) which is \(23.4 g\), and volume of the solvent (Water - \(H_{2}O\)) expressed in moles, which is 10.5mol.

Convert Moles of Solvent to Mass

Convert the moles of water to grams using water’s molar mass (18.02 g/mol). So, the mass of the water = 10.5 mol * 18.02 g/mol = 189.21 g.

Calculate the total mass of the solution

Add the mass of the solute (\(CaF_{2}\)) to the mass of the solvent (water) to find the total mass of the solution. The total mass = 23.4g (\(CaF_{2}\)) + 189.21g (water) = 212.61 g.

Calculate Weight Percentage

Use the weight percentage formula: (Mass of solute / Total mass of solution) * 100. So, weight percent = (23.4 g / 212.61 g) * 100 = 11.01%.

Key concepts

Calcium Fluoride

Calcium fluoride, commonly represented as \( \text{CaF}_2 \), is an ionic compound that consists of calcium and fluoride ions. It is naturally found in the mineral fluorite and has many applications, including in the production of certain glasses and ceramics. The structure of calcium fluoride is typically crystalline, and due to its ionic nature, it has a high melting point.
One of the important applications of calcium fluoride in chemistry, especially in solution chemistry, is its role as a source of fluoride ions in reactions. The compound dissolves to release fluoride ions which can participate in further chemical reactions. Understanding the behavior of calcium fluoride in solutions, such as how much can be dissolved at a certain temperature, is crucial for applications in industrial processes and laboratory settings.

Solubility

Solubility is a measure of how much of a substance can be dissolved in a solvent at a given temperature and pressure. When we talk about the solubility of calcium fluoride, it generally refers to the amount of \( \text{CaF}_2 \) that can be dissolved in water before the solution becomes saturated.
Unlike substances like table salt, calcium fluoride has quite a low solubility in water. This is partly because both calcium and fluoride form strong ionic bonds, which require a lot of energy to break. Thus, only a limited amount of calcium fluoride will dissolve in water to form a solution. For students studying solution chemistry, understanding the solubility principles helps in predicting the outcomes of dissolving reactions and is a fundamental concept for calculating concentrations like the weight percent of a solution.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and helps in relating the amount of a substance in moles to its mass in grams. In the context of solution chemistry, knowing the molar masses of substances involved is essential for making accurate calculations.
For example, the molar mass of water (\( \text{H}_2\text{O} \)) is approximately \( 18.02 \) g/mol, which is used to convert moles of water to grams in various calculations. Similarly, the molar mass of calcium fluoride (\( \text{CaF}_2 \)) is essential when calculating how much of the compound is present in grams if you know the quantity in moles. This conversion allows chemists to prepare solutions with precise concentrations, crucial for experiments and industrial processes.

Solution Chemistry

Solution chemistry is the study of how substances dissolve and interact with each other in a solvent to form a solution. It encompasses concepts such as solubility, concentration, saturation, and the formation of various types of solutions.
In the case of the exercise regarding calcium fluoride, solution chemistry principles are applied to find the weight percent of \( \text{CaF}_2 \) in a solution by considering the solute's mass and the total mass of the solution. Weight percent is a commonly used unit for expressing concentration, which helps in understanding the proportion of a solute in a solution relative to the entire solution mass.

• Weight percent formula: \( \text{Weight percent} = \frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100 \)
• It provides a simple and communicative measure of how concentrated a solution is, which can be critical for applications like formulating mixtures to specific specifications or understanding chemical reactions.

Overall, solution chemistry is a pivotal area that combines physical concepts, mathematical calculations, and practical applications to explain the behaviors of substances in solutions.