Question

How many grams of NaF are present in \(4.5 \mathrm{~L}\) of a \(1.19 \mathrm{~b}\) NaF solution by mass? The density of the solution is \(1.0 \mathrm{~g} / \mathrm{mL}\).

Short answer

The mass of NaF in the solution is 53.55 grams.

Step-by-step solution

Calculate the mass of the solution

Convert the volume of the solution to milliliters by using the conversion factor that 1 L equals 1000 mL. Then multiply the volume by the density to obtain the mass of the solution in grams.

Calculate the mass of NaF

Use the percent by mass \(b\) to find the mass of NaF in the solution by multiplying the total mass of the solution by the mass percentage (expressed as a decimal).

Convert mass of NaF to grams

The mass of NaF has already been calculated in grams, so no additional conversion is needed.

Key concepts

Molarity and Solution Preparation

Understanding molarity and solution preparation is crucial for students embarking on laboratory experiments and industrial applications. Molarity, denoted by the symbol M, refers to the concentration of a solution expressed as the number of moles of solute per liter of solution. It's calculated by dividing the moles of solute by the volume of the solution in liters.

Preparing a solution with a specific molarity involves dissolving a measured amount of solute, usually in grams, into a solvent to reach a specific total volume. To convert from grams to moles, the molecular weight of the solute is used. For example, when preparing a NaF solution, we need to consider the molar mass of NaF. A higher molarity means a more concentrated solution.

In the exercise given, concentration is expressed as percent by mass rather than molarity, but the concepts intersect when it comes to solution preparation. After determining the mass of the solute (NaF) present in the solution, one could also calculate molarity if the molar mass of NaF was known and provided.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in chemical reactions. It is fundamental in chemistry because it ensures that equations are balanced, enabling accurate predictions about the outcomes of reactions.

The core principle of stoichiometry is based on the law of conservation of mass, which states that matter is neither created nor destroyed during a chemical reaction. As a result, the amount of each element must be the same in both the reactants and products. Stoichiometry relies on a balanced chemical equation to provide the mole ratios of reactants and products which are used to calculate the amounts needed or produced.

Even though our exercise doesn't involve a reaction, concepts of stoichiometry apply when determining the mass of NaF in a solution. The percent by mass tells us, stoichiometrically, what fraction of the total mass is due to NaF. This concept ties directly into the composition of solutions, where the concentration is an essential factor.

Concentration of Solutions

Concentration of solutions is a measure of how much solute is dissolved in a given amount of solvent. There are various ways to express concentration, including percent by mass, molarity, molality, and normality. Each expression provides a different perspective on how concentrated a solution is.

Percent by mass is one of the simplest forms of concentration, calculated by the formula: \[ \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\% \]. This measurement is intuitive for solid solutions or where temperature variations are significant, as it doesn't change with the temperature like volume-based concentrations do. In our exercise, the percent by mass of NaF is used to determine the mass of solute in the total solution.

The connection between percent by mass and molarity is one that often confuses students. While percent by mass focuses on the weight ratio of solute to solution, molarity considers the volume of the whole solution and the amount of solute in moles. Being adept at converting between these measures can be instrumental for many chemistry tasks.