Problem 22 - Introductory Chemistry Atoms First

Question

How many moles of \(\mathrm{CaF}_{2}\) are there in \(25.0 \mathrm{~mL}\) of \(0.350 \mathrm{M} \mathrm{CaF}_{2}(a q) ?\)

Step-by-Step Solution

Answer

The number of moles of \(\mathrm{CaF}_{2}\) present in \(25.0 \mathrm{~mL}\) of \(0.350 \mathrm{M} \mathrm{CaF}_{2}(a q)\) is \(0.00875\) moles.

Step 1: Convert the volume of solution to liters

Since the volume of the solution is given in milliliters, convert it to liters by dividing by 1000: \(25.0 \: \mathrm{mL} \times \frac{1 \: \mathrm{L}}{1000 \: \mathrm{mL}} = 0.025 \: \mathrm{L}\)

Step 2: Calculate the moles of solute present in the solution

Use the formula moles of solute = concentration × volume of solution (in liters), and plug in the values: Moles of \(\mathrm{CaF}_2\) = \(0.350\: \mathrm{M} \times 0.025 \: \mathrm{L} = 0.00875\) moles

Step 3: Present the final answer

The number of moles of \(\mathrm{CaF}_{2}\) present in \(25.0\: \mathrm{mL}\) of \(0.350\: \mathrm{M} \: \mathrm{CaF}_{2}(a q)\) is: \(0.00875\) moles.

Key Concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. The molarity (M) is frequently used in chemistry to describe the strength of a solution. Understanding molarity is key for diluting solutions or mixing chemicals in a lab setting. The formula for calculating molarity is:
\[\begin{equation} M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \end{equation}\]
In our exercise, we use molarity to determine how many moles of \(\mathrm{CaF}_{2}\) are present in a given volume of solution. The solution concentration of \(0.350\mathrm{M}\) indicates that each liter of solution contains 0.350 moles of \(\mathrm{CaF}_{2}\).

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations based on the balanced chemical equations and enables chemists to predict the amounts of substances consumed and produced in a given reaction.

Even though the current exercise does not involve a chemical reaction, the principles of stoichiometry are still applicable. We apply stoichiometric calculations to determine the quantity of solute (in moles) based on known concentrations and volumes. It's an essential skill in chemistry that ensures precise measurement and aids understanding chemical formulations.

Solution Concentration

Solution concentration refers to the amount of solute that is dissolved in a given quantity of solvent. Several units can be used to express concentration, including molarity, molality, and parts per million (ppm). Among these, molarity is one of the most commonly used units in chemistry for its convenience in stoichiometric calculations involving aqueous solutions.

Being familiar with different ways to express solution concentration is crucial when performing chemical analyses and comparing results from different experiments. The solution in our exercise is an aqueous solution with a known molarity which provides us with information on how concentrated the solute, \(\mathrm{CaF}_{2}\), is within the solution.

Unit Conversion

Unit conversion is a fundamental skill in science, particularly in chemistry, where it's necessary to convert between units such as milliliters to liters or grams to moles. Proper conversion ensures accuracy in both experimental setups and calculations.

In the given problem, converting milliliters (\(\mathrm{mL}\)) to liters (\(\mathrm{L}\)) was an essential step because the molarity formula requires the volume in liters. The conversion factor from milliliters to liters is \(\frac{1 \mathrm{L}}{1000 \mathrm{mL}}\), which reflects that there are 1000 milliliters in one liter. The correct unit conversion is thus crucial for the accurate calculation of moles of a substance in a solution, as demonstrated in the exercise.