Problem 23 - Introductory Chemistry Atoms First

Question

What volume of \(0.350 \mathrm{M} \mathrm{CaF}_{2}\) solution is required to obtain \(0.00875\) mole of \(\mathrm{CaF}_{2} ?\)

Step-by-Step Solution

Answer

The volume of the 0.350 M CaF₂ solution required to obtain 0.00875 moles of CaF₂ is 0.025 liters or 25 mL.

Step 1: Identify the given information

We are given: - Molarity (M) of CaF₂ solution: 0.350 M - Moles of CaF₂: 0.00875 Our goal is to find the volume of the solution (in liters) containing the given amount of CaF₂.

Step 2: Use the molarity equation to find the volume

We'll use the formula: Molarity (M) = moles of solute / volume of solution (L) Rearrange the formula to solve for the volume: Volume of solution (L) = moles of solute / Molarity (M) Now, plug the given values into the equation: Volume of solution (L) = \( \frac{0.00875\text{ moles of CaF}_{2}}{0.350\text{ M}} \)

Step 3: Calculate the volume of the solution

Divide the given values: Volume of solution (L) = \( \frac{0.00875}{0.350} \) = 0.025 L Therefore, 0.025 liters (25 mL) of the 0.350 M CaF₂ solution is required to obtain 0.00875 moles of CaF₂.

Key Concepts

Moles of solute

Moles of solute are the actual amount of substance we have in terms of the number of molecules or atoms. It is a fundamental concept in chemistry that allows us to count particles in a given mass and connect this mass to the macroscopic world of solutions. The term "mole" represents Avogadro's number, which is approximately 6.022 x 10²³ particles (atoms, molecules, ions, etc.).

To calculate moles, we typically use the formula:

• \( ext{moles} = \frac{ ext{mass}}{ ext{molar mass}} \)

However, when dealing with solutions, we often start with moles instead of mass. Knowing the moles of solute is crucial for determining concentrations and conducting solution-related calculations.

In our exercise, we were provided with 0.00875 moles of CaF₂, which is directly used in the molarity equation to find the required volume of the solution. This helps identify the source quantity of the solute in the chemical process outlined.

Volume of solution

The volume of a solution refers to the overall space that the solute plus solvent occupy together. This could be expressed in liters, milliliters, or any other appropriate unit of volume measurement. Calculating volumes is critical when it’s necessary to dilute or concentrate solutions to meet specific requirements.

When solving for volume, knowing the moles of solute and the molarity of the solution lets us determine how much of the total solution we need.

• The equation: \( ext{Volume of solution (L)} = \frac{ ext{moles of solute}}{ ext{Molarity (M)}} \), allows us to calculate volume.

Using this formula, we find the answer by rearranging and inserting our knowns, which gives us a holistic view of the solution's makeup in physical terms.

In practical applications, understanding volume is important in laboratories, medicine, and industries where solution preparation is common.

Concentration calculation

Concentration is a measure of how much solute is present in a given amount of solution. This is often represented by molarity in the context of chemical solutions. Molarity (M) quantifies the concentration by expressing the moles of solute per liter of solution.

The molarity formula is:

• \( ext{Molarity (M)} = \frac{ ext{moles of solute}}{ ext{volume of solution (L)}} \)

For the concentration calculation, you rearrange this equation to solve for the desired component, whether that is moles, volume, or molarity itself.

In our specific problem, this formula helped us determine the volume of 0.350 M CaF₂ solution needed to get a certain number of moles. By calculating concentration, we ensure the solution has the desired chemical properties and behavior, which is critical in any scientific or industrial activity involving solutions.