Problem 72 - Chemistry Matter and Change

Question

What is the volume of a 3.00\(M\) solution made with 122 g of LiF?

Step-by-Step Solution

Answer

The volume of the solution is approximately 1.57 liters.

Step 1: Calculate Molar Mass of LiF

First, calculate the molar mass of Lithium Fluoride (LiF). The atomic mass of lithium (Li) is approximately 6.94 g/mol, and that of fluorine (F) is approximately 19.00 g/mol. Therefore, the molar mass of LiF is the sum of these two atomic masses: \[ \text{Molar Mass of LiF} = 6.94 \, \text{g/mol} + 19.00 \, \text{g/mol} = 25.94 \, \text{g/mol}. \]

Step 2: Determine Moles of LiF

To find out how many moles of LiF are in 122 grams, use the formula: \[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}. \] Plug in the values: \[ \text{Number of moles of LiF} = \frac{122 \, \text{g}}{25.94 \, \text{g/mol}} \approx 4.70 \, \text{mol}. \]

Step 3: Use Molarity Formula to Find Volume

We know the molarity (\(M\)) of the solution and moles of solute, and we need to find the volume. Molarity is defined as \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}. \] Rearrange to find volume: \[ \text{Volume} = \frac{\text{moles of solute}}{M}. \] Substitute the known values: \[ \text{Volume} = \frac{4.70 \, \text{mol}}{3.00 \, M} \approx 1.57 \, \text{L}. \]

Step 4: Conclusion: Find the Volume of the Solution

The calculated volume of the 3.00M LiF solution made with 122 g of LiF is approximately 1.57 liters.

Key Concepts

Solution Volume Calculation

Finding the volume of a solution starts with understanding the concept of molarity, which is the concentration of a solution expressed as the number of moles of solute per liter of solution. In our example, we have a solution with a molarity of 3.00 M that includes 122 grams of lithium fluoride (LiF). To find the volume, we rearrange the molarity formula:

• Molarity (M) = moles of solute / volume of solution (in liters)

This formula tells us how concentrated the solution is. For instance, for a 3.00 M solution, there are 3 moles of solute in every liter of solution. By rearranging the formula to find the volume, we can calculate:

• Volume = moles of solute / molarity

Plugging in the numbers from the solution, we find that our 3.00 M solution requires approximately 1.57 liters of volume.

Molar Mass

The molar mass of a compound is a crucial concept when dealing with chemical solutions and reactions. It represents the mass of one mole of a given substance. For lithium fluoride (LiF), we calculate the molar mass by adding together the atomic masses of its constituent elements: lithium (Li) and fluorine (F).

• Atomic mass of Li = 6.94 g/mol
• Atomic mass of F = 19.00 g/mol

The total molar mass of LiF can be calculated as: \[ 6.94 \, \text{g/mol} + 19.00 \, \text{g/mol} = 25.94 \, \text{g/mol} \]This value allows us to convert between grams of a substance and moles, which is invaluable for making solution calculations.

Moles of Solute

Understanding the concept of moles is key to measuring the quantity of a substance in a chemical solution. A mole is like a 'chemist's dozen'—it is an amount of substance that contains as many particles as there are atoms in 12 grams of pure carbon-12. When dealing with lithium fluoride (LiF), the number of moles can be found by dividing the mass of the compound by its molar mass.

• Formula: Number of moles = mass / molar mass

Using our example of 122 grams of LiF with a molar mass of 25.94 g/mol: \[ \text{Number of moles of LiF} = \frac{122 \, \text{g}}{25.94 \, \text{g/mol}} \approx 4.70 \, \text{mol} \]This conversion is essential for determining the concentration of a solution through the molarity formula.

Lithium Fluoride

Lithium fluoride (LiF) is an inorganic compound used in various chemical applications, especially in solutions. It is composed of lithium and fluorine atoms, forming a stable ionic compound. LiF is known for its high melting point and utility in optics and nuclear reactors.

• Composition: Lithium (Li) and Fluorine (F)
• Molecular formula: LiF
• Molar mass: 25.94 g/mol

In solution preparation, the molar mass of LiF is critical for calculating how many moles it contains, which allows us to determine solution concentration, or molarity. Understanding its properties and calculations associated with it helps in achieving the desired concentrations for practical applications.