Question

Fluorite, a mineral of calcium, is a compound of the metal with fluorine. Analysis shows that a 2.76 -g sample of fluorite contains \(1.42 \mathrm{~g}\) of calcium. Calculate the (a) mass of fluorine in the sample; (b) mass fractions of calcium and fluorine in fluorite; (c) mass percents of calcium and fluorine in fluorite.

Short answer

The mass of fluorine is 1.34 g. The mass fractions of calcium and fluorine are 0.514 and 0.486, respectively. The mass percents of calcium and fluorine are 51.4% and 48.6%, respectively.

Step-by-step solution

- Determine the mass of fluorine

Calculate the mass of fluorine in the sample by subtracting the mass of calcium from the total mass of the compound.Formula: \[\text{Mass of fluorine} = \text{Total mass} - \text{Mass of calcium}\]Given: \[\text{Total mass} = 2.76 \text{ g}\]\[\text{Mass of calcium} = 1.42 \text{ g}\]So,\[\text{Mass of fluorine} = 2.76 \text{ g} - 1.42 \text{ g} = 1.34 \text{ g}\]

- Calculate the mass fractions

To find the mass fraction of calcium, use the formula:\[\text{Mass fraction of calcium} = \frac{\text{Mass of calcium}}{\text{Total mass}}\]Substitute the values:\[\text{Mass fraction of calcium} = \frac{1.42 \text{ g}}{2.76 \text{ g}} \ \text{Mass fraction of calcium} \ = 0.514\]To find the mass fraction of fluorine, use the formula:\[\text{Mass fraction of fluorine} = \frac{\text{Mass of fluorine}}{\text{Total mass}}\]Substitute the values:\[\text{Mass fraction of fluorine} = \frac{1.34 \text{ g}}{2.76 \text{ g}} \ \text{Mass fraction of fluorine} \ = 0.486\]

- Calculate the mass percents

To find the mass percent of calcium, use the formula:\[\text{Mass percent of calcium} = \text{Mass fraction of calcium} \times 100\]Substitute the value:\[\text{Mass percent of calcium} = 0.514 \times 100 = 51.4\%\]To find the mass percent of fluorine, use the formula:\[\text{Mass percent of fluorine} = \text{Mass fraction of fluorine} \times 100\]Substitute the value:\[\text{Mass percent of fluorine} = 0.486 \times 100 = 48.6\%\]

Key concepts

mass of fluorine

To start solving the problem, it is important to understand how to determine the mass of fluorine in a compound. Fluorite, for instance, is composed of calcium and fluorine. Given a sample of fluorite, you can find the mass of fluorine by subtracting the mass of calcium from the total mass of the compound. This approach is based on the conservation of mass principle.
Suppose you have a sample of fluorite that weighs 2.76 g, and it contains 1.42 g of calcium. You can calculate the mass of fluorine using the formula:
\[ \text{Mass of fluorine} = \text{Total mass} - \text{Mass of calcium} \]
Here's how it works:

• Total mass of compound: 2.76 g
• Mass of calcium: 1.42 g

By substituting these values into the formula, you get:
\[ \text{Mass of fluorine} = 2.76 \text{ g} - 1.42 \text{ g} = 1.34 \text{ g} \]
That's how you find the mass of fluorine, which in this case is 1.34 g.

mass fractions

Mass fractions are an essential concept in chemistry, especially when dealing with mixtures and compounds. They tell you how much a particular component contributes to the total mass of the mixture.
For fluorite, you can determine the mass fractions of calcium and fluorine. First, calculate the mass fraction of calcium using the formula:
\[ \text{Mass fraction of calcium} = \frac{\text{Mass of calcium}}{\text{Total mass}} \]
Using our values:
\[ \text{Mass fraction of calcium} = \frac{1.42 \text{ g}}{2.76 \text{ g}} = 0.514 \]
To find the mass fraction of fluorine, use the formula:
\[ \text{Mass fraction of fluorine} = \frac{\text{Mass of fluorine}}{\text{Total mass}} \]
Again, substitute the values:
\[ \text{Mass fraction of fluorine} = \frac{1.34 \text{ g}}{2.76 \text{ g}} = 0.486 \]
Mass fractions help you see the proportion of each component in the compound. In fluorite, 51.4% of the mass comes from calcium, and 48.6% comes from fluorine.

mass percents

Mass percents are another useful concept that helps you understand the composition of compounds. Mass percent tells you the percentage of a component's mass relative to the total mass of the compound.
To find the mass percent of calcium in fluorite, you need to use the mass fraction of calcium and multiply it by 100.
The formula is:
\[ \text{Mass percent of calcium} = \text{Mass fraction of calcium} \times 100 \]
From our values:
\[ \text{Mass percent of calcium} = 0.514 \times 100 = 51.4\text{ %} \]
Similarly, calculate the mass percent of fluorine using its mass fraction:
\[ \text{Mass percent of fluorine} = \text{Mass fraction of fluorine} \times 100 \]
With our values:
\[ \text{Mass percent of fluorine} = 0.486 \times 100 = 48.6\text{ %} \]
Therefore, fluorite is composed of 51.4% calcium and 48.6% fluorine. Understanding mass percents is helpful when analyzing substances and determining their composition in a simple and clear manner.