Question

What is the empirical formula of stannous fluoride, the first fluoride compound added to toothpaste to protect teeth against decay? Its mass percent composition is \(24.25 \% \mathrm{~F}\) and \(75.75 \% \mathrm{Sn}\).

Short answer

The empirical formula is \(\text{SnF}_2\).

Step-by-step solution

Convert Percent to Mass

Assume you have 100 g of the compound, which means you have 24.25 g of F and 75.75 g of Sn. These values represent the mass percentages directly as masses.

Convert Mass to Moles

Calculate the moles of each element.For fluorine, use its atomic mass (19.00 g/mol) and for tin, use its atomic mass (118.71 g/mol).\[\text{Moles of F} = \frac{24.25 \text{ g}}{19.00 \text{ g/mol}} \approx 1.276 \text{ mol}\]\[\text{Moles of Sn} = \frac{75.75 \text{ g}}{118.71 \text{ g/mol}} \approx 0.638 \text{ mol}\]

Find the Simplest Moles Ratio

Divide each mole value by the smallest number of moles calculated to find the smallest whole number ratio.For F:\[\frac{1.276}{0.638} \approx 2\]For Sn:\[\frac{0.638}{0.638} = 1\]

Write the Empirical Formula

Now that we have the simplest whole number ratio, we can write the empirical formula using this ratio. It is \(\text{SnF}_2\) because the smallest ratio is 1:2.

Key concepts

Molecular Composition

Understanding molecular composition is key to determining the empirical formula of a compound. The molecular composition tells us the types of atoms present in a compound and the relative percentage of each. Imagine having a pie, where each slice represents a different element, showing what fraction of the pie each element makes up.

This concept is represented using mass percent composition, like in the example of stannous fluoride, which consists of 24.25% fluorine and 75.75% tin. These percentages indicate that for 100 grams of this compound, 24.25 grams are fluorine and 75.75 grams are tin.

• Mass percent composition gives a tangible sense of how much of each element there is in a compound.
• This data provides a foundation for further calculations, like converting these percentages into moles, which helps simplify and find the empirical formula.

By starting with the percentages, scientists can effectively translate the relative amounts into a simple and understandable chemical formula, which leads us to our next step in the process.

Moles Calculation

The next critical step in determining the empirical formula is converting mass into moles. Moles are a chemical unit that measures the amount of a substance. This conversion is crucial because it transitions the percentage data into a numerical form that is easier to work with.

To convert grams to moles, you use the atomic mass of each element, which acts like a conversion factor:

• For fluorine (F), with an atomic mass of 19.00 g/mol, you divide the mass of fluorine (24.25 g) by its atomic mass.
• For tin (Sn), with an atomic mass of 118.71 g/mol, you use the same process.

This gives the following calculations:
\[\text{Moles of F} = \frac{24.25 \text{ g}}{19.00 \text{ g/mol}} \approx 1.276 \text{ mol}\]
\[\text{Moles of Sn} = \frac{75.75 \text{ g}}{118.71 \text{ g/mol}} \approx 0.638 \text{ mol}\]
Calculating moles translates the mass into a more precise measure of quantity, preparing it for comparison and for finding the smallest integer ratio needed for the empirical formula. This step bridges the gap between the raw mass data and the chemical formula we aim to construct.

Chemical Formula Determination

Once the moles are calculated, the final step is to determine the empirical formula by finding the simplest whole number ratio of moles of each element. This ratio gives the basic proportional relationship of elements in the compound.

To get this ratio, divide each computed moles value by the smallest number of moles from the elements calculated:

• For fluorine, it is calculated as: \[\frac{1.276}{0.638} \approx 2\].
• For tin, it is exactly: \[\frac{0.638}{0.638} = 1\].

This simplifies the number of moles of fluorine to twice as many as tin, providing the smallest whole number ratio required.

Applying this ratio, we write the empirical formula as \(\mathrm{SnF}_2\), revealing the component count of each atom in the simplest form. Understanding these basic ratios allows scientists to understand not just what elements a compound comprises, but also how these elements interact to form the stable compound.

In summary, determining the empirical formula involves converting percent composition to moles, finding the simplest mole ratio, and translating that into a formula that reveals the elemental makeup. This is vital for comprehending molecular structure and behavior.