Question

Tin(II) fluoride \(\left(\mathrm{SnF}_{2}\right)\) is often added to toothpaste as an ingredient to prevent tooth decay. What is the mass of \(\mathrm{F}\) in grams in \(24.6 \mathrm{~g}\) of the compound?

Short answer

The mass of Fluorine in 24.6 grams of SnF2 is approximately 5.96 grams.

Step-by-step solution

Understand the problem

We are given a total mass of 24.6 g for the compound \( \text{SnF}_2 \) and need to find the mass of the element Fluorine (F) present in this compound.

Find the Molar Mass of \( \text{SnF}_2 \)

Calculate the molar mass of \( \text{SnF}_2 \) using the periodic table. Tin (Sn) has an atomic mass of approximately 118.71 g/mol and Fluorine (F) 19.00 g/mol. The formula \( \text{SnF}_2 \) has one Sn and two F atoms:\[\text{Molar mass of SnF}_2 = (1 \times 118.71) + (2 \times 19.00) = 156.71 \text{ g/mol}\]

Determine the Mass Fraction of Fluorine

Calculate the mass of Fluorine in one mole of \( \text{SnF}_2 \), then find the mass fraction. With 2 Fluorine atoms:\[\text{Mass of F in SnF}_2 = 2 \times 19.00 = 38.00 \text{ g}\]The mass fraction of Fluorine is:\[\text{Mass fraction of F} = \frac{38.00}{156.71}\]

Calculate Mass of F in Given Sample

Use the mass fraction to find the mass of Fluorine in 24.6 g of \( \text{SnF}_2 \):\[\text{Mass of F} = \text{Total mass} \times \text{Mass fraction of F} = 24.6 \times \left(\frac{38.00}{156.71}\right)\]

Solve the Calculation

Perform the arithmetic:\[\text{Mass of F} = 24.6 \times 0.2426 \approx 5.96 \text{ g}\]

Key concepts

Molar Mass

Understanding molar mass is essential for solving chemistry problems that involve calculations with substances. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
It's computed by adding up the atomic masses of all the atoms in a given formula, which are readily found in the periodic table.
For example, in tin(II) fluoride, or \( \text{SnF}_2 \), the molar mass is determined as follows:

• Tin (\( \text{Sn} \)) has an atomic mass of about 118.71 g/mol.
• Fluorine (\( \text{F} \)) has an atomic mass of about 19.00 g/mol.
• The formula \( \text{SnF}_2 \) includes one Sn atom and two F atoms.

Calculating, we find:\[\text{Molar mass of SnF}_2 = (1 \times 118.71) + (2 \times 19.00) = 156.71 \text{ g/mol}.\] This value tells us how much one mole of tin(II) fluoride weighs.

Stoichiometry

Stoichiometry is the area of chemistry that involves the relative quantities of reactants and products in chemical reactions. It connects deeply with molar mass by allowing us to transition between amounts of chemicals in moles and their masses in grams.
In exercises like the one tackled here, stoichiometry helps deduce how much of a specific component, like fluorine in \( \text{SnF}_2 \), is present in any given mass of the whole compound.
This process involves setting up a ratio based on the molar masses and then using proportions to find unknown quantities. Using stoichiometry ensures that we're accounting for every part of the molecules in reactions, whether they are reactants or products.

Mass Fraction

The mass fraction is a way to determine the ratio of the mass of a part to the total mass of a compound. It is highly useful when assessing how much of a specific component is in a compound.
Calculating the mass fraction of an element involves dividing the total mass of that element in one mole of the compound by the total molar mass of the compound itself.
In our example, to find the mass of fluorine in \( \text{SnF}_2 \):

• The total mass of fluorine in one mole of \( \text{SnF}_2 \) is 38.00 g.
• The molar mass of \( \text{SnF}_2 \) is 156.71 g/mol, as calculated earlier.

The mass fraction of fluorine is then:\[\text{Mass fraction of F} = \frac{38.00}{156.71} \approx 0.2426\]
This value means that 24.26% of \( \text{SnF}_2 \)'s mass is from fluorine.

Tin(II) fluoride

Tin(II) fluoride, sometimes referred to as stannous fluoride, is commonly known for its use in dental care products, particularly toothpaste.
Its chemical formula \( \text{SnF}_2 \) consists of one tin atom and two fluorine atoms.

• The element tin in this compound contributes to the structural stability of the molecule.
• Fluoride, derived from fluorine, plays a significant role in preventing tooth decay.

In mass calculations, understanding the composition of \( \text{SnF}_2 \) allows us to ascertain how much fluoride, an essential component for oral hygiene, is present in any given sample of the compound. When performing calculations like finding the mass of fluorine, these details about the compound help bridge its chemical properties with practical applications.