Problem 42 - Chemistry

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?

Step-by-Step Solution

Answer

The mass of F in \(24.6 \mathrm{~g}\) of \(\mathrm{SnF}_{2}\) is given by \(24.6 \mathrm{~g}\) times the ratio of the molar mass of F to the molar mass of the compound.

Step 1: Determination of Molar Mass

First, the molar mass of the entire compound, \(\mathrm{SnF}_{2}\), must be determined.\nThe molar mass of Sn (Tin) is \(\approx118.71\) g/mol, and the molar mass of F (Fluorine) is \(\approx18.998\) g/mol. Since there are two F atoms in the compound, the total molar mass is \(118.71 + 2 * 18.998 = 156.706\) g/mol.

Step 2: Ratio Calculation

The next step involves calculating the ratio of each element's molar mass to the total molar mass of the compound. For fluorine,\n\[ \frac {2 * 18.998} {156.706} \]

Step 3: Mass of F in the compound

Then apply this ratio to the given mass of the compound to find the mass of F in \(24.6 \mathrm{~g}\) of the compound. Multiply \(24.6 \mathrm{~g}\) by the ratio calculated above to get the mass of F.

Key Concepts

molar mass

When dealing with stoichiometry and chemical reactions, understanding the concept of molar mass is crucial. It is the mass of one mole of a substance and is expressed in grams per mole (g/mol). The molar mass is calculated by adding the atomic masses of all atoms present in a compound. For instance, let's consider the molar mass of Tin(II) fluoride \(SnF_2\). Tin has an atomic mass of approximately 118.71 g/mol. Meanwhile, Fluorine has an atomic mass of around 18.998 g/mol. Since there are two fluorine atoms in the compound, the molar mass of \(SnF_2\) is computed as follows: \[\text{Molar Mass of } SnF_2 = 118.71 + 2 \times 18.998 = 156.706 \text{ g/mol}.\] Understanding molar mass helps us transition from the microscopic world of atoms to the macroscopic world we observe. It serves as a bridge allowing chemists to count particles by weighing them. If ever in doubt when calculating, remember to reference the periodic table for the most accurate atomic masses!

chemical compounds

A chemical compound consists of two or more different elements that are chemically bonded together. These compounds have unique properties different from the individual elements that compose them. In our example, Tin(II) fluoride \(SnF_2\) is a compound formed by bonding tin (Sn) with fluorine (F).
A few key points about chemical compounds:

• Compounds can possess ionic or covalent bonds. Tin(II) fluoride is ionic since it consists of metal and non-metal.
• The formula \(SnF_2\) tells us there's one tin atom and two fluorine atoms.
• Properties such as boiling point, hardness, and solubility arise from these chemical bonds.

Understanding how elements interact within compounds is fundamental in chemistry. From the taste of your toothpaste to the life-saving reactions in pharmaceuticals, compounds shape much of the world around us.
Recognizing forms and bond types also aids in predicting reactivity and stability. Observing how compounds like \(SnF_2\) function in practical applications, such as preventing tooth decay, highlights their importance.

mass calculation

Mass calculation in chemistry involves determining how much of a particular element is present in a chemical compound. This is crucial for stoichiometry, allowing chemists to measure accurate amounts of reactants and products in a reaction. To calculate the mass of an element within a compound, follow these steps:
For example, let's calculate the mass of fluorine in 24.6 g of Tin(II) fluoride (\(SnF_2\)):

• First, determine the ratio of the total molar mass of the element to the total molar mass of the compound. For fluorine, this ratio is \[\frac {2 \times 18.998}{156.706}\].
• Next, apply this ratio to the given mass of the compound to compute the mass of fluorine. This process can be expressed as: \[\text{Mass of F} = 24.6 \times \frac {2 \times 18.998}{156.706}.\]
• The calculation will provide the mass of fluorine in the given 24.6 g of \(SnF_2\).

Mass calculations are invaluable in experiments and industrial processes as they ensure precision and manage resources efficiently. Exploring these calculations with real-world examples helps demystify chemical principles, making chemistry more accessible to learners.