Question

Freon-12 \(\left(\mathrm{CCl}_{2} \mathrm{F}_{2}\right)\) is used as a refrigerant in air conditioners and as a propellant in aerosol cans. Calculate the number of molecules of Freon-12 in 5.56 mg of Freon-12. What is the mass of chlorine in 5.56 mg of Freon-12?

Short answer

In 5.56 mg of Freon-12, there are \(2.77 \times 10^{19}\) molecules, and the mass of chlorine present in this sample is 3.26 mg.

Step-by-step solution

Calculate the Molecular Weight of Freon-12

To determine the molecular weight of Freon-12, we need to know the atomic weights of each element involved. The atomic weights are as follows: - Carbon (C): 12.01 g/mol - Chlorine (Cl): 35.45 g/mol - Fluorine (F): 19.00 g/mol Using the molecular formula \(\mathrm{CCl}_{2} \mathrm{F}_{2}\), we can calculate the molecular weight of Freon-12: \(\text{Molecular weight }= (1 \times 12.01) + (2 \times 35.45) + (2 \times 19.00) = 120.91 \text{ g/mol} \)

Convert Milligrams to Grams

We're given the mass of Freon-12 in milligrams, but to calculate moles, we need to convert this amount into grams. 5.56 mg = 0.00556 g

Calculate the Number of Moles

To find the number of moles of a substance, we can use the formula: \(\text{Number of Moles} = \frac{\text{Mass}}{\text{Molecular weight}} \) Using the mass (0.00556 g) and the molecular weight (120.91 g/mol) calculated earlier, we find: \(\text{Number of Moles} = \frac{0.00556 \text{ g}}{120.91 \text{ g/mol}} = 4.6 \times 10^{-5} \text{ mol}\)

Calculate the Number of Molecules

To find the number of molecules, we use Avogadro's Number (approximately \(6.022 \times 10^{23}\) molecules/mol) and multiply it by the number of moles calculated earlier. \(\text{Number of molecules} = (4.6 \times 10^{-5} \text{ mol}) \times (6.022 \times 10^{23} \text{ molecules/mol}) = 2.77 \times 10^{19} \text{ molecules}\)

Calculate the Mass of Chlorine

To calculate the mass of chlorine in the given mass of Freon-12, we need to first determine the fractional mass of chlorine in the molecule. There are 2 chlorine atoms in each molecule, so the total mass of chlorine in one molecule of Freon-12 is: \(2 \times 35.45 \text{ g/mol} = 70.90 \text{ g/mol}\) Now, we can determine the fractional mass of chlorine in the molecule: \(\frac{70.90 \text{ g/mol}}{120.91 \text{ g/mol}} = 0.586\) Next, multiply the fractional mass of chlorine by the mass of the Freon-12 given: \(0.586 \times 0.00556 \text{ g} = 0.00326 \text{ g}\) Finally, convert the mass to milligrams: \(0.00326 \text{ g} = 3.26 \text{ mg}\) So, in 5.56 mg of Freon-12, there are 2.77 x 10^19 molecules, and the mass of chlorine present in this sample is 3.26 mg.

Key concepts

Avogadro's Number

Avogadro's Number is a fundamental concept in chemistry that helps us understand the relationship between moles and individual particles, like atoms or molecules. It is denoted as \(6.022 \times 10^{23}\) and represents the number of atoms, molecules, or particles in one mole of a substance. This colossal number indicates how tiny individual molecules are, making it easier for chemists to discuss things at a standardized scale. It was named after Amedeo Avogadro, who first proposed the idea that equal volumes of gases (at the same temperature and pressure) contain the same number of particles.

When working with microscopic particles, Avogadro's Number allows chemists to translate microscopic scales to usable macroscopic scales. In practice, when you know the number of moles of a substance, you can multiply it by Avogadro's Number to find the total number of molecules, as shown in the exercise. Using the given example, multiplying \(4.6 \times 10^{-5}\) moles of Freon-12 by \(6.022 \times 10^{23}\) molecules per mole gives \(2.77 \times 10^{19}\) molecules of Freon-12.

Molecular Weight

Molecular weight, also known as molecular mass or molar mass, is the sum of the atomic weights of all atoms in a molecule. It is expressed in grams per mole (g/mol) and is essential for converting between mass and moles. By understanding the molecular weight of a compound, you can determine how much a certain quantity weighs and vice versa. This calculation involves adding the atomic weights of each atom present in the formula.

In the Freon-12 example, its molecular formula is \(\text{CCl}_2\text{F}_2\). By using the atomic weights of carbon (12.01 g/mol), chlorine (35.45 g/mol), and fluorine (19.00 g/mol), we calculate the molecular weight: \[ (1 \times 12.01) + (2 \times 35.45) + (2 \times 19.00) = 120.91 \text{ g/mol} \].

Knowing this, you can easily describe a smaller sample's mass in a more manageable unit by converting it into moles.

Mass Conversion

Mass conversion is the process of changing one mass unit to another, making it possible to work with quantities more effectively. In chemistry, you may need to convert between milligrams, grams, and even kilograms to make calculations consistent with molar quantities.

For instance, the problem began with knowing the mass of Freon-12 in milligrams (5.56 mg) but needed the mass in grams for further calculations. Changing milligrams to grams requires dividing by 1000 (since 1 gram = 1000 milligrams), giving \(0.00556\) g. This conversion helped translate the given mass into a useable form for calculating moles of Freon-12 in the subsequent steps.

Proper conversion makes calculations more manageable and ensures compatibility with data expressed in different units. It is a crucial skill in scientific calculations that require high precision and accuracy.

Stoichiometry

Stoichiometry deals with the quantitative relationships in chemical reactions and the conversion between reactants and products. It involves using balanced chemical equations along with the mole concept to deduce the amounts needed or produced in a chemical process.

The exercise utilized stoichiometric principles to determine the mass of chlorine from the amount of Freon-12 provided. By knowing the molecular weight and calculating the fraction of chlorine in the compound, you could find the corresponding mass. The detailed steps are: calculating the mass of chlorine atoms in one mole of Freon-12 and determining their fraction. This fraction (0.586) was used to find the mass of chlorine present in 0.00556 g of Freon-12: \[ 0.586 \times 0.00556 \text{ g} = 0.00326 \text{ g} \]. Finally, converting grams to milligrams showed that \(3.26\) mg of chlorine was present.

Stoichiometry is the backbone of quantitative chemistry, allowing precise prediction of reaction yields and reactant requirements.