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 \(5.56 \mathrm{mg}\) of Freon-12. What is the mass of chlorine in \(5.56 \mathrm{mg}\) of Freon- \(12 ?\)

Short answer

There are \(2.77 × 10^{19}\) molecules of Freon-12 in 5.56 mg of Freon-12, and the mass of chlorine in 5.56 mg of Freon-12 is 3.25 mg.

Step-by-step solution

1. Find the molar mass of Freon-12 (CCl2F2)

To find the molar mass, we will add up the atomic masses of its constituent atoms: one carbon (C), two chlorine (Cl) and two fluorine (F) atoms. \(Molar ~mass~ of ~Freon=-12 = 1 × C + 2 × Cl + 2 × F\) Using the atomic masses for C, Cl, and F: \(1 × 12.01 ~g/mol + 2 × 35.45 ~g/mol + 2 × 19.00 ~g/mol = 120.91 ~g/mol\)

2. Calculate the moles of Freon-12

To calculate the number of moles, we will use the equation: \(moles = \frac{mass}{molar~mass}\) Here we are given the mass of Freon-12 as 5.56 mg, so first convert it into g: \(5.56 ~mg = 0.00556 ~g\) Now calculating the moles: \(moles = \frac{0.00556 ~g}{120.91~g/mol} = 4.60 × 10^{-5} ~mol\)

3. Calculate the number of molecules

To calculate the number of molecules in the given mass of Freon-12, we use Avogadro's constant (6.022 x 10^23 mol^-1) and multiply it by the amount of moles we just calculated: \(Number~of~molecules = moles × Avogadro's~constant\) \(Number~of~molecules = 4.60 × 10^{-5}~mol × 6.022 × 10^{23} ~mol^{-1} = 2.77 × 10^{19} ~molecules\)

4. Calculate the mass of chlorine in the given mass of Freon-12

To calculate the mass of chlorine, we first need to determine the mass fraction of chlorine in one molecule of Freon-12: \(Mass~fraction~ of~ chlorine = \frac{Mass~of~chlorine}{Molar~mass~of~Freon-12}\) \(Mass~fraction~ of~ chlorine = \frac{2 × 35.45 ~g/mol}{120.91 ~g/mol} = 0.585\) Now that we have the mass fraction of chlorine, we multiply it by the given mass of Freon-12 (5.56 mg) to find the mass of chlorine: \(Mass~of~chlorine = 0.00556 ~g × 0.585 = 0.00325 ~g = 3.25 ~mg\) So, there are \(2.77 × 10^{19}\) molecules of Freon-12 in 5.56 mg of Freon-12, and the mass of chlorine in 5.56 mg of Freon-12 is 3.25 mg.

Key concepts

Molar Mass

To find the molar mass of a chemical compound, you need to add up the atomic masses of all the atoms present in the compound. Molar mass is expressed in grams per mole (g/mol). For example, to determine the molar mass of Freon-12 (CCl2F2), you sum the atomic masses of its components: one carbon (C), two chlorine (Cl), and two fluorine (F) atoms.

Here's how it's done:

• The atomic mass of carbon (C) is approximately 12.01 g/mol.
• Each chlorine (Cl) atom has an atomic mass of about 35.45 g/mol.
• Each fluorine (F) atom has an atomic mass of about 19.00 g/mol.

Adding these together gives:\[ 1 \times 12.01 \, \text{g/mol} + 2 \times 35.45 \, \text{g/mol} + 2 \times 19.00 \, \text{g/mol} = 120.91 \, \text{g/mol} \]

Understanding molar mass is essential in calculating how much of each substance is used or produced in a chemical reaction, as it serves as a bridge from the microscopic world of molecules to the macroscopic world of grams.

Avogadro's Constant

Avogadro's constant, also known as Avogadro's number, is a key figure in chemistry that connects the macroscopic and microscopic realms. It defines the number of constituent particles (usually atoms, ions, or molecules) in one mole of a substance, and it's approximately \(6.022 \times 10^{23}\, \text{mol}^{-1}\).

Why is this constant important? Because it allows chemists to express quantities of substances in a convenient form. Instead of dealing with extraordinarily large numbers of individual molecules or atoms, you can deal in moles, making stoichiometry calculations more manageable.

For example, if you know the number of moles of a substance you have, you can easily determine the number of molecules using Avogadro’s constant. In the case of Freon-12, with \(4.60 \times 10^{-5}\) moles, the calculation is:\[\text{Number}\, \text{of}\, \text{molecules} = 4.60 \times 10^{-5} \, \text{mol} \times 6.022 \times 10^{23} \, \text{mol}^{-1} \approx 2.77 \times 10^{19} \, \text{molecules}\]

Understanding Avogadro's constant is fundamental for converting between moles and molecules, helping to quantify the microscopic world of chemistry.

Mass Fraction

Mass fraction in chemistry is a way to express the mass of a component of a compound relative to the total mass of that compound. It's often used as a percentage or fraction. The mass fraction can be useful when determining how much of a particular element is present in a given amount of a compound.

To calculate the mass fraction of chlorine in Freon-12, you start by finding the total mass of chlorine in the compound, which means multiplying the atomic mass of chlorine by the number of chlorine atoms in a molecule of Freon-12.

• The mass of chlorine is \(2 \times 35.45 \, \text{g/mol}\).
• The molar mass of Freon-12 is \(120.91 \, \text{g/mol}\).

Thus, the mass fraction of chlorine is:\[ \text{Mass}\, \text{fraction}\, \text{of}\, \text{chlorine} = \frac{2 \times 35.45 \, \text{g/mol}}{120.91 \, \text{g/mol}} \approx 0.585\]

This means that chlorine makes up about 58.5% of the mass of Freon-12. This concept helps when you need to figure out how much of an element is present without analyzing every single molecule.

Moles Calculation

Calculating the number of moles involves understanding the relationship between mass and molar mass. The formula used is: \[ \text{moles} = \frac{\text{mass in grams}}{\text{molar mass} \, (\text{g/mol})} \]

In the exercise, we converted 5.56 mg of Freon-12 into grams by using the relation \(1 \, \text{mg} = 0.001 \, \text{g}\). Therefore, \(5.56 \, \text{mg}\) is \(0.00556 \, \text{g}\). Using the molar mass of Freon-12 (120.91 g/mol): \[ \text{moles of Freon-12} = \frac{0.00556 \, \text{g}}{120.91 \, \text{g/mol}} \approx 4.60 \times 10^{-5} \, \text{mol} \]

These calculations are essential for reactions and converting between grams and moles, which can then be used for further chemical calculations such as finding the number of molecules using Avogadro's constant or the mass fraction of components.