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?

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: \(\text{Molecular weight }= (1 \times 12.01) + (2 \times 35.45) + (2 \times 19.00) = 120.91 \text{ g/mol} \)

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

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: \(\text{Number of Moles} = \frac{0.00556 \text{ g}}{120.91 \text{ g/mol}} = 4.6 \times 10^{-5} \text{ mol}\)

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. \(\text{Number of molecules} = (4.6 \times 10^{-5} \text{ mol}) \times (6.022 \times 10^{23} \text{ molecules/mol}) = 2.77 \times 10^{19} \text{ molecules}\)

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.