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

We must first calculate the molecular weight of Freon-12 by adding the atomic weights of each element present in its molecule. The atomic weights are: C = 12.01 g/mol, Cl = 35.45 g/mol, and F = 19.00 g/mol. The molecular formula of Freon-12 is CCl₂F₂, which means we have: Molecular weight of Freon-12 = 1 * C + 2 * Cl + 2 * F \(= 12.01 + 2(35.45) + 2(19.00)\) \(= 12.01 + 70.90 + 38.00\) \(= 120.91 \, \text{g/mol}\)

We need to convert the mass of Freon-12 given in mg (5.56 mg) to g for easier calculation. Mass of Freon-12 = 5.56 mg \(= \dfrac{5.56}{1000} \, \text{g}\) \(= 0.00556 \, \text{g}\)

Now that we have the molecular weight and the mass in grams, we can calculate the number of moles of Freon-12. We can use the following formula: Number of moles = \( \dfrac{\text{Mass of Substance (g)}}{\text{Molecular Weight (g/mol)}}\) Number of moles = \( \dfrac{0.00556}{120.91}\) Number of moles ≈ \(4.6 \times 10^{-5} \, \text{moles}\)

Now that we have the number of moles, we can calculate the number of molecules using Avogadro's number: \(6.022 \times 10^{23} \, \text{molecules/mol}\). Number of molecules = Number of moles × Avogadro's number Number of molecules = \((4.6 \times 10^{-5}) (6.022 \times 10^{23})\) Number of molecules ≈ \(2.77 \times 10^{19} \, \text{molecules}\)

To calculate the mass of chlorine in Freon-12, we need to find the mass percentage of chlorine in the molecule. Mass percentage of Cl in Freon-12 = \( \dfrac{\text{Total mass of Cl in the molecule}}{\text{Molecular weight of Freon-12}} \times 100\) Mass percentage of Cl in Freon-12 = \( \dfrac{2 \times 35.45}{120.91} \times 100\) Mass percentage of Cl in Freon-12 ≈ 58.51 % Now we can find the mass of chlorine in 5.56 mg of Freon-12 by multiplying the mass of Freon-12 with the mass percentage of chlorine. Mass of chlorine = (Mass of Freon-12) × (Mass percentage of Cl / 100) Mass of chlorine = \(0.00556 \times \dfrac{58.51}{100}\) Mass of chlorine ≈ 0.00315 g or 3.25 mg So, in 5.56 mg of Freon-12, there are approximately \(2.77 \times 10^{19}\) molecules of Freon-12, and the mass of chlorine is approximately 3.25 mg.