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Chapter 3: Problem 63

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

Expert verified
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

01

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: \(1 × 12.01 ~g/mol + 2 × 35.45 ~g/mol + 2 × 19.00 ~g/mol = 120.91 ~g/mol\)
02

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: \(moles = \frac{0.00556 ~g}{120.91~g/mol} = 4.60 × 10^{-5} ~mol\)
03

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: \(Number~of~molecules = moles × Avogadro's~constant\) \(Number~of~molecules = 4.60 × 10^{-5}~mol × 6.022 × 10^{23} ~mol^{-1} = 2.77 × 10^{19} ~molecules\)
04

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.

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