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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?

Short Answer

Expert verified
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.

Step by step solution

01

Calculate the molecular weight of Freon-12 (CClâ‚‚Fâ‚‚)

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 CClâ‚‚Fâ‚‚, which means we have: Molecular weight of Freon-12 = 1 * C + 2 * Cl + 2 * F \(= 12.01 + 2(35.45) + 2(19.00)\) \(= 12.01 + 70.90 + 38.00\) \(= 120.91 \, \text{g/mol}\)
02

Convert mass of Freon-12 from mg to g

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 \(= \dfrac{5.56}{1000} \, \text{g}\) \(= 0.00556 \, \text{g}\)
03

Calculate the number of moles of Freon-12

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 ≈ \(4.6 \times 10^{-5} \, \text{moles}\)
04

Calculate the number of molecules of Freon-12

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 ≈ \(2.77 \times 10^{19} \, \text{molecules}\)
05

Calculate the mass of chlorine in Freon-12

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Avogadro's Number
Avogadro's number is a fundamental constant used in chemistry to calculate the number of entities, usually atoms or molecules, present in one mole of a substance. The value is approximately \(6.022 \times 10^{23}\) entities per mole. This profound number allows chemists to bridge the gap between the atomic scale and the macroscopic scale we observe. In our case of Freon-12, once we know the number of moles, we can easily determine the number of molecules by multiplying the number of moles by Avogadro's number. This conversion is essential for chemical calculations and offers insights into the massive quantity of molecules present even in seemingly small amounts of a substance. By using Avogadro's number as part of our calculations, we can determine that in 5.56 mg of Freon-12, there are approximately \(2.77 \times 10^{19}\) molecules.
Mass Percentage
Mass percentage is a way of describing the composition of a compound by dividing the mass of a particular element by the total molecular mass, then multiplying by 100 to get a percentage. This is very useful for understanding how much of a specific element, like chlorine in Freon-12, is present in a compound. To find the mass percentage of chlorine in Freon-12, we calculate the total mass of the chlorine atoms in the molecule and divide it by the molecular weight of Freon-12. In our case, Freon-12 has a mass percentage of chlorine of approximately 58.51%. This essentially means that 58.51% of the mass of Freon-12 is due to chlorine atoms. Knowing the mass percentage allows us to easily calculate the actual mass of chlorine in any given amount of Freon-12, such as the 5.56 mg discussed earlier, resulting in roughly 3.25 mg of chlorine.
Moles Calculation
Calculating the number of moles is a fundamental skill in chemistry that involves dividing the mass of a substance by its molecular weight. This is essential for linking the mass of a sample to the number of molecules or atoms contained within. In the context of Freon-12, after converting the mass from milligrams to grams, we divide by the molecular weight of 120.91 g/mol.The process results in a number of moles for the given mass, providing insight into the amount of substance in a measurable way. For the 5.56 mg of Freon-12, we calculated approximately \(4.6 \times 10^{-5}\) moles. Establishing the number of moles acts as a crucial step for further calculations, such as determining the total number of molecules using Avogadro's number.
Freon-12 Properties
Freon-12, chemically known as dichlorodifluoromethane and represented by the formula \(\text{CCl}_2\text{F}_2\), has been widely used as a refrigerant and as a propellant in aerosol cans. The compound consists of one carbon atom, two chlorine atoms, and two fluorine atoms. Each of these atoms contributes to the molecular weight and properties of Freon-12. The presence of chlorine contributes to the cooling properties and stability of the compound. Freon-12 was a popular choice in refrigeration because of its non-flammable and relatively non-toxic nature. However, Freon-12 is also known for its environmental impact, particularly its role in ozone layer depletion, leading to its phasedown under international regulations like the Montreal Protocol. Understanding the basic properties and structure of Freon-12 is essential for both its practical applications and environmental considerations. Its use and phase-out demonstrate the intersection of chemistry, industrial application, and environmental science.

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Most popular questions from this chapter

When the supply of oxygen is limited, iron metal reacts with oxygen to produce a mixture of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) In a certain experiment, 20.00 \(\mathrm{g}\) iron metal was reacted with 11.20 \(\mathrm{g}\) oxygen gas. After the experiment, the iron was totally consumed, and 3.24 \(\mathrm{g}\) oxygen gas remained. Calculate the amounts of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed in this experiment.

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The aspirin substitute, acetaminophen \(\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}\right),\) is produced by the following three-step synthesis: $$ \mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q) $$ $$ \mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow $$ $$ \mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) $$ The first two reactions have percent yields of 87\(\%\) and 98\(\%\) by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}\) reacted. a. What is the percent yield by mass for the overall process? b. What is the percent yield by mass of Step III?

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