Question

A Freon Th leak in the air conditioning system of a large building re- leases 12 \(\mathrm{kg}\) of \(\mathrm{CHF}_{2} \mathrm{Cl}\) per month. If the leak is allowed to continue, how many kilograms of Cl are emitted into the atmosphere each year?

Short answer

59.04 kg of chlorine are emitted into the atmosphere each year if the leak continues.

Step-by-step solution

Calculate the monthly emission of Cl

Since Freon Th has a molecular formula of \(\mathrm{CHF}_{2}\mathrm{Cl}\), it contains one chlorine atom per molecule. The molar mass of \(\mathrm{CHF}_{2}\mathrm{Cl}\) is approximately 86.47 g/mol, with the atomic mass of chlorine being about 35.45 g/mol. Calculate the fraction of chlorine in the compound by dividing the atomic mass of Cl by the molar mass of the compound: \(\frac{35.45 \mathrm{g/mol}}{86.47 \mathrm{g/mol}} = 0.410\).

Convert the mass of Cl from g to kg per month

To find out how much chlorine is in 12 kg of \(\mathrm{CHF}_{2}\mathrm{Cl}\), you multiply the mass of the leaked Freon by the fraction of chlorine within it: \((12 \mathrm{kg}) \cdot 0.410 = 4.92 \mathrm{kg}\) of Cl are emitted per month.

Calculate the yearly emission of Cl

To find out the annual emissions, multiply the monthly emissions of Cl by the number of months in a year: \((4.92 \mathrm{kg/month}) \times 12 \mathrm{months/year} = 59.04 \mathrm{kg/year}\).

Key concepts

Molar Mass Calculation

Understanding molar mass calculation is essential for chemists and students alike. Molar mass, often expressed in grams per mole (g/mol), is the weight of one mole of a given substance. A mole is a standard unit in chemistry and represents Avogadro's number (\(6.022 \times 10^{23}\) atoms, molecules, or particles). The molar mass of a substance is determined by summing the atomic masses of all the atoms in a single molecule of that substance. For example, to calculate the molar mass of water (H_{2}O\text), one would multiply the number of hydrogen atoms by their atomic mass and add that to the atomic mass of oxygen.

Calculation of the molar mass serves as a bridge between the mass of a substance and the amount of substance in moles. This conversion is crucial when determining the proportions of reactants and products in chemical reactions, often referred to as stoichiometry. In the given exercise, the molar mass of CHF_{2}Cl (Freon Th) is about 86.47 g/mol. This figure is key to finding out how Chlorine (Cl), as part of the compound, contributes to the total weight, which is fundamental for solving the Freon Th leak problem.

Chemical Compound Composition

Chemical compound composition refers to the elements that comprise a compound and the proportion in which these elements combine. By knowing the composition, one can determine the percentage of each element within a compound. In practical terms, if you imagine a molecule as a recipe, the composition tells you what ingredients you need and in what amounts.

The fractional composition, as seen in the solution provided, represents the portion of the total mass of the compound that is made up of a specific element. This is found by dividing the atomic mass of the element by the molar mass of the entire compound. Having calculated this fraction for chlorine in CHF_{2}Cl, it is clear that chlorine accounts for approximately 41% of the compound’s total mass. This calculation is crucial when assessing the impact of a chemical leak, like the one from our example, as it helps to understand how much of each element is being emitted into the environment.

Stoichiometric Conversions

The concept of stoichiometric conversions is the heart of quantitative relationships in chemical reactions. Stoichiometry helps us to predict the amounts of substances consumed and produced in a reaction. To perform these conversions, one must understand the mole ratio of reactants to products found in the balanced chemical equation and be able to use molar masses to convert between mass and moles.

After determining the proportion of chlorine in CHF_{2}Cl, the next step naturally follows into stoichiometric conversions. In our example, this involves converting the total mass of a compound to the mass of a specific element it contains, and then scaling it up to understand a bigger picture – such as the yearly impact of a chemical leak. By applying stoichiometry, it was possible to convert the known mass of Freon Th leaked each month into the mass of chlorine it contained, and then into an annual figure. It tells us that the seemingly abstract numbers associated with chemical properties have real-world implications, especially in terms of environmental pollution in the given scenario.