Question

A Freon" leak in the air conditioning system of an old car releases 25 g of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) per month. What mass of chlorine does this car emit into the atmosphere each year?

Short answer

The vehicle emits 219 g of chlorine into the atmosphere each year.

Step-by-step solution

Identify the molecular composition of Freon

Analyze the chemical formula for Freon, cF_{2}Cl_{2}, to determine the proportion of chlorine in the compound. Each molecule contains two chlorine atoms.

Calculate the mass of chlorine in the monthly Freon leak

Calculate the mass of chlorine in 25 g of cF_{2}Cl_{2} by using its molar mass (120.91 g/mol for cF_{2}Cl_{2}, 35.45 g/mol for Cl) and the fact that there are two moles of Cl for every mole of cF_{2}Cl_{2}. This gives the following equation: Mass of Cl in 25 g of cF_{2}Cl_{2} = (25 g * 2 * 35.45 g/mol Cl) / (120.91 g/mol cF_{2}Cl_{2}).

Convert the monthly emission to annual emission

Multiply the monthly mass of Cl by 12 to find the annual emission: Annual mass of Cl = Monthly mass of Cl * 12.

Key concepts

Chemical Composition Analysis of Freon

To understand the environmental impact of Freon, a refrigerant commonly used in air conditioning systems, it is essential to start by analyzing its chemical composition. Freon is a trade name for a group of chlorofluorocarbons (CFCs), where a widely used member is dichlorodifluoromethane, with the chemical formula \(\mathrm{CF}_2\mathrm{Cl}_2\). When investigating the composition of Freon molecules, we find that each molecule contains two atoms of chlorine. This detail is crucial as chlorine, when released into the atmosphere, plays a major role in ozone depletion.

Freon's overall impact on the environment can be attributed to the presence of these chlorine atoms. When Freon leaks, the chlorine liberated contributes directly to the degradation of the ozone layer, leading to increased UV radiation reaching the Earth's surface, which can cause health issues and affect ecosystems. By understanding its chemical structure, we can better assess and quantify the emissions and their effects.

Molar Mass Calculation for Chlorine Emissions

Molar mass is a concept used to calculate how many grams are in one mole of a substance, which in turn allows us to convert between mass and number of particles. Given our focus on the environmental impact of Freon leaks, we specifically need to calculate the molar mass of both \(\mathrm{CF}_2\mathrm{Cl}_2\) and elemental chlorine (Cl). The molar mass of \(\mathrm{CF}_2\mathrm{Cl}_2\) is 120.91 g/mol, while the molar mass of Cl, based on one chlorine atom, is 35.45 g/mol. Since there are two chlorine atoms in each \(\mathrm{CF}_2\mathrm{Cl}_2\) molecule, the total mass of chlorine that can be derived from one mole of \(\mathrm{CF}_2\mathrm{Cl}_2\) would actually be 70.9 g/mol (2 * 35.45 g/mol).

Using molar mass, we can calculate the mass of chlorine released in a Freon leak. For instance, from 25 g of Freon, we can determine the proportion of chlorine, leading to an understanding of the quantity of potentially ozone-depleting substances being emitted.

Chlorine Emissions Estimation

To estimate chlorine emissions from a Freon leak, we use both the chemical composition and the molar mass to find the mass of chlorine in the emitted Freon and then extrapolate it over a period of time. Taking the example given in our exercise, a leak releases 25 g of \(\mathrm{CF}_2\mathrm{Cl}_2\) per month. Using the molar masses provided, we derive that for every mole of \(\mathrm{CF}_2\mathrm{Cl}_2\), there are two moles of Cl, which corresponds to 70.9 g of Cl. Therefore, the calculation will give us the monthly mass of chlorine, which we then multiply by 12 to project the annual emission figure.

Estimating these emissions is a crucial step in understanding the scale of the impact on the ozone layer. Regulators, scientists, and policy-makers use such data to assess environmental health and make informed decisions to regulate substances like Freon and mitigate the potential damage to the atmosphere.