Question

Chlorine atoms cause chain reactions in the stratosphere that destroy ozone that protects the earth's surface from ultraviolet radiation. The chlorine atoms come from chlorofluorocarbons, compounds that contain carbon, fluorine, and chlorine, which were used for many years as refrigerants. One of these compounds is Freon-12, \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\). If a sample contains \(1.0 \times 10^{-9} \mathrm{~g}\) of \(\mathrm{Cl}\), how many grams of \(\mathrm{F}\) should be present if all of the \(\mathrm{F}\) and \(\mathrm{Cl}\) atoms in the sample came from \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) molecules?

Short answer

The mass of F in the sample will be equal to the mass of Cl, which is 1.0 x 10^-9 g.

Step-by-step solution

Determine the molar mass of Cl and F

Determine the atomic mass of Chlorine (Cl) and Fluorine (F) from the periodic table. The atomic mass of Cl is approximately 35.45 g/mol and the atomic mass of F is approximately 19.00 g/mol.

Calculate the moles of Cl in the given sample

Use the mass of Cl and its molar mass to calculate how many moles of Cl are in the sample. The formula to calculate moles is:\[\text{moles of Cl} = \frac{\text{mass of Cl in grams}}{\text{molar mass of Cl in g/mol}}\]

Determine the mole ratio of Cl to F in Freon-12

Analyze the chemical formula of Freon-12 (\(\mathrm{CF}_2\mathrm{Cl}_2\)) to establish the mole ratio of Cl to F. In one molecule of Freon-12, there are 2 atoms of F for every 2 atoms of Cl, which gives a 1:1 mole ratio between Cl and F.

Calculate the moles of F based on the moles of Cl

Since Cl and F are in a 1:1 mole ratio in Freon-12, the moles of F will be equal to the moles of Cl.\[\text{moles of F} = \text{moles of Cl}\]

Convert the moles of F to grams

Multiply the moles of F by the molar mass of F to find the mass of F in grams.\[\text{mass of F in grams} = \text{moles of F} \times \text{molar mass of F}\]

Key concepts

Mole Ratio

Understanding the mole ratio in chemical reactions is crucial for determining how substances react in fixed proportions. The mole ratio, derived from the coefficients of substances in a balanced chemical equation, guides us in figuring out the amount of reactants needed and the amount of products formed.

For example, consider Freon-12 with the chemical formula \(\mathrm{CF}_{2}\mathrm{Cl}_{2}\). Analyzing its composition, we notice that there are two fluorine (F) atoms and two chlorine (Cl) atoms in each molecule. This setup indicates a 1:1 mole ratio of Cl to F, meaning that for every mole of Cl we would expect one mole of F. This ratio is critical when trying to determine the quantity of one substance, given the amount of another, as seen in the step-by-step solution for Freon-12.

Molar Mass

Molar mass, defined as the mass of one mole of a substance, is expressed in grams per mole (g/mol). It is calculated by summing the individual atomic masses (from the periodic table) of all the atoms in a molecule.

Knowing the molar mass allows you to convert between grams and moles, a fundamental step in stoichiometry. In the provided solution, the molar mass of Cl is 35.45 g/mol and the molar mass of F is 19.00 g/mol. So if a reaction involves Cl and F, like in Freon-12, being able to calculate the moles from a given mass helps us predict how these elements would combine in a chemical reaction.

Chemical Formula

The chemical formula of a substance represents the types and number of atoms present in a molecule. In Freon-12, the chemical formula is \(\mathrm{CF}_{2}\mathrm{Cl}_{2}\), indicating two atoms of carbon (C), two atoms of fluorine (F), and two atoms of chlorine (Cl).

Understanding the chemical formula is essential for stoichiometric calculations because it shows the actual number of each kind of atom involved. Knowing this, chemists can determine the quantitative relationships between reactants and products in a chemical reaction.

Chlorofluorocarbons

Chlorofluorocarbons (CFCs), like Freon-12, are compounds containing carbon, chlorine, and fluorine. They were widely used due to their stability and low reactivity. But despite their practical applications, CFCs have a dark side. Released into the atmosphere, they travel to the stratosphere where they release chlorine atoms capable of destroying ozone — a phenomenon our problem statement refers to.

A single Cl atom can catalyze the breakdown of thousands of ozone molecules, leading to ozone layer depletion. This highlights the environmental importance of understanding and controlling the use of substances like Freon-12.

Ozone Depletion

Ozone depletion refers to the thinning of the Earth's ozone layer, most notably caused by compounds such as CFCs. This layer, high in the stratosphere, absorbs and scatters the majority of the sun's harmful ultraviolet radiation.

Chlorine atoms from CFCs, once released and activated by UV light, break down ozone molecules in a chain reaction. Reducing the ozone layer's density enhances the penetration of UV-B rays, increasing risks like skin cancer and cataracts in humans, and impacting the environment. Hence, by solving stoichiometric problems, students also learn about the broader implications of these chemicals on environmental health.