Question

Freon- 12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass \(=137.4 \mathrm{~g} / \mathrm{mol}\) ) is \(1.07: 1 .\) The formula of Freon- 12 is one of the following: \(\mathrm{CF}_{4}, \mathrm{CF}_{3} \mathrm{Cl}, \mathrm{CF}_{2} \mathrm{Cl}_{2}, \mathrm{CFCl}_{3}\), or \(\mathrm{CCl}_{4} .\) Which formula is correct for Freon- \(12 ?\)

Short answer

The correct formula for Freon-12 is CF2Cl2 with a molar mass of 120.91 g/mol, which is closest to the calculated molar mass of 120.93 g/mol using the given rate of effusion and Graham's Law of Effusion.

Step-by-step solution

Using Graham's Law of Effusion

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of the gas. Mathematically, we can write this relation as: \(\dfrac{\text{Rate of Effusion of Gas 1}}{\text{Rate of Effusion of Gas 2}} = \sqrt{\dfrac{\text{Molar Mass of Gas 2}}{\text{Molar Mass of Gas 1}}}\) In this case, Gas 1 is Freon-12, and Gas 2 is Freon-11. We are given the rate of effusion of Freon-12 to Freon-11 as 1.07:1, and the molar mass of Freon-11 is 137.4 g/mol. Using this information, we can set up the following equation: \(\dfrac{1.07}{1} = \sqrt{\dfrac{137.4 \text{ g/mol}}{\text{Molar Mass of Freon-12}}}\) Now, we need to solve this equation for the molar mass of Freon-12.

Solve for Molar Mass of Freon-12

To solve for the molar mass of Freon-12, we can first square both sides of the equation: \((1.07)^2 = \dfrac{137.4 \text{ g/mol}}{\text{Molar Mass of Freon-12}}\) Next, multiply both sides by the molar mass of Freon-12: \((1.07)^2 (\text{Molar Mass of Freon-12}) = 137.4 \text{ g/mol}\) Now, divide both sides by (1.07)^2: \(\text{Molar Mass of Freon-12} = \dfrac{137.4 \text{ g/mol}}{(1.07)^2}\) Finally, calculate the molar mass of Freon-12: \(\text{Molar Mass of Freon-12} = 120.93 \text{ g/mol}\) Use this value to determine the correct formula for Freon-12.

Identify the Correct Formula for Freon-12

Now that we have the molar mass of Freon-12 (120.93 g/mol), we can evaluate each of the given options to see which one has the closest molar mass: 1. CF4: Molar mass = (1)(12.01 g/mol) + (4)(19.00 g/mol) = 88.01 g/mol 2. CF3Cl: Molar mass = (1)(12.01 g/mol) + (3)(19.00 g/mol) + (1)(35.45 g/mol) = 104.46 g/mol 3. CF2Cl2: Molar mass = (1)(12.01 g/mol) + (2)(19.00 g/mol) + (2)(35.45 g/mol) = 120.91 g/mol 4. CFCl3: Molar mass = (1)(12.01 g/mol) + (1)(19.00 g/mol) + (3)(35.45 g/mol) = 137.36 g/mol 5. CCl4: Molar mass = (1)(12.01 g/mol) + (4)(35.45 g/mol) = 153.81 g/mol We can see that the molar mass of option 3 (CF2Cl2) is the closest to the calculated molar mass of Freon-12, so the correct formula for Freon-12 is CF2Cl2.

Key concepts

Effusion Rate Comparison

Understanding the rate of effusion can be very intriguing yet straightforward with the aid of Graham's Law. This law offers a method for comparing the effusion rates of two gases. Effusion is the process by which a gas escapes through a small hole into a vacuum. According to Graham's Law, the effusion rate is inversely proportional to the square root of the molar mass of the gas.

This means that a lighter gas (one with a lower molar mass) will effuse faster than a heavier gas. For example, if Gas 1 and Gas 2 have the same volume and are under the same conditions, but Gas 1 has half the molar mass of Gas 2, Gas 1 will effuse at a rate that is roughly 1.41 times (the square root of 2) faster than Gas 2.

When students encounter problems that require them to use this law, they must carefully determine the given rate of effusion and any provided molar masses. Then, using the straightforward formula derived from Graham's Law, they can effectively compare the effusion rates of different gases.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is typically measured in grams per mole (g/mol) and it can be calculated by summing the atomic masses of all the atoms present in a molecule.

A common mistake students make is not accounting for the number of atoms of each element. When faced with complex molecules, it's essential to multiply the atomic mass of each element by the number of times that element appears in the molecule. Remember that periodic tables provide the atomic mass of elements, making it a handy reference for these calculations.

In the case of effusion rate problems, knowledge of molar mass is not merely theoretical. By determining the molar mass of a gas, students can plug this value into the formula derived from Graham's Law to solve problems related to effusion rates. Mathematics becomes an essential tool in this process, and precision in calculation can lead to the correct identification of an unknown gas.

Chemical Formula Identification

Selecting the correct chemical formula from a set of possibilities can seem like a daunting task, but it is a crucial skill in deciphering and understanding chemical compositions. To identify the correct formula, you must often rely on data about the compound's properties, such as molar mass.

In situations where you're given molar mass data for comparison, calculate the molar mass for each candidate formula. The correct formula will have a molar mass that closely aligns with the experimental or given value.

When working on problems related to the effusion of gases, students must first calculate the molar mass of an unknown gas, and then compare it to the molar mass of known compounds. The correct formula is the one for which the calculated and known molar masses match most closely. The process requires careful attention to both calculation and comparison, ensuring that the chosen formula is truly the best fit based on the presented evidence.