Question

A given sample of a xenon fluoride compound contains molecules of the type \(\mathrm{XeF}_{n}\), where \(n\) is some whole number. Given that \(9.03 \times 10^{20}\) molecules of \(\mathrm{XeF}_{n}\) weigh \(0.368 \mathrm{~g}\), determine the value for \(n\) in the formula.

Short answer

The value of \(n\) in the given xenon fluoride compound formula \(\mathrm{XeF}_{n}\) is approximately 6, making the compound \(\mathrm{XeF}_{6}\).

Step-by-step solution

Recall the formula relating moles, mass, and molar mass

To find the number of moles of the given compound (XeFn), we will use the formula: \[moles = \frac{mass}{molar \thinspace mass}\] We are given the mass of the sample (0.368 g) and need to determine the molar mass of the compound to find the number of moles.

Find the molar mass of Xe and F

Refer to a periodic table to find the molar mass of Xenon (Xe) and Fluorine (F). The molar mass of Xe is approximately 131 g/mol, and the molar mass of F is approximately 19 g/mol.

Find the molar mass of XeFn

To calculate the molar mass of XeFn, add the molar mass of Xenon and n times the molar mass of Fluorine: \[Molar \thinspace mass \thinspace of \thinspace XeFn = 131 + 19n\]

Find the number of moles of XeFn

Now, we can use the number of molecules given (9.03 x 10^20) and Avogadro's number (6.022 x 10^23) to find the number of moles of XeFn: \[moles \thinspace of \thinspace XeFn = \frac{9.03 \times 10^{20}}{6.022 \times 10^{23}}\] Calculate the number of moles: \[moles \thinspace of \thinspace XeFn ≈ 1.5 \times 10^{-3} \thinspace moles\]

Calculate the molar mass of XeFn using the mass and moles

We can now use the mass of the sample (0.368 g) and the number of moles calculated (1.5 x 10^-3) to find the molar mass of XeFn: \[molar \thinspace mass \thinspace of \thinspace XeFn = \frac{0.368}{1.5 \times 10^{-3}}\] Calculate the molar mass: \[molar \thinspace mass \thinspace of \thinspace XeFn ≈ 245.333 \thinspace g/mol\]

Determine the value of n from the molar mass equation

Now, we can use the molar mass of XeFn found in step 5 to determine the value of n in the equation: \[245.333 = 131 + 19n\] Subtract 131 from both sides and divide by 19: \[n ≈ 6\] The value of n in the given xenon fluoride compound formula XeFn is approximately 6, making the compound XeF6.

Key concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry, serving as the bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. It's defined as a specific number of particles, be it atoms, ions, or molecules. In terms of a standard reference, one mole is equal to Avogadro's number of particles, which is roughly 6.022 x 10^23 particles.

To better understand the mole concept, imagine you have a dozen eggs. A dozen is a count of 12, whether it's 12 eggs, 12 cars, or 12 atoms. Similarly, a mole is like the chemist's 'dozen'. If you have one mole of eggs (a humorous thought!), you'd have Avogadro's number of eggs. When working with chemical reactions, it's not practical to count out individual atoms because they are so small and so numerous. That's where the mole concept becomes valuable as it allows chemists to count atoms and molecules in practical terms by weighing them.

In exercises, such as calculating the formula of a xenon fluoride compound, the mole concept allows us to convert between mass, number of particles, and volume (in the case of gases), based on the relationships discovered through empirical observations. This concept provides a crucial foundation for solving stoichiometry problems and grasping chemical quantities in a meaningful way.

Molar Mass

The molar mass is another core concept in chemistry, essential for solving stoichiometry problems. It represents the mass of one mole of a substance and is typically measured in grams per mole (g/mol). In essence, molar mass tells us how much one mole of a substance weighs and serves as a conversion factor between mass and number of moles.

To find the molar mass of a compound like XeFn, you need the molar masses of its constituent elements, xenon (Xe) and fluorine (F). These can be found on the periodic table: xenon is approximately 131 g/mol and fluorine is approximately 19 g/mol. By summing the molar mass of xenon with 'n' times the molar mass of fluorine, you get the molar mass of the compound. Knowing the molar mass then allows you to calculate the number of moles in a given sample of compound by dividing the mass of the sample by the compound's molar mass (as seen in step 5 of the original solution).

Understanding molar mass is critical for students as it is used in almost all chemical calculations involving mass and moles. If the compounds in a reaction are thought of as teams of atoms, the molar mass would be the 'team weight'. And just as different sports teams have different numbers and types of players, compounds have different formulas and, consequently, different molar masses.

Avogadro's Number

Avogadro's number is a constant that represents the number of units in one mole of any substance, named after scientist Amedeo Avogadro. It is equal to approximately 6.022 x 10^23 particles per mole. This number is crucial because it allows chemists to correlate the mass of a substance with the number of atoms, ions, or molecules it contains.

In the context of the exercise with xenon fluoride, Avogadro's number is used to convert the given number of molecules (9.03 x 10^20) into moles. By dividing the number of XeFn molecules by Avogadro's number, you can determine how many moles of XeFn are present in the sample (step 4 of the solution). Without this conversion, relating microscopic particle counts to macroscopic amounts for practical laboratory work would be impossible.

Avogadro's number plays a pivotal role in many areas of chemistry, including stoichiometry, gas laws, and determining atomic and molecular weights. For students, understanding Avogadro's number is important for any calculation involving moles, making it a cornerstone of chemical quantitation.