Question

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. What is the atomic mass of X?

Short answer

The atomic mass of element X in the compound \(\mathrm{XF}_{3}\) is approximately 30.54 g/mol.

Step-by-step solution

Calculate the mass of F in \(\mathrm{XF}_{3}\)

Since \(\mathrm{XF}_{3}\) consists of 65% F by mass, it means that the remaining mass (100%-65%=35%) will be element X. We can assume a total mass of 100 grams for the compound, which would give us 65 grams of F and 35 grams of X. Now, we move on to the following steps.

Calculate moles of F

To find the moles of F in the compound, we will use the molar mass of F, which is approximately 19 g/mol. Moles of F = Mass of F / Molar mass of F = 65 g / 19 g/mol = \( \frac{65}{19} \) moles.

Calculate the ratio of X to F in moles

Since the empirical formula is \(\mathrm{XF}_{3}\), this means there are 3 moles of F per mole of X. We can use this information to find the moles of X in the compound. Moles of X = \( \frac{1}{3} \times \frac{65}{19} \) = \( \frac{65}{57} \) moles.

Calculate the atomic mass of X

Now that we have the moles of X and mass of X, we can find the atomic mass of X using the formula: Atomic mass of X = Mass of X / Moles of X Atomic mass of X = \( \frac{35 \text{ g}}{\frac{65}{57} \text{ moles}} \) Atomic mass of X = \( 35 \times \frac{57}{65} \) Atomic mass of X ≈ 30.54 g/mol Thus, the atomic mass of element X is approximately 30.54 g/mol.

Key concepts

Molar Mass

Molar mass is a crucial concept in chemistry that helps us determine the amount of a substance in a mole. It is defined as the mass of one mole of a given substance, typically measured in grams per mole (g/mol). Understanding molar mass is essential when solving problems involving chemical formulas and reactions.
The molar mass of an element is calculated by taking the atomic mass of each element in a molecule and summing them based on the number of atoms present. For example, in the exercise, we determined the moles of fluorine (F), using its molar mass of approximately 19 g/mol. The calculation for moles is straightforward:

• First, find the molar mass of each element in the compound.
• Then, add them for a compound or take each element as needed.
• Finally, divide the given mass by the molar mass to get moles.

This process is invaluable for converting between grams of a substance and the number of moles, making it easier to perform stoichiometric calculations.

Atomic Mass

Atomic mass is similar to molar mass but focuses specifically on an individual atom's mass, usually presented in atomic mass units (amu). Each element has a unique atomic mass, which can be found on the periodic table.
In the context of the given exercise, calculating the atomic mass of an unknown element (X) is essential. To find the atomic mass, we took advantage of the empirical formula \( XF_3 \), which provided vital information regarding the ratio of fluorine to element X in the compound.
The calculation was completed using the formula:

• Find the mass of the unknown element given in the problem.
• Compute the number of moles using the empirical formula.
• Divide the mass of the element by the calculated number of moles to obtain the atomic mass.

For element X in the exercise, the atomic mass was determined to be approximately 30.54 g/mol, making this method an effective tool for identifying unknown elements.

Mole Concept

The mole concept is foundational in chemistry and acts as a bridge between the atomic and macroscopic worlds. It allows chemists to count particles at the atomic scale by weighing them at the macroscopic scale.
A mole represents Avogadro's number, which is \(6.022 \times 10^{23}\) particles, and serves as a standard measurement in chemistry to express amounts of a chemical substance.

• One mole corresponds to the quantity of substance that includes Avogadro's number of particles.
• Using the mole allows chemists to easily calculate and understand substance quantities in terms of mass and volume.
• The mole concept aids in balancing chemical equations and predicting product amounts in reactions.

In our exercise, understanding the mole concept enabled us to calculate the number of moles of both fluorine and the unknown element X, based on their known masses and molar ratios. This exemplifies how integral comprehending moles is for problem-solving in chemistry.