Question

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

Short answer

The atomic mass of element X in the compound \(XF_3\) is approximately 30.7 g/mol.

Step-by-step solution

Obtain molar mass of F

Find the molar mass of an F atom which is approximately 19 g/mol.

Assume the mass of the XF3 compound

Assume 100 grams of the compound XF3. This way, we can use mass percentage directly without the need for calculations.

Calculate the mass of F in the compound

Given that the compound is 65% F by mass, calculate the mass of F in the 100 grams of XF3 compound: Mass of F = 65% * 100 grams = 65 grams

Find moles of F in the compound

Divide the mass of F by its molar mass to find the moles of F in the compound: Moles of F = Mass of F / Molar mass of F = 65 grams / 19 g/mol ≈ 3.42 moles

Calculate moles of X in the compound

Since each molecule of XF3 contains 3 F atoms, divide the moles of F by 3 to obtain the moles of X: Moles of X = Moles of F / 3 ≈ 3.42 moles / 3 ≈ 1.14 moles

Calculate the mass of X in the compound

Subtract the mass of F from the assumed total mass of 100 grams to find the mass of X: Mass of X = 100 grams - 65 grams = 35 grams

Calculate the atomic mass of X

Divide the mass of X by the moles of X to find the atomic mass of X: Atomic mass of X = Mass of X / Moles of X = 35 grams / 1.14 moles ≈ 30.7 g/mol The atomic mass of element X is approximately 30.7 g/mol.

Key concepts

Atomic Mass

Atomic mass is a fundamental concept in chemistry. It refers to the mass of a single atom of a chemical element, typically measured in units of grams per mole (g/mol), which reflects the weighted average of the isotopes of that element. The atomic mass is important not just for understanding the element itself but also for grasping how it reacts and combines with other elements. When you know the atomic masses of elements, you can calculate the mass of compounds they form. This is key to determining their empirical formulas, which show the simplest whole-number ratio of elements in a compound. In exercises like the one given, knowing the atomic mass allows us to unravel and identify unknown elements by comparing their mass to that of known elements.

Molar Mass

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance. The units are grams per mole (g/mol). It is essentially a measure of how much "one mole" of a specific compound weighs. A mole is a way of counting particles in chemistry, equivalent to Avogadro's number, \(6.022 \times 10^{23}\) particles.

Molar mass is significant when working with chemical reactions and stoichiometry because it links mass to the number of atoms or molecules present. By knowing the molar mass and mass percentage of elements within a compound, like the fluorine (F) in this compound, you can accurately deduce how many moles of each element are present, ultimately helping in determining the compound's empirical or molecular formula.

Moles Calculation

Moles calculation is crucial in chemistry to understand the amount of substance involved in a reaction or present in a compound. The mole is a unit of measurement for amount of substance, and it connects the microscale (atoms and molecules) to the macroscale we observe (grams and liters).

To perform moles calculations, you need to know:

• The mass of the substance (in grams).
• The molar mass of the substance (in g/mol).

You can calculate the number of moles by dividing the mass of the element or compound by its molar mass: \[\text{Moles} = \frac{\text{Mass (grams)}}{\text{Molar Mass (g/mol)}}\].
In the given problem, calculating the moles of fluorine allowed us to work backwards to find the atomic mass of the unknown element, X. This shows the interconnected nature of chemical quantities, helping you make sense of chemical compositions and reactions.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more different elements. Compounds have distinct properties different from those of their component elements, and they usually exist in a fixed ratio reflected by their chemical formula.

Empirical formulas provide the simplest whole-number ratio of the elements in a compound. They are essential for understanding the composition of a compound and are often used as a starting point for further chemical analysis. For instance, in the compound \(XF_3\), the empirical formula indicates that there is one atom of X for every three atoms of fluorine.

• This information, combined with percentage composition by mass and molar masses, lets chemists determine specific details about a compound, such as the identity and atomic masses of its constituent elements.
• The ability to determine these characteristics is a fundamental skill in chemistry, aiding in the study of reactions and properties of various substances.

Understanding chemical compounds and their formulas is a gateway to exploring the world of chemical interactions and reactions.