Question

A compound used in the nuclear industry has the following composition: uranium, \(67.61 \% ;\) fluorine, 32.39\%. Determine the empirical formula of the compound.

Short answer

The empirical formula of the compound is UF6.

Step-by-step solution

Convert percentages to gram amounts

Assuming we have 100 grams of the compound, we can directly use the percentages as gram amounts of uranium and fluorine. Uranium constitutes \(67.61 \%\) which means there are \(67.61\) grams of uranium, and fluorine constitutes \(32.39 \%\) which means there are \(32.39\) grams of fluorine in the compound.

Convert gram amounts to mole amounts

To convert grams to moles, we will use the molar mass of each element. The molar mass of uranium is \(238.03 \frac{g}{mol}\) and the molar mass of fluorine is \(19.00 \frac{g}{mol}\). Moles of uranium = \( \frac{67.61 \, g}{238.03 \, \frac{g}{\text{mol}}} = 0.284 \, \text{mol} \) Moles of fluorine = \( \frac{32.39 \, g}{19.00 \, \frac{g}{\text{mol}}} = 1.705 \, \text{mol} \)

Find the ratio of moles

To find the empirical formula, we must find the simplest whole-number ratio of moles of uranium to fluorine. To do this, we will divide both mole amounts by the smaller mole amount. Ratio of moles of uranium = \( \frac{0.284}{0.284} = 1 \) Ratio of moles of fluorine = \( \frac{1.705}{0.284} = 6.0 \) The simplest whole-number ratio of moles is 1:6.

Determine the empirical formula

Based on the ratio of moles of uranium and fluorine (1:6), the empirical formula of the compound is UF6.

Key concepts

Chemical Composition

Understanding the chemical composition of a substance is essential for a multitude of scientific applications, ranging from pharmacology to materials science. Chemical composition refers to the identity and quantity of elements that make up a compound. In the context of the given exercise, it is described in terms of percentages of uranium and fluorine in the compound.

This information is crucial because it enables us to determine the formula of the compound, which is a representation of the types and amounts of atoms that constitute a single molecule or formula unit of that substance. Recognizing that a compound’s empirical formula represents the simplest whole-number ratio of atoms in the compound, we convert these percentages to find out how many moles of each element are present, which then leads us to the empirical formula. Extracting an empirical formula provides a foundational understanding of a compound's composition, making it a fundamental step in chemical analysis and reaction design.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we live in. By definition, a mole is the amount of substance that contains as many entities (atoms, molecules, etc.) as there are atoms in 12 grams of pure carbon-12. This definition connects mass to a countable number of particles.

In our exercise, the mole concept is applied by converting the mass of uranium and fluorine to moles using their respective atomic weights. This allows us to answer how many atoms we're dealing with in a given amount of material. Understanding moles leads to a deeper appreciation for the stoichiometry of chemical reactions, as stoichiometry deals with the quantitative relationships between reactants and products. Learning to convert mass to moles and vice versa is an invaluable tool in every chemist's repertoire, as it enables precise calculations in chemical reactions and compound formation.

Stoichiometry

At its core, stoichiometry is the aspect of chemistry that pertains to the quantitative relationships within a chemical reaction. It is all about proportion, ratios, and the conservation of mass. Thanks to stoichiometry, we understand that reactants are transformed into products in amounts that can be predicted and measured.

In our example, stoichiometry is evident when we determine the empirical formula of the compound used in the nuclear industry. We use stoichiometry to calculate the simplest whole-number mole ratio of uranium to fluorine. It is this very ratio that dictates the empirical formula, indicating how many atoms of each element are present in the simplest form of the compound. In the broader context of chemistry, stoichiometry enables us to predict the outcomes of chemical reactions, design chemical processes, and synthesize compounds efficiently, making it a cornerstone concept in the study and practice of chemical sciences.