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 \(UF_6\).

Step-by-step solution

Convert the given percentage composition to grams

Assume that we have 100 grams of the compound. Then, the mass of uranium would be 67.61 grams, and the mass of fluorine would be 32.39 grams, following their percentages.

Convert the mass of each element to moles

To find the moles of each element, use their respective molar masses. For uranium (U), the molar mass is approximately 238.03 g/mol, while for fluorine (F), the molar mass is approximately 18.998 g/mol. Moles of uranium (U): Moles = (Mass of U) / (Molar mass of U) = \(\frac{67.61}{238.03}\) = 0.284 moles Moles of fluorine (F): Moles = (Mass of F) / (Molar mass of F) = \(\frac{32.39}{18.998}\) = 1.705 moles

Find the mole-to-mole ratio between uranium and fluorine

Find the smallest whole number ratio by dividing both moles by the smaller number of moles. Ratio (U/F): \( \frac{0.284\, \text{moles} \, \text{U}}{0.284\, \text{moles}\, \text{U}} : \frac{1.705\, \text{moles} \, \text{F}}{0.284\, \text{moles}\, \text{U}} \) = 1 : 6.00 (approx.)

Determine the empirical formula

The mole-to-mole ratio is approximately 1:6, meaning there is 1 uranium atom for every 6 fluorine atoms in the compound. So, the empirical formula for the compound is UF6.

Key concepts

Molar Mass

The concept of molar mass is essential when dealing with chemical compounds. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Understanding molar mass allows chemists to connect the mass of individual molecules to macroscopic quantities we can measure in the lab.
To calculate molar mass, you sum the atomic masses of all atoms in a molecule. For example, uranium (U) has a molar mass of approximately 238.03 g/mol, while fluorine (F) is about 18.998 g/mol. These values can be found using the periodic table.

• Atomic mass: from the periodic table based on naturally occurring isotopes.
• Molar mass: derived from adding atomic masses in one mole of a compound.

By converting the mass of each element into moles using their molar masses, you can quantitatively analyze compounds like the nuclear compound comprised of uranium and fluorine.

Mole Ratio

The idea of a mole ratio is a cornerstone in the study of chemical formulas and reactions. Mole ratio refers to the ratio between the amounts in moles of any two substances involved in a chemical reaction. This ratio is determined from the coefficients of a balanced chemical equation or from the elements in a compound.
In our example, to find the empirical formula of the uranium-fluorine compound, we calculated the moles of each element. Using their amounts, we determined how many moles of fluorine are present for each mole of uranium:
1 mole U : 6 moles F.

• Find mole ratio: Divide each element's moles by the smallest value among them.
• Simplify the ratio: Ensure the ratio is in the smallest whole numbers possible to establish the empirical formula.

Empirical formulas like UF₆ give the smallest whole number mole ratio of the elements in the compound, critical for understanding compound composition on a molecular level.

Nuclear Compound Composition

Nuclear compounds, notable for their significance in energy generation, often have compositions that are carefully analyzed for efficiency and safety. Their composition by elements reveals not just their structural formula, but also insights into their stability and reactivity within nuclear reactions.
Understanding the composition of a nuclear compound involves both qualitative and quantitative analysis of each component. The example given describes a compound with uranium and fluorine, specifically UF₆.

• Qualitative aspect: Identifying which elements are in the compound, such as uranium and fluorine.
• Quantitative aspect: Determining the proportion of each element like the 1:6 uranium to fluorine ratio.

Grasping the detailed composition of nuclear compounds informs their role in industrial processes, specifically how they might behave under nuclear reactions.