Problem 26 - Chemistry The Science in Context

Question

Composition of Uranium Ores The uranium used for nuclear fuel exists in nature in several minerals. Calculate how many moles of uranium are in 1 mole of the following: a. carnotite, \(\mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2}\). b. uranophane, \(\mathrm{CaU}_{2} \mathrm{Si}_{2} \mathrm{O}_{11}\). c. autunite, \(\mathrm{Ca}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2}\).

Step-by-Step Solution

Answer

Answer: In each of the minerals carnotite, uranophane, and autunite, there are 2 moles of uranium present in 1 mole of the mineral.

Step 1: a. Calculation for carnotite.

In carnotite, \(\mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2}\), there are 2 moles of \(\mathrm{UO}_{2}\) in every mole of carnotite. Thus, we have 2 moles of \(\mathrm{U}\): $$\text{Moles of Uranium in 1 mole of Carnotite} = 1\,\text{mole Carnotite} \times \frac{2\,\text{moles}\, \mathrm{U}}{1\,\text{mole Carnotite}} =2\,\text{moles}\,\mathrm{U}$$

Step 2: b. Calculation for uranophane.

In uranophane, \(\mathrm{CaU}_{2} \mathrm{Si}_{2} \mathrm{O}_{11}\), there are 2 moles of \(\mathrm{U}\) in each mole of uranophane: $$\text{Moles of Uranium in 1 mole of Uranophane} = 1\,\text{mole Uranophane} \times \frac{2\,\text{moles}\, \mathrm{U}}{1\,\text{mole Uranophane}} =2\,\text{moles}\,\mathrm{U}$$

Step 3: c. Calculation for autunite.

In autunite, \(\mathrm{Ca}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2}\), there are 2 moles of \(\mathrm{UO}_{2}\) in every mole of autunite. Thus, we have 2 moles of \(\mathrm{U}\): $$\text{Moles of Uranium in 1 mole of Autunite} = 1\,\text{mole Autunite} \times \frac{2\,\text{moles}\, \mathrm{U}}{1\,\text{mole Autunite}} =2\,\text{moles}\,\mathrm{U}$$ To summarise, there are 2 moles of uranium present in each mole of carnotite, uranophane, and autunite.

Key Concepts

Molecular Composition

Every mineral or compound has a unique molecular structure, which is made up of different kinds of atoms bonded together. This structure defines its molecular composition. In the context of uranium minerals like carnotite, uranophane, and autunite, we examine what specific atoms are present and how many.
For example, the mineral carnotite is represented by the chemical formula \( \mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2} \). This tells us that it contains potassium (K), uranium (U), oxygen (O), and vanadium (V) atoms. Knowing the molecular composition allows us to determine the proportional amounts of each atom within the mineral's structure.
The molecular composition is crucial for understanding the properties and behavior of a mineral. It dictates how the mineral interacts with other substances and can also affect its stability and reactivity. Being able to identify and quantify each component is vital in fields like chemistry and geology.

Mole Calculations

The concept of moles is central in chemistry for quantifying substances. A mole represents \(6.022 \times 10^{23}\) of anything, usually atoms or molecules. This is a convenient way to describe large numbers of tiny entities.
In uranium minerals, we often need to calculate how many moles of a particular element are present. For the exercise involving carnotite, uranophane, and autunite, we calculate the moles of uranium. Given their chemical formulas:

• Carnotite: \( \mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2} \)
• Uranophane: \( \mathrm{CaU}_{2} \mathrm{Si}_{2} \mathrm{O}_{11} \)
• Autunite: \( \mathrm{Ca}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2} \)

We need to find out how many uranium atoms are in one mole of the entire mineral. The key is to look closely at the subscripts in each formula. They show how many moles of each atom are present in one mole of the compound. This makes mole calculations a straightforward but powerful tool for translating chemical information into actionable data.

Uranium Minerals

Uranium is a naturally occurring element that is vital for nuclear energy production. It is typically found within various minerals in the earth's crust. Understanding these uranium minerals helps in both resource management and environmental studies.
Carnotite, uranophane, and autunite are three examples of uranium-bearing minerals. Each of these minerals contains uranium within their complex structures:

• Carnotite: Often found in sandstone formations and used historically as a uranium ore.
• Uranophane: A secondary uranium mineral typically occurring in hydrated forms.
• Autunite: Known for its distinctive bright yellow color and found in phosphate-rich environments.

Knowledge about these minerals is important for identifying potential sources of uranium. Their study informs mining operations and helps geologists understand geological formations where uranium-mineral deposits are found. They also pose environmental concerns due to their radioactive nature, emphasizing the need for careful handling and study.

Chemical Formulas

Chemical formulas are a shorthand way of representing the elements and the number of each atom in a compound. They are like a recipe, specifying which ingredients are needed and in what amount.
For complex minerals such as those containing uranium, these formulas provide a wealth of information quickly. Take, for instance, the formula for uranophane, \( \mathrm{CaU}_{2} \mathrm{Si}_{2} \mathrm{O}_{11} \). This tells us there are 2 uranium atoms, 2 silicon atoms, 1 calcium atom, and 11 oxygen atoms per formula unit of uranophane.
The role of chemical formulas extends beyond just telling us what is inside a compound. They also inform us about the ratio of elements, which is crucial for chemical reactions and processes. Understanding chemical formulas is essential for anyone studying chemistry as they tie together various concepts such as stoichiometry, balancing reactions, and predicting the products of reactions.