Uranium oxides used in the preparation of fuel for nuclear...

Uranium oxides used in the preparation of fuel for nuclear reactors are separated from other metals in minerals by converting the uranium to $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z},$ where uranium has a positive charge ranging from $3+$ to $6+$ a. Roasting UO $_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ at $400^{\circ} \mathrm{C}$ leads to loss of itrogen oxides, leaving behind a product with the formula $\mathrm{U}_{a} \mathrm{O}_{b}$ that is $83.22 \% \mathrm{U}$ by mass. What are the values of $a$ and $b ?$ What is the charge on $\mathrm{U}$ in $\mathrm{U}_{a} \mathrm{O}_{b} ?$b. Higher temperatures produce a different uranium oxide, $\mathrm{U}_{c} \mathrm{O}_{d},$ with a higher uranium content, $84.8 \% \mathrm{U} .$ What are the values of $c$ and $d ?$ What is the charge on $\mathrm{U}$ in $\mathrm{U}_{a} \mathrm{O}_{b} ?$ c. The values of $x, y,$ and $z$ in $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ are found by gently heating the compound to remove all of the water. In a laboratory experiment, $1.328 \mathrm{g}$ of $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ produced $1.042 \mathrm{g}$ of $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}$ Continued heating generated $0.742 \mathrm{g}$ of $\mathrm{U}_{n} \mathrm{O}_{m} .$ Using the information in parts (a) and (b), calculate $x, y,$ and $z$.

Uranium oxides used in the preparation of fuel for nuclear reactors are separated from other metals in minerals by converting the uranium to $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z},$ where uranium has a positive charge ranging from $3+$ to $6+$
a. Roasting UO $_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ at $400^{\circ} \mathrm{C}$ leads to loss of itrogen oxides, leaving behind a product with the formula $\mathrm{U}_{a} \mathrm{O}_{b}$ that is $83.22 \% \mathrm{U}$ by mass. What are the values of $a$ and $b ?$ What is the charge on $\mathrm{U}$ in $\mathrm{U}_{a} \mathrm{O}_{b} ?$b. Higher temperatures produce a different uranium oxide, $\mathrm{U}_{c} \mathrm{O}_{d},$ with a higher uranium content, $84.8 \% \mathrm{U} .$ What are the values of $c$ and $d ?$ What is the charge on $\mathrm{U}$ in $\mathrm{U}_{a} \mathrm{O}_{b} ?$
c. The values of $x, y,$ and $z$ in $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ are found by gently heating the compound to remove all of the water. In a laboratory experiment, $1.328 \mathrm{g}$ of $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}\left(\mathrm{H}_{2} \mathrm{O}\right)_{z}$ produced $1.042 \mathrm{g}$ of $\mathrm{UO}_{x}\left(\mathrm{NO}_{3}\right)_{y}$
Continued heating generated $0.742 \mathrm{g}$ of $\mathrm{U}_{n} \mathrm{O}_{m} .$ Using the information in parts (a) and (b), calculate $x, y,$ and $z$.

Key Concepts

Oxidation States

Oxidation states are important in understanding how electrons are distributed in a compound and predicting the chemical reactivity and bonding of an element. For elements like uranium that can exhibit multiple oxidation states, determining the correct oxidation state helps in finding the accurate formula for compounds and is essential for balancing chemical equations.

Dehydration of Hydrated Compounds

Dehydration is the process of removing water molecules that are incorporated into a compound's structure, typically by gentle heating. Understanding dehydration is essential for determining the stoichiometry of the anhydrous compound, as it involves quantifying the loss of water to reveal the composition of the remaining structure.

Thermal Decomposition Reactions

Thermal decomposition involves heating a chemical compound to break it down into simpler substances. In analytical contexts, controlled thermal decomposition can be used to remove components such as water or nitrogen oxides from a compound, leading to new products whose compositions provide critical information about the original material.

Empirical Formula Determination

Determining an empirical formula involves establishing the simplest whole-number ratio of atoms in a compound. By using data such as mass percentages or product yields from thermal reactions, one can deduce the formula that best represents the proportion of the constituent elements.

Mass Percentage Composition

Mass percentage composition refers to the proportion of the total mass of a compound that is contributed by a particular element. This concept is crucial when one is given a compound’s percentage composition by mass and is required to back-calculate the formula or compare it with expected stoichiometric ratios.

Stoichiometric Calculations

This concept involves the use of mole relationships and mass measurements to deduce the ratios of elements in a compound. In problems where mass percentages are given, the stoichiometric calculations allow one to convert the mass data into moles, thereby determining the empirical formula and infer the relative numbers of atoms present in the chemical formula.

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