The uranium minerals found in nature must be refined and...

The uranium minerals found in nature must be refined and enriched in $^{235} \mathrm{U}$ before the uranium can be used as a fuel in nuclear reactors. One procedure for enriching uranium relies on the reaction of $\mathrm{UO}_{2}$ with HF to form UF $_{4}$, which is then converted into UF $_{6}$ by reaction with fluorine: $$\begin{array}{c}\mathrm{UO}_{2}(g)+4 \mathrm{HF}(a q) \rightarrow \mathrm{UF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\\mathrm{UF}_{4}(g)+\mathrm{F}_{2}(g) \rightarrow \mathrm{UF}_{6}(g) \end{array}$$.a. How many kilograms of HF are needed to completely react with $5.00 \mathrm{kg}$ of $\mathrm{UO}_{2} ?$ b. How much UF $_{6}$ can be produced from $850.0 \mathrm{g}$ of $\mathrm{UO}_{2} ?$

The uranium minerals found in nature must be refined and enriched in $^{235} \mathrm{U}$ before the uranium can be used as a fuel in nuclear reactors. One procedure for enriching uranium relies on the reaction of $\mathrm{UO}_{2}$ with HF to form UF $_{4}$, which is then converted into UF $_{6}$ by reaction with fluorine: $$\begin{array}{c}\mathrm{UO}_{2}(g)+4 \mathrm{HF}(a q) \rightarrow \mathrm{UF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\\mathrm{UF}_{4}(g)+\mathrm{F}_{2}(g) \rightarrow \mathrm{UF}_{6}(g)
\end{array}$$.a. How many kilograms of HF are needed to completely react with $5.00 \mathrm{kg}$ of $\mathrm{UO}_{2} ?$
b. How much UF $_{6}$ can be produced from $850.0 \mathrm{g}$ of $\mathrm{UO}_{2} ?$

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on balanced chemical equations. It involves using mole ratios derived from the reaction coefficients to convert between amounts of substances, whether measured in moles, grams, or other units. This process ensures that the proportions of substances used or produced adhere to the conservation of mass.

Molar Mass Calculations

Molar mass calculations involve determining the mass of one mole of a substance using its atomic or molecular weights. This concept is crucial for converting between the mass of a substance and the number of moles, which is a necessary step in stoichiometric calculations to relate quantities in chemical reactions.

Mass-Mass Conversions

Mass-mass conversions entail using the molar ratios from a balanced reaction to translate the mass of one reactant or product into the mass of another. This process requires converting the given mass to moles using the molar mass, applying the reaction’s stoichiometric ratio, and then converting back to mass using the molar mass of the target substance.

Unit Conversions

Unit conversions are the process of converting quantities from one measurement unit to another, such as from grams to kilograms. In chemical calculations, ensuring that the units are consistent throughout the problem is essential for obtaining a correct and meaningful answer.

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