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Problem 92

To prepare nuclear fuel, $\mathrm{U}_{3} \mathrm{O}_{8}(\text { "yellow cake" ) is converted }$ to $\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2}$, which is then converted to $\mathrm{UO}_{3}$ and finally UO2. The fuel is enriched (the proportion of the 235U is increased) by a two-step conversion of $\mathrm{UO}_{2}$ into$\mathrm{UF}_{6}$ , a volatile solid, followed by a gaseous-diffusion separation of the 235U and 238U isotopes:
\begin{aligned} \mathrm{UO}_{2}(s)+4 \mathrm{HF}(g) & \longrightarrow \mathrm{UF}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{UF}_{4}(s)+\mathrm{F}_{2}(g) & \longrightarrow \mathrm{UF}_{6}(s) \end{aligned}
Calculate $\Delta G^{\circ}$ for the overall process at $85^{\circ} \mathrm{C} :$

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Chapter 20
Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions
CHEMISTRY: The Molecular Nature of Matter and Change 2016

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