Uranium is used as a fuel, primarily in the form of uranium(IV) oxide, in
nuclear power plants. This question considers some uranium chemistry.
(a) A small sample of uranium metal \((0.169 \mathrm{g})\) is heated to between
800 and \(900^{\circ} \mathrm{C}\) in air to give \(0.199 \mathrm{g}\) of a dark
green oxide, \(\mathrm{U}_{x} \mathrm{O}_{y} .\) How many moles of uranium metal
were used? What is the empirical formula of the oxide, \(\mathrm{U}_{x}
\mathrm{O}_{y} ?\) What is the name of the oxide? How many moles of
\(\mathrm{U}_{x} \mathrm{O}_{y}\) must have been obtained?
(b) The naturally occurring isotopes of uranium are \(^{234} \mathrm{U},^{235}
\mathrm{U},\) and \(^{238} \mathrm{U} .\) Knowing that uranium's atomic weight is
\(238.02 \mathrm{g} / \mathrm{mol},\) which isotope must be the most abundant?
(c) If the hydrated compound \(\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2}
\cdot z \mathrm{H}_{2} \mathrm{O}\) is
heated gently, the water of hydration is lost. If you have \(0.865 \mathrm{g}\)
of the hydrated compound and obtain \(0.679 \mathrm{g}\) of
\(\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) on heating, how many waters
of hydration are in each formula unit of the original compound? (The oxide
\(\mathrm{U}_{x} \mathrm{O}_{y}\) is obtained if the hydrate is heated to
temperatures over \(800^{\circ} \mathrm{C}\) in the air.)