General Zod has sold Lex Luthor what Zod claims to be a new copper-colored
form of kryptonite, the only substance that can harm Superman. Lex, not
believing in honor among thieves, decided to carry out some tests on the
supposed kryptonite. From previous tests, Lex knew that kryptonite is a metal
having a specific heat capacity of \(0.082 \mathrm{J} / \mathrm{g}
\cdot^{\circ} \mathrm{C}\) and a density of \(9.2 \mathrm{g} / \mathrm{cm}^{3}.\)
Lex Luthor's first experiment was an attempt to find the specific heat
capacity of kryptonite. He dropped a \(10 \mathrm{g} \pm 3 \mathrm{g}\) sample
of the metal into a boiling water bath at a temperature of \(100.0^{\circ}
\mathrm{C} \pm 0.2^{\circ} \mathrm{C} .\) He waited until the metal had reached
the bath temperature and then quickly transferred it to \(100 \mathrm{g} \pm 3
\mathrm{g}\) of water that was contained in a calorimeter at an initial
temperature of \(25.0^{\circ} \mathrm{C} \pm 0.2^{\circ} \mathrm{C} .\) The
final temperature of the metal and water was \(25.2^{\circ} \mathrm{C} .\) Based
on these results, is it possible to distinguish between copper and kryptonite?
Explain. When Lex found that his results from the first experiment were
inconclusive, he decided to determine the density of the sample. He managed to
steal a better balance and determined the mass of another portion of the
purported kryptonite to be \(4 \mathrm{g} \pm 1\) g. He dropped this sample into
water contained in a 25-mL graduated cylinder and found that it displaced a
volume of \(0.42 \mathrm{mL} \pm 0.02 \mathrm{mL} .\) Is the metal copper or
kryptonite? Explain. Lex was finally forced to determine the crystal structure
of the metal General Zod had given him. He found that the cubic unit cell
contained four atoms and had an edge length of \(600 . \mathrm{pm} .\) Explain
how this information enabled Lex to identify the metal as copper or
kryptonite. Will Lex be going after Superman with the kryptonite or seeking
revenge on General Zod? What improvements could he have made in his
experimental techniques to avoid performing the crystal structure
determination?
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