The overall cell reaction for aluminum production is $$ 2 \mathrm{Al}_{2}
\mathrm{O}_{3}\left(\text { in } \mathrm{Na}_{3} \mathrm{AlF}_{6}\right)+3
\mathrm{C}(\mathrm{graphite}) \longrightarrow 4 \mathrm{Al}(t)+3
\mathrm{CO}_{2}(g) $$ (a) Assuming \(100 \%\) efficiency, how many metric tons
(t) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) are consumed per metric ton of Al
produced? (b) Assuming \(100 \%\) efficiency, how many metric tons of the
graphite anode are consumed per metric ton of Al produced? (c) Actual
conditions in an aluminum plant require \(1.89 \mathrm{t}\) of \(\mathrm{Al}_{2}
\mathrm{O}_{3}\) and \(0.45 \mathrm{t}\) of graphite per metric ton of Al. What
is the percent yicld of \(\mathrm{Al}\) with respect to \(\mathrm{Al}_{2}
\mathrm{O}_{3} ?\) (d) What is the percent yield of Al with respect to
graphite? (e) What volume of \(\mathrm{CO}_{2}\) (in \(\mathrm{m}^{3}\) ) is
produced per metric ton of Al at operating conditions of \(960 .{ }^{\circ}
\mathrm{C}\) and exactly 1 atm?