Question

The mass of carbon anode consumed (giving the only carbon dioxide) in the production of $270{\text{kg}}$ aluminium metal from bauxite by the Hall process is:
A.$180{\text{kg}}$
B.$270{\text{kg}}$
C.$540{\text{kg}}$
D.$90{\text{kg}}$

Answer 1

The method of scientific extraction of minerals from their ores is known as metallurgy. Aluminium metal can be obtained from its ore bauxite using various methods, the most common methods being, Bayer’s process and Hall- Heroult process. We shall calculate the mass of aluminium produced using the stoichiometric ratios from the reaction equation.

Formula used:
${\text{moles = }}\dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$

Complete step by step solution:
The Hall-Heroult process is the most common method of extracting aluminium from its ore bauxite.
In this process, we mix pure aluminium oxide, $A{l_2}{O_3}$, with calcium fluoride, $Ca{F_2}$ which lowers the melting point of the solution and increases its conductivity. This mixture is then electrolyzed and aluminium in aluminium oxide is reduced to obtain aluminium metal at the cathode. The anode is a carbon anode which undergoes oxidation to form carbon dioxide.
The overall reaction of the process can be written as:
$2A{l_2}{O_3} + 3C \to 4Al + 3C{O_2}$.
In the question we are supposed to find the amount of carbon used up to result in the production of $270{\text{kg}}$ of aluminium metal. From the reaction, we can see that three moles of carbon are used to form four moles of aluminium. We know that the mass of carbon and aluminum are $12{\text{g/mol}}$ and $27{\text{g/mol}}$ respectively.
So, the mass of carbon consumed $= 3 \times 12 = 36{\text{g}}$
And the mass of aluminium produced$= 4 \times 27 = 108{\text{g}}$
Thus, we can say that $36{\text{g}}$ carbon is consumed to produce $108{\text{g}}$ aluminium. So the amount of carbon consumed in the production of $270{\text{kg}}$ aluminium will be:
$= \dfrac{{36}}{{108}} \times 270 \approx 90{\text{kg}}$.

Thus, the correct option is D.

Note:
The Hall- Heroult process is widely used for extraction of aluminium over carbon reduction because carbon reduction requires a high temperature and is thus not as economical as the electrolysis process.