Question

Bauxite, the principal source of aluminum oxide, contains \(55 \% \mathrm{Al}_{2} \mathrm{O}_{3} .\) Calculate how much bauxite is required to produce the \(5.0 \times 10^{6}\) tons of \(\mathrm{Al}\) produced annually by electrolysis.

Short answer

Around 17.2 million tons of bauxite are needed.

Step-by-step solution

Find the molecular weight of Al2O3

To solve the problem, we first need to calculate the molar mass of aluminum oxide (Al2O3). The atomic weight of aluminum (Al) is approximately 26.98 g/mol, and for oxygen (O), it is approximately 16.00 g/mol. Therefore, \( \mathrm{Al}_2\mathrm{O}_3 \) has a molar mass of: \( (2 \times 26.98) + (3 \times 16.00) = 53.96 + 48.00 = 101.96 \) g/mol.

Calculate the amount of Al in Al2O3

Next, we determine the percentage of aluminum in aluminum oxide. Since aluminum oxide is \(\mathrm{Al}_2\mathrm{O}_3\), we use the two aluminum atoms in the calculation: \( \frac{2 \times 26.98}{101.96} \approx 0.529 \) or 52.9%. This means that 52.9% of the mass of Al2O3 is aluminum.

Calculate the required Al2O3 to produce given aluminum

Given that we need \(5.0 \times 10^6\) tons of aluminum, and knowing that aluminum is 52.9% of aluminum oxide, we can calculate the required aluminum oxide. Rearrange the relationship to find the total mass: \( \text{mass of Al2O3} = \frac{5.0 \times 10^6}{0.529} \approx 9.45 \times 10^6 \) tons of Al2O3 required.

Calculate the amount of bauxite needed

Bauxite contains 55% Al2O3. To find the total bauxite needed, use the equation: \( \text{mass of bauxite} = \frac{9.45 \times 10^6}{0.55} \approx 1.72 \times 10^7 \) tons. So, approximately 17.2 million tons of bauxite are needed to produce \(5.0 \times 10^6\) tons of aluminum.

Key concepts

Electrolysis

Electrolysis is a fascinating process used to extract elements from their compounds using an electric current. This is especially crucial in industries like aluminum production. When it comes to obtaining aluminum from aluminum oxide, electrolysis plays a starring role.
Aluminum does not occur in pure form naturally and is most commonly found in bauxite, a mineral rich in aluminum oxide (Al2O3). To isolate aluminum, aluminum oxide is dissolved in molten cryolite, and then electricity is applied.
This process occurs in large cells where the electric current causes the aluminum ions to migrate to the cathode (a negative electrode), forming pure aluminum metal. Oxygen ions migrate to the anode (a positive electrode) and release oxygen gas.
Here's a simple outline of the electrolysis process:

• An electrical current is passed through the electrolyte, containing dissolved aluminum oxide.
• At the cathode, aluminum ions gain electrons (reduction) and form aluminum metal.
• At the anode, oxygen ions lose electrons (oxidation) and release oxygen gas.

This method is energy-intensive, but it is the most practical way to produce large quantities of aluminum.

Aluminum oxide

Aluminum oxide, or Al2O3, is a crucial compound in the extraction of aluminum metal. It consists of aluminum and oxygen, with aluminum having a +3 oxidation state and oxygen having a -2 state. In Al2O3, there are two aluminum atoms and three oxygen atoms, giving it a balanced charge.
This compound is obtained from bauxite ore, which is treated to remove impurities and isolate the Al2O3. Understanding the composition of Al2O3 is essential because it directly relates to its use in producing aluminum.
Aluminum oxide has several important features:

• It is an amphoteric compound, meaning it can act as both an acid and base, reacting with both acidic and basic substances.
• Al2O3 is notably hard with a high melting point, attributed to its strong ionic bonds.
• Its structure makes it useful not only in metallurgical processes but also in various industrial applications like abrasives and ceramics.

In aluminum production, the percentage of aluminum within Al2O3 is critical to calculate how much raw material is needed to produce a certain amount of aluminum.

Molar mass calculation

Molar mass plays a pivotal role in chemistry calculations, helping bridge the gap between atoms and grams, which is particularly useful in industrial chemistry. For aluminum oxide (Al2O3), calculating molar mass is the first step in determining how much of this compound is needed for producing aluminum.
Here's a detailed look at the calculation:

• Identify the atomic masses: Aluminum (Al) has an atomic mass of approximately 26.98 g/mol and Oxygen (O) around 16.00 g/mol.
• Use the chemical formula Al2O3 to determine composition: Two aluminum atoms and three oxygen atoms.
• Calculate the sum to find the molar mass: \( (2 \times 26.98) + (3 \times 16.00) = 53.96 + 48.00 = 101.96 \) g/mol.

This calculated molar mass helps determine the weight of aluminum within each mole of Al2O3, making it a fundamental factor in larger industrial calculations, such as extracting pure aluminum from bauxite through electrolysis.