Question

The most useful ore of aluminum is bauxite, in which Al is present as hydrated oxides, Al2O3 * xH2O.

a) The number of kilowatt-hours of electricity required to produce 3.00kg of aluminum from electrolysis of compounds from bauxite is __________ when the applied emf is 5.00 V.

Answer 1

44.7 kWh

Step-by-step explanation:

Let's consider the reduction of Al₂O₃ to Al in the Bayer process.

6 e⁻ + 3 H₂O + Al₂O₃ → 2 Al + 6 OH⁻

We can establish the following relations:

• The molar mass of Al is 26.98 g/mol.
• 2 moles of Al are produced when 6 moles of e⁻ circulate.
• 1 mol of e⁻ has a charge of 96468 c (Faraday's constant).
• 1 V = 1 J/c
• 1 kWh = 3.6 × 10⁶ J

When the applied electromotive force is 5.00 V, the energy required to produce 3.00 kg (3.00 × 10³ g) of aluminum is:

`3.00 * 10^(3) gAl.(1molAl)/(26.98gAl) .(6mole^(-))/(2molAl).(96468c)/(1mole^(-)).(5.00J)/(c).(1kWh)/(3.6 * 10^(6)J) =44.7kWh`