Question

Aluminum is produced commercially by the electrolysis of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) in the presence of a molten salt. If a plant has a continuous capacity of \(1.00\) million A, what mass of aluminum can be produced in \(2.00 \mathrm{~h} ?\)

Short answer

The mass of Aluminum that can be produced in 2.00 hours using a 1.00 million amperes capacity is approximately 2,017,092.61 g or 2.02 metric tons.

Step-by-step solution

Calculate the total charge passed through the electrolyte

We are given the current is 1.00 million A = 1.00 * 10^6 A and the time is 2.00 hours. We can find the total charge Q (in coulombs) by multiplying the current (in amperes) by time (in seconds). We should firstly convert time from hours to seconds, i.e. 2.00 hours = 2.00 * 3600 seconds. Q = current × time Q = (1.00 * 10^6 A)(2.00 * 3600 s) Q = 7.20 * 10^9 C

Calculate the amount of Aluminum (in moles) produced

Now we need to convert the charge (Q) into moles of Aluminum. This will be done using Faraday's law which states that: Moles of substance = (Q * n) / (F * v) Where Q is charge (in C), n is the number of electrons, F is Faraday's constant (96500 C/mol) and v is the valency of the substance. For Aluminum, it has a valency of 3 as it is an electropositive element with 3 valence electrons (losing 3 electrons to become \(\mathrm{Al}^{3+}\)). Therefore, v = 3 and we know F (Faraday's constant) = 96500 C/mol. Moles of Aluminum = (7.20 * 10^9 C *3) / (96500 C/mol *3) Moles of Aluminum = 74758.55 mol

Calculate the mass of Aluminum produced

Now, we need to convert the moles of Aluminum into mass using the molar mass. We know that the molar mass of Aluminum is approximately 26.98 g/mol. Mass of Aluminum = Moles of Aluminum × Molar Mass of Aluminum Mass of Aluminum = 74758.55 mol × 26.98 g/mol Mass of Aluminum = 2017092.61 g Hence, the mass of Aluminum that can be produced in 2.00 hours using a 1.00 million amperes capacity is approximately 2,017,092.61 g or 2.02 metric tons.

Key concepts

Faraday's Law

Faraday's Law is a fundamental principle in electrochemistry, connecting the flow of electric charge to chemical change. It states that the amount of substance produced at an electrode during electrolysis is directly proportional to the total electric charge passed through the system. This can be explained by the formula:\[\text{Moles of substance} = \frac{Q \times n}{F \times v}\]

• \(Q\) is the total charge in coulombs.
• \(n\) is the number of moles of electrons involved.
• \(F\) is Faraday's constant, approximately 96500 C/mol.
• \(v\) is the valency of the substance.

This law provides a way to directly calculate the moles of a substance reacted or produced in electrolysis, making it essential for processes like aluminum production.

Aluminum Production

The production of aluminum via electrolysis involves using electric current to extract aluminum from its ore, alumina (\(\mathrm{Al}_2\mathrm{O}_3\)). This process occurs in a molten salt solution that makes the alumina an excellent conductor of electricity. The primary reaction involves the conversion of \(\mathrm{Al}_2\mathrm{O}_3\) into pure aluminum metal and oxygen gas.In the Hall-Héroult process:

• Alumina is dissolved in molten cryolite.
• Electric current causes the oxygen anions to migrate to the anode, releasing oxygen gas.
• Aluminum cations, \(\mathrm{Al}^{3+}\), migrate to the cathode, forming aluminum metal.

This efficient yet electricity-intensive method is vital worldwide, enabling mass production of aluminum, a key material in industries ranging from aerospace to packaging.

Charge Calculation

In electrolysis, the charge calculated represents the electricity that flows through the circuit. For aluminum production, calculating the charge is crucial to determining how much metal can be produced. The charge \(Q\) in coulombs can be determined using the formula:\[Q = \text{current} \times \text{time}\]

• Current is measured in amperes (A).
• Time must be in seconds when using this formula.

For instance, a plant operating at a capacity of \(1.00 \times 10^6\) A for 2 hours will produce a charge of \(7.20 \times 10^9\) C. This conversion helps determine how much aluminum can be extracted from bauxite, the ore in question.

Molar Mass Conversion

Molar mass conversion translates moles of a substance into grams, a necessary step in understanding the weight of the product obtained from electrolysis. The molar mass of aluminum is approximately 26.98 g/mol, meaning each mole of aluminum weighs 26.98 grams.To convert moles of aluminum to grams, use:\[\text{Mass of Aluminum} = \text{Moles of Aluminum} \times \text{Molar Mass of Aluminum}\]For example, if 74758.55 moles of aluminum are produced, converting it using its molar mass will yield a mass of approximately 2,017,092.61 grams or about 2.02 metric tons.This conversion ensures accurate scaling from laboratory calculations to full-scale industrial production, helping industries work efficiently and economically.