Question

. It takes \(15 \mathrm{kWh}\) (kilowatt-hours) of electrical energy to produce \(1.0 \mathrm{~kg}\) of aluminum metal from aluminum oxide by the Hall-Heroult process. Compare this to the amount of energy necessary to melt \(1.0 \mathrm{~kg}\) of aluminum metal. Why is it economically feasible to recycle aluminum cans? (The enthalpy of fusion for aluminum metal is \(10.7 \mathrm{~kJ} / \mathrm{mol}[1\) watt \(=1 \mathrm{~J} / \mathrm{s}] .\) )

Short answer

The energy required to produce aluminum from aluminum oxide is 54000 kJ, whereas the energy needed to melt aluminum is only 396.12 kJ. The significant difference in energy requirements makes it economically feasible to recycle aluminum cans. By recycling aluminum cans, industries can save a substantial amount of energy and reduce electricity costs.

Step-by-step solution

Calculate the energy needed to produce 1 kg of aluminum from aluminum oxide

According to the problem, 15 kWh of electrical energy are required to produce 1 kg of aluminum metal from aluminum oxide. To make the comparison, we need to convert this energy to the same units as the enthalpy of fusion (which is given in kJ/mol). Energy for production = 15 kWh × (3600 s/h) × (1 J/s) × (1 kJ/1000 J) Energy for production = 54000 kJ

Determine the number of moles of aluminum in 1 kg

In order to calculate the energy required to melt 1 kg of aluminum, we must first determine the number of moles of aluminum in it. The molar mass of aluminum is approximately 26.98 g/mol. Number of moles = (1 kg aluminum) × (1000 g/kg) × (1 mol/26.98 g) Number of moles ≈ 37.04 mol

Calculate the energy needed to melt 1 kg of aluminum

Now that we have determined the number of moles of aluminum in 1 kg, we can calculate the energy required to melt it using the enthalpy of fusion, given as 10.7 kJ/mol. Energy for melting = (37.04 mol) × (10.7 kJ/mol) Energy for melting ≈ 396.12 kJ

Compare the energies required for both processes

We now have the energy required to produce aluminum from aluminum oxide and the energy required to melt it. Let's compare the two values: Energy for production = 54000 kJ Energy for melting = 396.12 kJ As we can see, the energy required to produce aluminum from aluminum oxide (54000 kJ) is significantly higher than the energy needed to melt aluminum (396.12 kJ).

Explain why recycling aluminum cans is economically feasible

Based on our calculations, we can conclude that the recycling of aluminum cans is economically feasible due to the significant difference in energy requirements between producing aluminum from aluminum oxide and melting it. By recycling aluminum cans, industries can save a substantial amount of energy (and, by extension, save on electricity costs) as the energy needed to melt the aluminum is far lower than the energy required to produce it from aluminum oxide.

Key concepts

Hall-Heroult Process

The Hall-Heroult process is the primary method used to extract aluminum from its oxide, also known as alumina. This process takes place in an electrolytic cell, where alumina is dissolved in molten cryolite and subjected to a strong electrical current. The electricity causes a chemical reaction that separates the aluminum ions from the oxygen, allowing pure aluminum to deposit at the cathode. This method, however, is incredibly energy-intensive. Understanding this process is fundamental when discussing the energy requirements and the sustainability of aluminum production.

The comparison between the energy consumed during the Hall-Heroult process and the melting of aluminum illustrates why recycling is more energy-efficient. As can be seen from the textbook exercise, the production of aluminum from its oxide through this electrochemical procedure requires a considerable amount of energy, compared to simply melting the metal.

Enthalpy of Fusion

The enthalpy of fusion is the amount of energy needed to change a substance from solid to liquid at its melting point without changing its temperature. For aluminum, the enthalpy of fusion is relatively low, at 10.7 kJ/mol. This means that once aluminum is produced, it requires relatively little energy to melt it down again. This is a crucial fact when considering the benefits of recycling.

Using the information provided in the exercise, it's clear that there's a stark contrast in energy demand between producing aluminum and melting it, emphasizing the natural advantage of recycling over producing new aluminum from ore.

Aluminum Recycling Economics

Recycling aluminum is economically beneficial because it requires significantly less energy than producing new aluminum from ore. According to the calculations in the textbook exercise, melting aluminum only needs about 0.73% of the energy required to produce it from aluminum oxide. This huge difference translates to reduced energy costs, making recycling an economically viable and preferred process.

In other words, recycling not only conserves resources but also offers financial incentives due to its lower energy requirements. It reduces the demand for electricity and the associated costs, while also minimizing environmental impact.

Molar Mass of Aluminum

The molar mass of a substance is the mass of one mole of that substance. It is a critical factor in converting between mass and number of moles, which is essential when dealing with chemical reactions and processes. For aluminum, the molar mass is approximately 26.98 g/mol. This value is used in energy conversion calculations because it allows one to determine the moles present in a given mass of aluminum, which is necessary to calculate the energy needed for its transformation.

In the context of our exercise, knowing the molar mass of aluminum enables us to calculate the number of moles in 1 kg of aluminum, which in turn helps us determine the total energy needed to melt it from its solid state using its enthalpy of fusion.

Energy Conversion Calculations

Energy conversion calculations involve converting different units of energy to facilitate comparisons or perform chemical calculations. These conversions allow us to understand and compare the energy consumption of different processes quantitatively. In the provided solution, we convert electrical energy from kilowatt-hours (kWh) to kilojoules (kJ), as this common unit allows comparison with the enthalpy of fusion, which is also in kJ/mol.

Students must grasp this conversion since it enables us to compare the energy requirements of creating aluminum via the Hall-Heroult process versus simply melting already available aluminum. The textbook exercise uses these calculations to illustrate the immense energy savings associated with the recycling of aluminum, providing a quantitative foundation for understanding recycling's economic benefits.