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Chapter 18: Problem 131

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

Short Answer

Expert verified
The energy required to produce 1 kg of aluminum from aluminum oxide is 54,000,000 J, while the energy needed to melt 1 kg of aluminum metal is only 395,900 J. Recycling aluminum cans consumes significantly less energy compared to producing new aluminum from its oxide, making it economically feasible and resource-efficient.

Step by step solution

01

Find the energy spent producing 1 kg of aluminum from aluminum oxide

We are given that it takes 15 kWh of electrical energy to produce 1 kg of aluminum from aluminum oxide. First, let's convert this kilowatt-hours to joules (one watt = one joule per second, and 1 kW = 1000 W): \( 15 \, \mathrm{kWh} \times \dfrac{1000 \, \mathrm{J}}{\mathrm{W} \cdot \mathrm{s}} \times \dfrac{3600 \, \mathrm{s}}{\mathrm{hr}} = 54,000,000 \, \mathrm{J} \) So, it takes 54,000,000 J of electrical energy to produce 1 kg of aluminum from aluminum oxide.
02

Calculate the energy needed to melt 1 kg of aluminum metal

First, we need to find the amount of aluminum in moles. The molar mass of aluminum is about 27 g/mol. So, 1 kg (1000 g) of aluminum corresponds to: \(\dfrac{1000 \, \mathrm{g}}{27 \, \mathrm{g/mol}} ≈ 37 \, \mathrm{moles}\) Now, we multiply the moles of aluminum by the enthalpy of fusion (10.7 kJ/mol) to find the energy needed to melt this mass of aluminum: \( 37 \, \mathrm{moles} \times 10.7 \, \dfrac{\mathrm{kJ}}{\mathrm{mol}} = 395.9 \, \mathrm{kJ} \) Let's convert this to joules: \(395.9 \, \mathrm{kJ} \times \dfrac{1000 \, \mathrm{J}}{\mathrm{kJ}} = 395,900 \, \mathrm{J} \) So, it takes 395,900 J of energy to melt 1 kg of aluminum metal.
03

Compare the energy spent producing vs. melting aluminum

Now we compare the energy required to produce new aluminum (54,000,000 J) to the energy required to melt aluminum (395,900 J).
04

Determine the economic feasibility of recycling aluminum cans

It is evident that the energy required to produce new aluminum from aluminum oxide is significantly greater than the energy needed to melt aluminum. Recycling aluminum cans requires only melting the aluminum, which consumes considerably less energy compared to producing new aluminum from its oxide. This difference in energy consumption makes recycling aluminum cans economically feasible, as it saves a significant amount of energy and resources that would otherwise be used to extract aluminum from aluminum oxide.

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