Question

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 $10.7\mathrm{kJ}/\mathrm{mol}\text{ ( }1\text{ watt }=1\mathrm{J}/\mathrm{s}\text{ ). }]$

Short answer

The energy required to produce 1 kg of aluminum from aluminum oxide is approximately 14.89 kWh more than the energy required to recycle 1 kg of aluminum by melting it. Hence, it is economically feasible to recycle aluminum cans, as it saves a significant amount of energy, which leads to lower production costs and a smaller environmental impact.

Step-by-step solution

For 1 kg (1000 g) of aluminum: Number of moles = Mass / Molar Mass Number of moles = 1000 g / 27 g/mol Number of moles ≈ 37.04 mol #Step 2: Calculate the energy required to melt the aluminum# Now that we have the number of moles required, we can use the enthalpy of fusion (10.7 kJ/mol) to calculate the energy required to melt the aluminum.

Energy required = Number of moles × Enthalpy of fusion Energy required ≈ 37.04 mol × 10.7 kJ/mol Energy required ≈ 396.1 kJ #Step 3: Convert energy to kilowatt-hours (kWh)# To compare the energy required for both processes, convert the calculated energy to kilowatt-hours (kWh). We know that 1 watt is equal to 1 J/s, and 1 kilowatt-hour is equal to 3,600,000 joules.

Energy required (kWh) = Energy required (kJ) × (1kW * 3600 s) / (1 J/s * 1000 J) Energy required (kWh) = 396.1 kJ × (1/3.6) kWh/kJ Energy required (kWh) ≈ 0.11003 kWh #Step 4: Calculate the energy difference to compare the processes# We have the energy required for both processes: 15 kWh to produce 1 kg of aluminum from aluminum oxide and 0.11003 kWh to recycle 1 kg of aluminum by melting it.

Energy difference = Energy for production – Energy for recycling Energy difference ≈ 15 kWh - 0.11003 kWh Energy difference ≈ 14.88997 kWh #Conclusion:# The energy required to produce 1 kg of aluminum from aluminum oxide is approximately 14.89 kWh more than the energy required to recycle 1 kg of aluminum by melting it. Hence, it is economically feasible to recycle aluminum cans, as it saves a significant amount of energy. This reduced energy consumption leads to lower production costs and a smaller environmental impact.

Key concepts

Enthalpy of fusion

Understanding the energy involved in state changes is crucial in thermodynamics. One key concept here is the **enthalpy of fusion**. The enthalpy of fusion for a substance is the amount of energy needed to change a given amount of a solid into a liquid at its melting point. This energy is needed because the molecules in the solid need to overcome their attractions to start moving freely as a liquid. For aluminum, the enthalpy of fusion is given as 10.7 kJ/mol. When we need to melt aluminum, we use this value to calculate how much energy is necessary for this process. By multiplying the number of moles of aluminum by the enthalpy of fusion, we can find the total energy required. In our example, for melting 1 kg (or 1000 g) of aluminum, this process requires approximately 396.1 kJ. This number tells us how much energy is needed purely for the transition from solid to liquid, not involving any other processes like heating the aluminum to its melting point or any heat lost to the surroundings during this process.

Energy conversion

Energy conversion is the process of changing energy from one form to another, and it's vital in understanding efficiency across different systems. When dealing with energies in different units, conversion becomes essential. In our exercise, we initially have energy in kilojoules (kJ), used typically in chemistry and physics contexts. However, to compare it with electrical energy, which is often billed in kilowatt-hours (kWh), we need to switch units. One kilowatt-hour is equal to 3,600,000 joules (or 3.6 million joules). Thus, to convert from kJ to kWh, we divide the energy value in kJ by 3,600. Using this conversion factor, the energy needed to melt aluminum (396.1 kJ) is approximately 0.11003 kWh. This reveals just how efficient recycling is compared to initial production, considering the enormous difference in energy usage for the same amount of aluminum work.

Recycling aluminum

Recycling aluminum is not just beneficial—it is a game-changer in both economic and environmental terms. The production of aluminum from raw materials, specifically aluminum oxide, requires a substantial amount of energy, which stands at 15 kWh per kilogram. However, when we recycle aluminum, the only significant energy cost comes from melting the existing aluminum down, which takes just around 0.11003 kWh per kilogram. This striking difference highlights the benefits of recycling:

• **Cost-effectiveness**: Recycling requires far less energy, reducing overall production costs.
• **Environmental impact**: Lower energy use translates directly to a smaller environmental footprint, with decreased greenhouse gas emissions and resource consumption.
• **Resource conservation**: Recycling preserves natural resources as it diminishes the need to mine new aluminum, conserving the raw materials.

Overall, the significant energy savings from recycling make it economically feasible and environmentally responsible, contributing to sustainable practices.