Chapter 17: 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 \(10.7 \mathrm{kJ} / \mathrm{mol} \text { ( } 1 \text { watt }=1 \mathrm{J} / \mathrm{s} \text { ). }]\)

Short Answer

Expert verified

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.