Question

It takes 15 kWh (kilowatt hours) of electrical energy toproduce 1.0 kg of aluminum metal from aluminium oxide by the Hall-Heroult process. Compare this value with the amount of energy necessary to melt 1.0 kg of aluminum metal. Why is it economically feasible to recycle aluminum cans? (The enthalpy of fusion for aluminium metal is 10.7 kJ/mol and 1 watt = 1 J/s.)

Short answer

Theenergy needed for aluminum recycling is 397 kJ/kg Al.The energy needed for aluminum recycling is less than the production of metal by the electrolysis method. It is more feasible for aluminum recycling than production using the Hall-Heroult process.

Step-by-step solution

Reaction for the Hall-Heroult process

The reaction for the Hall-Heroult process can be denoted as:

$2A{l}_2{O}_3+3C\to 4Al+3C{O}_2$

Finding the energy required to recycle aluminum

The energy required for the production of 1 kg Al metal and the amount of energy needed per Kg of Al can be denoted as:

$$\begin{gathered} Energy=\left(\frac{15 k wh}{1 kg Al}\right)\left(\frac{1000 jH}{1 s}\right)\left(\frac{3600 s}{1 h}\right) \\ Energy=5.4\times {10}^4 kJ/kg Al \end{gathered}$$

Then,

$$\begin{gathered} Energy=\left(\frac{10.7 kJ}{1 mol Al}\right)\left(\frac{1 mol Al}{26.98 g Al}\right)\left(\frac{{10}^3 g Al}{1 kg Al}\right) \\ =397 kJ/kg Al \end{gathered}$$

Theenergy needed for aluminum recycling is 397 kJ/kg Al.The energy needed for aluminum recycling is less than the production of metal by the electrolysis method. It is more feasible for aluminum recycling than production using the Hall-Heroult process.