Question

About 50,000 KJ of electrical energy is required to produce 1kg of Al from its $\mathit{A}\mathit{l}{\left(OH\right)}_{\mathbf{3}}$ore. The major energy lost in recycling aluminum cans is the melting of the aluminum. The enthalpy of fusion of $\mathit{A}\mathit{l}\left(s\right)$ is $\mathbf{10}\mathbf{.}\mathbf{7}\mathit{K}\mathit{J}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}$.Compare the energy cost for making new aluminum with that for recycling.

Short answer

Amount of energy required to melt 1 kg Aluminium= $\text{396.97} \text{KJ}$

0.8% of the total energy required for production of 1 kg of Aluminum is used for melting 1 kg Aluminum.

Step-by-step solution

Step (1):- Calculation of number of moles of Aluminium

Mass of Aluminum that is to be recycled $\text{= 1Kg = 1000 g}$

Molar mass of Aluminum $=26.98 \text{g/mol}$

Number of moles of Aluminium present in $\text{1000} \text{g =}\frac{\text{1000g}}{\text{26.98g/mol}}\text{=} \text{37.1} \text{moles}$

Step (2):- Calculation of energy required for the melting of  37.1mole.

Enthalpy of fusion of Al $\text{= 10.7} \text{KJ/mol}$

Amount of energy required to melt

$\text{37.1} \text{mole = 10.7} \text{KJ/mol}\times \text{37.1mol} \text{=} \text{396.97} \text{KJ}$

Step (3):- Comparison of the energy cost for new production with melting

Energy required to produce $\text{1kg}$Aluminium$=50,000 \text{KJ}$

Energy required to melt 1 kg Aluminium$=396.97 \text{KJ}$

Percentage of energy $=\frac{396.96}{50,000}\times 100\%=0.8\%$

Therefore, 0.8% of the total energy required for production of 1 kg of Aluminum is used for melting 1 kg Aluminum.