Question

It takes 45.0 kWh (kilowatt-hours) of electrical energy to produce 3.00 kg aluminum metal from aluminum oxide by the Hall-Heroult process.

What amount of energy is necessary to melt 3.00 kg aluminum metal? The enthalpy of fusion for aluminum metal is 10.7 kJ/mol (1 watt = 1 J/s).

Answer 1

Given Value,

(1 ) mass of Al= 3.00kg = 3000g

(2) 1j/s = 1watt

Or

1J = 1watt-s

1J = (10^-3kw)(1/3600)h

1J = 2.778×10^-7kwh

(3) enthalpy of fusion = 10.7kJ/mol

Enthalpy of fusion = 10.7×10³ J/mol

we know that,

molar mass of Al = 26.98g/mol

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Step(1) Calculation for number of moles of Al

number of moles = mass/Molar mass

Number of moles of Al = 3000g/(26.98g/mol)

Number of moles of Al = 111.193mol

Step(2) Calculation for necessary energy to melt Al

Energy = (number of moles of Al)×(Enthalpy of fusion of Al)

Energy = (111.193mol)×(10.7×10³ J/mol)

Energy = 1189.77×10³J

Energy = 1.18977×10⁷ J

using the value , 1J = 2.778×10^-7 kWh

Energy = (1.18977×10⁷ )×(2.778×10^-7kWh)

Energy = 3.305kWh

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