Question

Copper has been used for thousands of years, either as a pure metal or in alloys. It is frequently used today in the production of wires and cables. Copper can be obtained through smelting or recycling. Determine the energy associated with each of these processes in order to recycle 1.02 mol of Cu. The smelting of copper occurs by the balanced chemical equation: [equation]. Where ��H��f,CuO is -155 kJ/mol. Assume the process of recycling copper is simplified to just the melting of the solid Cu starting at 25��C. The melting point of Cu is 1084.5��C with ��H��fus = 13.0 kJ/mol and a molar heat capacity, Cp,Cu = 24.5 J/mol����C.

Answer 1

A total energy of 39687.135 J is needed to recycle 1.02 mol of copper, considering both the heating to the melting point and the melting itself using the enthalpy of fusion.

Step-by-step explanation:

To determine the energy associated with the recycling of 1.02 mol of Cu (copper), we need to consider the melting process of copper starting at 25°C. The amount of energy required to first raise the temperature of copper to its melting point and then melt it can be calculated using the following steps:

1. Calculate the energy needed to heat the copper to its melting point using the formula ΔH = n * Cp * ΔT, where n is the number of moles of copper, Cp is the molar heat capacity, and ΔT is the temperature change.
2. Calculate the energy required to melt the copper using ΔHfus, which is the enthalpy of fusion.

First, to heat the copper from 25°C to 1084.5°C, we use the formula:

ΔH₁ = 1.02 mol * 24.5 J/mol°C * (1084.5°C - 25°C) = 1.02 mol * 24.5 J/mol°C * 1059.5°C = 26427.135 J

Second, the energy required to melt 1.02 mol of copper at the melting point is:

ΔH₂ = 1.02 mol * 13.0 kJ/mol = 13.26 kJ = 13260 J

Adding both energy values gives the total energy required for recycling 1.02 mol of copper:

ΔH₁ + ΔH₂ = 26427.135 J + 13260 J = 39687.135 J

Therefore, 39687.135 J of energy is needed to recycle 1.02 mol of copper through the simplified melting process.