Final answer:
The total energy associated with the processes of smelting copper and recycling 1.43 mol of copper is approximately 51884.71 J.
Step-by-step explanation:
The total energy associated with the processes of smelting copper and recycling 1.43 mol of copper can be calculated by considering the enthalpy changes involved in each process. In the smelting process, copper oxide (CuO) is reduced to form copper (Cu) according to the given balanced chemical equation.
Using this equation, we can calculate the enthalpy change for the smelting process using the enthalpies of formation:
ΔH°rxn = nΔH°f,products - mΔH°f,reactants
Substituting the values, we get:
ΔH°rxn = 1 mol × (-155 kJ/mol) - 0 mol × (0 kJ/mol)
ΔH°rxn = -155 kJ/mol
For the process of recycling copper, we are given the molar heat capacity (Cp,Cu) and the enthalpy of fusion (ΔH°fus) for copper. To calculate the total energy, we need to consider the heat required to raise the temperature of 1.43 mol of copper from 25°C to its melting point (1084.5°C) and the heat required for the fusion (melting) process.
The amount of heat required to raise the temperature can be calculated using the equation:
q = nCΔT
Substituting the values, we get:
q = 1.43 mol × (24.5 J/mol·°C) × (1084.5°C - 25°C)
q = 33294.71 J
The amount of heat required for fusion can be calculated using the equation:
q = nΔH°fus
Substituting the values, we get:
q = 1.43 mol × (13.0 kJ/mol) × (1000 J/1 kJ)
q = 18590 J
The total energy associated with the recycling process is the sum of the heat required for temperature change and fusion:
Total energy = q1 + q2 = 33294.71 J + 18590 J
Total energy = 51884.71 J
Therefore, the total energy associated with the processes of smelting copper and recycling 1.43 mol of copper is approximately 51884.71 J.