Final answer:
The question involves calculating the cost of electrical energy to electrorefine copper by considering the electrochemical equivalent of copper and the cost of electricity. It requires knowledge of electrolytic cells and how to convert charge to energy cost.
Step-by-step explanation:
Calculating the Cost of Electrical Energy for Copper Electrorefining
To calculate the cost of the electrical energy required to electrorefine copper, we must first understand the electrorefining process. Copper is refined by using electrolytic cells to deposit copper metal from a solution of copper salts. For every mole of copper deposited at the cathode, two moles of electrons are required, making the process divalent. The electrochemical equivalent of copper is the amount of copper deposited per coulomb of charge, which is given as 0.00033 g/coulomb. To find the energy cost per kilogram, we need to calculate the total charge required to deposit one kilogram of copper and then multiply this by the voltage and the cost of electricity.
First, let's calculate the total amount of charge needed to deposit 1 kg of copper:
Given that the mass (m) of copper is 1 kg (1000 g), and the electrochemical equivalent (z) is 0.00033 g/C, we can use the formula q = m/z to find the charge (q). Next, we convert the required charge into kilowatt-hours (kWh), knowing that 1 C = 1 A·s and 1 kWh = 3,600,000 A·s. After finding the charge in kWh, the energy cost can be determined by multiplying the charge in kWh by the operating voltage and the cost of electricity.
It is important to note that industrial processes use much higher currents and the voltage supplied is typically higher than the theoretical voltage due to inefficiencies and additional resistances in the system. Therefore, the provided voltage of 0.33 V is an ideal scenario and the actual costs could be higher in a practical setting.