To determine the mass of calcium produced and the minimum voltage required for the electrolysis of molten CaCl2, we can use the following electrochemistry principles and equations:
1. Calculate the amount of charge passed through the electrolytic cell using the formula:
Charge (Coulombs) = Current (Amperes) × Time (seconds)
2. Use Faraday's laws of electrolysis to find the amount of substance (in moles) that corresponds to the charge passed:
Moles of substance = Charge (Coulombs) / Faraday's constant
3. Finally, calculate the mass of calcium produced using its molar mass and the number of moles obtained.
Let's start with Part A:
Given:
Current = 5800 A
Time = 44 hours = 44 hours × 3600 seconds/hour = 158400 seconds
Efficiency = 69%
First, calculate the charge passed through the cell:
Charge = Current × Time
Charge = 5800 A × 158400 s
Charge = 919,200,000 Coulombs
Now, apply Faraday's laws to find the moles of calcium produced:
Faraday's constant = 96,485 C/mol (this is the charge of one mole of electrons)
Moles of calcium = Charge / Faraday's constant
Moles of calcium = 919,200,000 C / 96,485 C/mol
Moles of calcium = 9522.94 mol
Since the efficiency is 69%, multiply the moles obtained by the efficiency to find the actual moles of calcium produced:
Actual moles of calcium = Moles of calcium × Efficiency
Actual moles of calcium = 9522.94 mol × 0.69
Actual moles of calcium = 6562.0 mol (rounded to two significant figures)
Now, calculate the mass of calcium produced using the molar mass of calcium (Ca):
Molar mass of Ca = 40.08 g/mol
Mass of calcium produced = Actual moles of calcium × Molar mass of Ca
Mass of calcium produced = 6562.0 mol × 40.08 g/mol
Mass of calcium produced = 263,195.36 g ≈ 260,000 g (rounded to two significant figures)
Therefore, the mass of calcium produced by this process is approximately 260,000 grams.
Now, let's move on to Part B:
The minimum voltage needed for electrolysis can be calculated using the formula:
Voltage = Energy / Charge
However, we need to find the energy first. The energy can be calculated using the formula:
Energy = Voltage × Charge
The efficiency of the electrolytic cell is not given. Therefore, let's assume 100% efficiency for this calculation.
Energy = Voltage × Charge
Voltage = Energy / Charge
Given:
Charge = 919,200,000 Coulombs (calculated earlier)
Assuming 100% efficiency for simplicity
Assuming standard conditions (ideal conditions), we'll use the equation:
Energy = Voltage × Charge
Voltage = Energy / Charge
Energy = 1 V × 919,200,000 C
Energy = 919,200,000 Joules
Now, use the equation to find the voltage:
Voltage = Energy / Charge
Voltage = 919,200,000 J / 919,200,000 C
Voltage = 1 Volt
Therefore, the minimum voltage needed to cause electrolysis in this setup, assuming 100% efficiency and standard conditions, is 1 Volt (rounded to three significant figures).
Elemental calcium is produced by the electrolysis of molten CaCl2
Part A
What mass of calcium can be produced by this process if a current of 5800 A is applied for 44 h? Assume that the electrolytic cell is 69 %% efficient.
Express your answer using two significant figures.
Part B
What is the minimum voltage needed to cause the electrolysis?
Express your answer using three significant figures.