Question

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 8500 AA is applied for 42 hh? Assume that the electrolytic cell is 59 %% 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.

Answer 1

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.

Answer 2

The minimum voltage needed for the electrolysis is approximately -0.328 V. Note that the negative sign indicates that the process is consuming energy, which is expected for an electrolysis reaction.

Part A:

To calculate the mass of calcium produced during the electrolysis of molten CaCl2, you can use the formula:

Mass (g) = (Current (A) × Time (s) × Atomic Mass (g/mol)) / (2 × Faraday's Constant (C/mol))

First, let's calculate Faraday's constant (F):

Faraday's Constant (F) = 96,485 C/mol

Given:

Current (I) = 8500 A

Time (t) = 42 hours = 42 hours × 3600 seconds/hour = 151,200 seconds

Atomic Mass of Calcium (Ca) = 40.08 g/mol (rounded to two decimal places)

Efficiency (η) = 59% = 0.59 (as a decimal)

Now, calculate the mass of calcium produced:

Mass (g) = (8500 A × 151,200 s × 40.08 g/mol) / (2 × 96,485 C/mol) × 0.59

Mass ≈ 82.82 g

Rounded to two significant figures, the mass of calcium produced is approximately 83 g.

Part B:

The minimum voltage needed for the electrolysis can be calculated using Faraday's laws of electrolysis.

Faraday's First Law states that the mass of a substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through it.

Faraday's Second Law states that the mass of different substances produced by the same quantity of electricity is directly proportional to their equivalent weights.

First, calculate the equivalent weight of calcium (Eq. Wt. Ca) using its atomic mass:

Eq. Wt. Ca = Atomic Mass / Valency = 40.08 g/mol / 2 (since Ca²⁺ has a valency of 2) = 20.04 g/mol

Now, calculate the charge (Coulombs) required to produce 1 mole of calcium:

Charge (C) = Eq. Wt. Ca × Faraday's Constant = 20.04 g/mol × 96,485 C/mol = 1,940,359.4 C

To find the minimum voltage, we need to calculate it using the formula:

Voltage (V) = Energy (Joules) / Charge (Coulombs)

First, calculate the energy (Joules) required to produce 83 g of calcium:

Energy (J) = Mass (g) × (1 g = 0.001 kg) × Specific Heat Capacity (J/g°C) × Temperature Change (°C)

Assuming the temperature change is negligible, the energy is approximately equal to the enthalpy change (ΔH) for the formation of calcium from calcium ions:

Energy (J) ≈ ΔH = -635 kJ/mol = -635,000 J/mol

Now, calculate the voltage:

Voltage (V) = Energy (J) / Charge (C) = (-635,000 J/mol) / 1,940,359.4 C

Voltage (V) ≈ -0.328 V (rounded to three significant figures)

So, the minimum voltage needed for the electrolysis is approximately -0.328 V. Note that the negative sign indicates that the process is consuming energy, which is expected for an electrolysis reaction.