# Elemental calcium is produced by the electrolysis of molten CaCl2.

a) What mass of calcium can be produced by this process if a current of 7.5 * 10^3 A is applied for 48h? Assume that the electrolytic cell is 68% efficient.

b) What is he minimum voltage needed to cause the electrolysis?

## Coulombs = amperes x seconds

Convert 48 hr to seconds and that x 7500.
That number is close to 173,000 but you should get a better number and that x 7500 = about 1.3E9 C.
96,485 coulombs will plate out 40/2 = 20 g Ca.
So you should be able to plate
20 x 1.3E9/96,485 = g Ca at 100% efficiency. That x 0.68 corrects for not being 100%.

2. Look in the tables and find voltage for Cl and voltage for Ca. The larger is the one you want(ignore the sign).

## To solve the given problems, we need to understand the process of electrolysis and use relevant equations.

a) To calculate the mass of calcium produced, we need to consider the Faraday's law of electrolysis. According to this law, the amount of substance produced (in moles) is directly proportional to the number of electrons (in Coulombs) passed through the electrolytic cell, which can be determined using the formula:

n = (Q / F)

Where:
n = moles of substance produced
Q = total charge passed through the cell (in Coulombs)
F = Faraday's constant (96,485 C/mol)

First, we will determine the charge passed through the cell using the formula:

Q = I * t

Where:
Q = charge (in Coulombs)
I = current (in Amperes)
t = time (in seconds)

Since the given time is in hours, we need to convert it to seconds:

t = 48 hours * 3600 seconds/hour = 172,800 seconds

Now, we can calculate the charge passed through the cell:

Q = (7.5 * 10^3 A) * (172,800 s) = 1.296 * 10^9 C

Next, we can determine the moles of calcium produced:

n = (1.296 * 10^9 C) / (96,485 C/mol) = 1.34 * 10^4 mol

However, the problem states that the electrolytic cell is 68% efficient. This means that only 68% of the moles calculated above will actually be produced as calcium:

n_actual = 0.68 * (1.34 * 10^4 mol) = 9.112 * 10^3 mol

Finally, we can calculate the mass of calcium produced by multiplying the moles by the molar mass of calcium (40.08 g/mol):

Mass = (9.112 * 10^3 mol) * (40.08 g/mol) = 3.654 * 10^5 g or 365.4 kg

Therefore, the mass of calcium produced by this process is approximately 365.4 kg.

b) The minimum voltage needed for electrolysis can be determined using the equation:

V = E_cell / n

Where:
V = voltage (in volts)
E_cell = cell potential (in volts)
n = number of electrons involved in the reaction

The reaction for the electrolysis of molten CaCl2 is:

Ca2+ + 2e- -> Ca

Here, 2 electrons are involved in the reaction. The standard reduction potential for this reaction is not given, so we can assume it to be zero for simplicity.

Therefore, V = 0 / 2 = 0 volts

Thus, the minimum voltage needed to cause the electrolysis is zero volts.