Determine the mass of chlorine produced when 200A of current flows for 24 hours through a cell of molten NaCl.
To determine the mass of chlorine produced, we need to use Faraday's law of electrolysis, which states that the mass of a substance produced at an electrode is directly proportional to the amount of electric charge passed through the cell.
1. Calculate the total charge passed through the cell:
Charge (Coulombs) = Current (Amperes) x Time (seconds)
Since the time is given in hours, we need to convert it to seconds:
Time (seconds) = 24 hours x 60 minutes/hour x 60 seconds/minute
Time (seconds) = 86,400 seconds
Charge (Coulombs) = 200 Amperes x 86,400 seconds
Charge (Coulombs) = 17,280,000 Coulombs
2. Determine the number of moles of electrons transferred:
1 Faraday (F) = 96,485 Coulombs (charge per mole of electrons)
Moles of electrons = Charge (Coulombs) / 96,485 Coulombs
Moles of electrons = 17,280,000 Coulombs / 96,485 Coulombs
Moles of electrons = 179.14 moles
3. Calculate the moles of chlorine produced:
According to the balanced chemical equation for the electrolysis of molten sodium chloride (2NaCl → 2Na + Cl2), for every 2 moles of electrons, 1 mole of chlorine is produced.
Moles of chlorine = Moles of electrons / 2
Moles of chlorine = 179.14 moles / 2
Moles of chlorine = 89.57 moles
4. Determine the molar mass of chlorine:
The molar mass of chlorine (Cl) is approximately 35.45 g/mol.
5. Calculate the mass of chlorine produced:
Mass of chlorine (g) = Moles of chlorine x Molar mass of chlorine
Mass of chlorine = 89.57 moles x 35.45 g/mol
Mass of chlorine = 3,177.10 g
Therefore, the mass of chlorine produced when 200A of current flows for 24 hours through a cell of molten NaCl is approximately 3,177.10 grams.
To determine the mass of chlorine produced, we need to use the equation relating the quantity of electricity (measured in coulombs) to the amount of substance produced during electrolysis.
First, let's find the total charge (Q) in coulombs that passes through the cell. We can do this by multiplying the current (I) in amperes by the time (t) in seconds:
Q = I * t
In this case, the current is given as 200A and the time is given as 24 hours. However, we need to convert the time to seconds, so:
Q = 200A * (24 hours * 3600 seconds/hour)
Now that we have the total charge, we can use Faraday's law of electrolysis to relate it to the amount of substance produced. Faraday's constant (F) represents the charge of one mole of electrons and is approximately 96,485 coulombs/mol.
The formula is:
n = Q / F
where n is the number of moles of electrons passed through the cell. Since each mole of electrons corresponds to one mole of chlorine produced, n also represents the number of moles of chlorine produced.
Next, we need to convert the number of moles of chlorine (n) to mass using its molar mass (M). The molar mass of chlorine (Cl₂) is approximately 35.45 g/mol.
The formula is:
mass = n * M
Now we can calculate the mass of chlorine produced by following these steps:
1. Calculate the total charge (Q): Q = 200A * (24 hours * 3600 seconds/hour)
2. Calculate the number of moles of chlorine (n): n = Q / Faraday's constant (F)
3. Calculate the mass of chlorine produced: mass = n * molar mass of chlorine (M)
Plug in the values into the formulas and perform the calculations to find the mass of chlorine produced.