Question

Molten magnesium chloride is electrolyzed with a current of 12.5 A for 40 minutes. Calculate the volume (at 25 °C and 1 atm) of chlorine that forms at the anode of the electrolytic cell. Also, calculate the mass of aluminum that is deposited at the cathode of an electrolytic cell containing its salt in the molten state when the same current is passed through the cell for 1.5 hours.

a) Volume of chlorine: ( 2.25 X 10^3 , L ), Mass of aluminum: ( 0.20 , g )

b) Volume of chlorine: ( 1.50 X 10^3 , L ), Mass of aluminum: ( 0.15 , g )

c) Volume of chlorine: ( 3.75 X 10^3 , L ), Mass of aluminum: ( 0.30 , g )

d) Volume of chlorine: ( 2.50 X 10^3 , L ), Mass of aluminum: ( 0.25 , g )

Answer 1

To calculate the volume of chlorine formed at the anode, we use Faraday's law and convert moles to volume using the ideal gas law. To calculate the mass of aluminum deposited at the cathode, we use Faraday's law and convert moles to mass using the molar mass of aluminum.

Step-by-step explanation:

For the first part of the question, to calculate the volume of chlorine formed at the anode, we need to use Faraday's law. The equation is:

moles of substance = (current × time) / (number of electrons × Faraday's constant)

In this case, the number of electrons involved in the reaction is 2 (since each chlorine ion accepts 2 electrons) and the Faraday's constant is 96485 C/mol. So, we can calculate:

moles of chlorine = (12.5 A × 40 min) / (2 × 96485 C/mol)

Then, we convert moles to volume using the ideal gas law:

volume of chlorine = moles of chlorine × molar volume at 25 °C and 1 atm

For the second part of the question, to calculate the mass of aluminum deposited at the cathode, we use the same approach. The equation is:

moles of substance = (current × time) / (number of electrons × Faraday's constant)

In this case, the number of electrons involved in the reaction is 3 (since each aluminum ion accepts 3 electrons). So, we can calculate:

moles of aluminum = (12.5 A × 1.5 hours) / (3 × 96485 C/mol)

Then, we convert moles to mass using the molar mass of aluminum:

mass of aluminum = moles of aluminum × molar mass of aluminum