Question

Metallic magnesium can be made by the electrolysis of molten MgCl2.

(a) What mass of Mg is formed by passing a current of 6.79 A through molten MgCl2 for 1.80 days? The unbalanced chemical reaction representing this electrolysis is shown below. MgCl2 Mg + Cl2 g of Mg is formed by this electrolysis.

(b) How many minutes are needed to plate out 11.00 g of Mg from molten MgCl2 using 5.46 A current? minutes are needed.

Answer 1

1. What mass of Mg is formed by passing a current of 6.79 A through molten MgCl2 for 1.80 days?

MgCl2 --------> Mg⁺² + 2 Cl^-

To obtain the mass of magnesium, we follow this way: we obtain Coulombs ---> then the mols of electrons present in the redox reaction ----> then we solve for the mols of Mg ----> and with the molar mass, we obtain the mass of Mg.

We need the following equation to solve for Coulombs:

C = A · s

1 C = 1 A · s ---> This means that 1 Coulomb is equivalent to the charge passing through any point of a conductor (in 1 second) with a current at constant intensity (1 Ampere).

1 mol of electrons = 96.500 Coulombs.

Molar Mass of Magnesium = 24,3050 g/mol

Current = 6,79 A

Time = 1,80 days

We convert days into seconds:

1,80 days (24 hours / 1 day) (60 min / 1 hour) (60 sec / 1 min) = 155.520 sec

Now, we write the half-reaction for Mg, the cathode (reduction):

Mg⁺² + 2e^- ------> Mg

We solve for Coulombs:

C = 6,79 A x 155.520 sec

C = 1.055.980,80

Now, we solve for mass of Magnesium:

1.055.980,80 C x (1 mol e^- / 96.500 C) (1 mol Mg / 2 mol e^-) (24,305 g Mg / 1 mol Mg) = 132.98 g of Mg.

Mass of Mg = 132.98 g

b) How many minutes are needed to plate out 11.00 g of Mg from molten MgCl2 using 5.46 A current? minutes are needed.

Here we start the problem knowing the mass of Mg and knowing the amperes, and we need to calculate time (in minutes).

First we calculate mols of Mg with the molar mass of Mg, then we calculate mols of electrons and finally we calculate time with Faraday constant.

11.00 g of Mg (1 mol Mg / 24.305 g Mg) (2 mol e^- / 1 mol Mg) = 0.9052 mols of e^-

We know that 1 ampere is equivalent to 1 Coulomb / second. So, 5.46 A = 5.46 C / s.

Faraday constant: 96.485 C / mol.

Mols of electrons = I (charge) x t (time) / F (Faraday constant)

0.9052 mols of e^- = 5.46 C s ^-1 x time in seconds / 96485 C mol^-1

S = 15.996,01

15.996,01 seconds (1 min / 60 sec) = 266,60 minutes