If an electrolysis plant operates its electrolytic cells at a total current of 1.4 × 10⁶ A,how long will it take to produce one metric ton (one million grams)of Mg(s)from seawater containing Mg²⁺? (1 faraday = 96,485 coulombs)

Question

Quizplus · Accepted Answer

1 metric ton of Mg is equal to 1,000,000 grams of Mg.
The stoichiometric ratio of Mg to electrons in the reaction is 2:2 or 1:1. Therefore, for every 1 mole of Mg produced, 2 faradays or 1.93 × 105 coulombs of charge must be passed through the cell.
The molar mass of Mg is 24.31 g/mol.
Using the given information, we can calculate the amount of charge required to produce 1.00 × 106 g of Mg:

(1.00 × 106 g Mg) / (24.31 g/mol) = 4.12 × 104 mol Mg
(4.12 × 104 mol Mg) × (1.93 × 105 C/mol) = 7.96 × 109 C

Thus, a total of 7.96 × 109 C of charge is required to produce 1.00 × 106 g of Mg.

The time required to produce this amount of charge can be found using the total current and the formula:

Charge = current x time

Therefore:

time = Charge / current

time = (7.96 × 109 C) / (1.4 × 1016 A)
time = 5.69 × 105 s

Converting to hours gives:

time = 5.69 × 105 s × (1 hr / 3600 s) ≈ 1.6 h

Therefore, the answer is C) 1.6 h.

If an Electrolysis Plant Operates Its Electrolytic Cells at a Total