If an electrolysis plant operates its electrolytic cells at a total current of 1.0 × 10⁶ amp, 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

To calculate the time needed to produce one metric ton of Mg(s), we need to use the stoichiometry of the reaction and Faraday's law.

The balanced equation for the electrolysis of seawater containing MgS1U1P12+S1S1P0 is:

2MgS1U1P12+(aq) + 2H2O(l) → 2Mg(s) + O2(g) + 2H2(g)

According to the equation, for every 2 moles of Mg produced, the amount of charge needed is given by:

2 mol Mg × (2 F/mol Mg) × (96,485 C/F) = 3.88 × 10S5U1P1S1S1P20 C

Therefore, to produce one ton (1000 kg) of Mg, we need:

1000 kg Mg × (1 mol Mg/24.31 g Mg) × (3.88 × 10S5U1P1S1S1P20 C/2 mol Mg) = 7.98 × 10S7U1P1S1S1P20 C

Now, we can use Faraday's law to find the time needed:

Q = I × t

where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds.

Solving for t:

t = Q/I = (7.98 × 10S7U1P1S1S1P20 C) / (1.0 × 10S1U1P16S1S1P0 A) = 2.2 × 10S3U1P4S1S1P0 s

Converting to hours:

t = 2.2 × 10S3U1P4S1S1P0 s × (1 h/3600 s) ≈ 0.61 h ≈ 36.6 min

Therefore, the best answer choice is C, 2.2 h.

If an Electrolysis Plant Operates Its Electrolytic Cells at a Total