Question

Metallic magnesium can be made by the electrolysis of molten \(\mathrm{MgCl}_{2}\). (a) What mass of \(\mathrm{Mg}\) is formed by passing a current of \(4.55\) A through molten \(\mathrm{MgCl}_{2}\), for \(3.50\) days? (b) How many minutes are needed to plate out \(10.00 \mathrm{~g} \mathrm{Mg}\) from molten \(\mathrm{MgCl}_{2}\), using \(3.50 \mathrm{~A}\) of current?

Short answer

(a) Approximately 692.00 g of Mg is formed by passing a current of 4.55 A through molten MgCl2 for 3.50 days. (b) It takes approximately 94.63 minutes to plate out 10.00 g of Mg from molten MgCl2 using 3.50 A of current.

Step-by-step solution

(a) Calculate the charge passed through molten MgCl2

First, we need to find the total charge passed through the molten MgCl2. We are given the current (4.55 A) and time (3.50 days). Convert the time to seconds and calculate the charge. Time = 3.50 days × 24 hours/day × 3600 seconds/hour = 302400 seconds Charge (Q) = Current (I) × Time (t) Q = 4.55 A × 302400 s Q = 1375920 Coulombs

(a) Calculate the moles of Mg formed

Now, we will calculate the number of moles of Mg formed during electrolysis. Magnesium has a valency of +2, so z = 2. n = (Q × z) / F n = (1375920 C × 2) / 96485 C/mol n = 28.490 moles

(a) Calculate the mass of Mg formed

Now, we will calculate the mass of Mg formed during electrolysis. The molar mass of Mg is 24.305 g/mol. Mass of Mg = Moles of Mg × Molar mass of Mg Mass of Mg = 28.490 moles × 24.305 g/mol Mass of Mg ≈ 692.00 g So, approximately 692.00 g of Mg is formed by passing a current of 4.55 A through molten MgCl2 for 3.50 days.

(b) Calculate the moles of Mg to plate out

We are given that 10.00 g of Mg needs to be plated out. We will first calculate the number of moles of Mg. Moles of Mg = Mass of Mg / Molar mass of Mg Moles of Mg = 10.00 g / 24.305 g/mol Moles of Mg ≈ 0.4116 moles

(b) Calculate the required charge for plating out Mg

Now, we will find the required charge to plate out the given moles of Mg. We will use the formula n = (Q × z) / F and solve for Q. Q = n × F / z Q = 0.4116 moles × 96485 C/mol / 2 Q ≈ 19874.42 Coulombs

(b) Calculate the time in minutes to plate out Mg

Now, we will find the time needed to plate out Mg using 3.50 A of current. We will use the formula Q = It and solve for t. Time (t) = Charge (Q) / Current (I) t = 19874.42 C / 3.50 A t ≈ 5678.12 seconds Now, convert the time to minutes: Time = 5678.12 seconds × (1 minute / 60 seconds) ≈ 94.63 minutes So, it takes approximately 94.63 minutes to plate out 10.00 g of Mg from molten MgCl2 using 3.50 A of current.