Metallic magnesium can be made by the electrolysis of molten MgCl2. (a) What mass of Mg is formed by passing a current of 4.55 A through molten MgCl2 for 4.50 days? (b) How many minutes are needed to plate out 25.00 g Mg from molten MgCl2 using 3.50 A of current?

Verified step by step guidance

1. Step 1: Determine the total charge passed through the system using the formula Q = I \times t, where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds. Convert the given time from days to seconds for part (a) and from minutes to seconds for part (b).
2. Step 2: Use Faraday's laws of electrolysis to relate the charge to the amount of substance. The number of moles of electrons (n_e) is given by n_e = \frac{Q}{F}, where F is Faraday's constant (approximately 96485 C/mol).
3. Step 3: For the electrolysis of MgCl_2, determine the stoichiometry of the reaction. The half-reaction for the formation of magnesium is Mg^{2+} + 2e^- \rightarrow Mg. This indicates that 2 moles of electrons are required to produce 1 mole of Mg.
4. Step 4: Calculate the moles of Mg produced using the stoichiometry from Step 3. For part (a), use the moles of electrons calculated to find the moles of Mg. For part (b), use the given mass of Mg to find the moles of Mg using its molar mass.
5. Step 5: Convert the moles of Mg to mass for part (a) using the molar mass of Mg (24.305 g/mol). For part (b), use the moles of Mg and the stoichiometry to find the total charge required, then calculate the time in seconds and convert it to minutes.