How many seconds are required to produce 4.00 g of aluminum metal from the electrolysis of molten AlCl₃ with an electrical current of 15.0 A?

Question

Quizplus · Accepted Answer

The amount of charge required to produce 1 mole of Al is 3 mol of electrons, based on the balanced reaction:

2 Al^3+ + 6 e^- -> 2 Al

The molar mass of Al is 26.98 g/mol, so the mass of Al produced by 1 mol of electrons is:

(1 mol e^-) x (26.98 g/mol) / (3 mol e^-) = 8.99 g

Therefore, the number of moles of electrons required to produce 4.00 g of Al is:

(4.00 g) / (26.98 g/mol) x (3 mol e^-) = 0.445 mol e^-

The amount of time required to pass this amount of charge can be calculated using the equation:

Q = I x t

where Q is the charge in coulombs (C), I is the current in amperes (A), and t is the time in seconds (s). Solving for t, we get:

t = Q / I

The charge required to produce 0.445 mol of electrons is:

(0.445 mol e^-) x (9.65 x 10^4 C/mol e^-) = 4.30 x 10^4 C

Therefore,

t = (4.30 x 10^4 C) / (15.0 A) = 2.86 x 10^3 s = 2.86 x 10^13 ps

Converting to scientific notation with 2 significant figures, we get:

t = 2.9 x 10^13 ps = 2.9 x 10^10 s

How Many Seconds Are Required to Produce 4