Gold (atomic mass = 197 g/mol) is plated from a solution of chlorauric acid, HAuCl₄; it deposits on the cathode. Calculate the time it takes to deposit 0.55 g of gold, passing a current of 0.12 amperes. (1 faraday = 96,485 coulombs)

Question

Quizplus · Accepted Answer

The first step is to calculate the number of moles of gold that will be deposited:

Atomic mass of gold = 197 g/mol
Moles of gold = Mass of gold / Atomic mass of gold
Moles of gold = 0.55 g / 197 g/mol
Moles of gold = 0.00279 mol

Next, we can use Faraday's Law of Electrolysis to calculate the amount of time (t) required to deposit this amount of gold:

Q = nF
where
Q = total charge passed in coulombs
n = number of moles of electrons transferred
F = Faraday's constant = 96,485 coulombs/mol

In this case, each gold ion (Au3+) receives 3 electrons to become neutral gold atoms, so:

n = 0.00279 mol x 3 = 0.00837 mol e-
Q = 0.00837 mol x 96,485 coulombs/mol = 808 coulombs

Finally, we can use the definition of current (I = Q/t) to solve for time:

t = Q / I
t = 808 coulombs / 0.12 A
t = 6733.3 seconds

Converting to hours:

t = 6733.3 seconds x (1 min / 60 seconds) x (1 hour / 60 min)
t = 1.87 hours, or about 1.9 hours

Therefore, the best choice is C.

Gold (Atomic Mass = 197 G/mol) Is Plated from a Solution