How long will it take to produce 78 g of Al metal by the reduction of Al³⁺ in an electrolytic cell with a current of 2.0 A?

Question

Quizplus · Accepted Answer

First, we need to balance the chemical equation:
2AlS1U1P13 + 6H2O → 3H2S1U1P2O7 + 4H3S1U1P4O4 + 2Al

We can see that for every 2 moles of AlS1U1P13, we get 2 moles of Al. Therefore, we need to calculate the number of moles of AlS1U1P13 from the given mass of Al.

78 g Al x (1 mol Al / 27 g Al) x (2 mol AlS1U1P13 / 2 mol Al) = 5.78 mol AlS1U1P13

Now we can use Faraday's law to calculate the time required for the given current to produce this amount of moles:
moles of electrons = current (in A) x time (in s) / Faraday's constant

Since each mole of Al requires 3 moles of electrons, we can write:
3(5.78 mol AlS1U1P13) = 2.0 A x t / 96500 C/mol

Solving for t, we get:
t = 116.31 hours

Therefore, the answer is D) 116 h.

How Long Will It Take to Produce 78 G of Al