Can I get help on this?

Question

Gallium is produced by the electrolysis of a solution made by dissolving gallium oxide in concentrated NaOH(aq). Calculate the amount of Ga(s) that can be deposited from a Ga(III) solution using a current of 0.860 A that flows for 20.0 min.\

Mass=G?

Answer 1

Ga³⁺(aq) + 3e- ==> Ga(s)

20 min x 60 sec / min = 1200 sec

1200 sec x 0.860 C / sec = 1032 C

1032 C x 1 mol e- / 96485 C =0.0107 moles of electrons

0.0107 mols e- x 1 mol Ga / 3 mols e- = 3.57x10^-3 mols Ga

3.57x10^-3 mols Ga x 69.7 g Ga / mol = 0.249 g Ga

Answer 2

The first step to solve this problem is to write the balanced chemical equation for the electrolysis of Ga(III) in the solution:

2 Ga(III) + 6 OH(-) → 2 Ga + 3 H2O + 6 e(-)

From this equation, we can see that for every six electrons transferred, two moles of Ga(III) ions are reduced to two moles of gallium atoms.

Next, we need to calculate the amount of charge (Q) that flows through the solution using the current (I) and time (t) given in the problem:

Q = I * t = 0.860 A * 20.0 min * 60 s/min = 1032 C

Then, we can use Faraday's law of electrolysis to relate the amount of charge passed to the amount of substance produced:

n = Q / (F * z)

where n is the number of moles of substance produced, Q is the amount of charge passed, F is the Faraday constant (96,485 C/mol e(-)), and z is the number of electrons transferred per mole of substance (in this case, z = 6 because six electrons are transferred for every two moles of Ga(III) ions reduced).

Substituting the values given, we obtain:

n = 1032 C / (96485 C/mol e(-) * 6) = 0.00286 mol

Finally, we can calculate the mass of gallium produced using its molar mass (69.72 g/mol):

Mass of Ga = n * Molar mass = 0.00286 mol * 69.72 g/mol = 0.199 g

Therefore, the amount of Ga that can be deposited from a Ga(III) solution using a current of 0.860 A that flows for 20.0 min is 0.199 g.