Question

Aluminium is manufactured by electrolysis(electrolytic decomposition) of bauxite, Al2O3. How much aluminium can be obtained from 1kg of pure bauxite?

Answer 1

I'm not sure what you mean by "pure" bauxite. If that implies pure Al2O3 I don't think that is so but that must be what we are to assume.
You can get 2 mols Al for every mol of Al2O3. How many mols Al2O3 do you have in 1 kg?

Answer 2

1 mol.

Answer 3

No, you don't have 1 mol Al2O3 in 1 kg. Do you know what a mol is. A mol of Al2O3 is (in grams) 2*atomic mass Al + 3*atomic mass O = approximately 2*27 + 3*16 = about 54 + 48 = about 102 grams. Therefore, 1 kg = 1000g so in 1000g there are 1000/102 = about 9.8 mols Al2O3.
So 9.8 mols Al2O3, if it is pure Al2O3, will give you 9.8*2 = about 20 mols Al. Then grams Al = mols Al x atomic mass Al = ?grams. You can go through and clean up my approximations and come up with an answer close to what I have here.