the major commercial aluminium ore is bauxite,AlO3.H2O(s).What is its molar mass?The analysis of a representive sample of bauxite shows it contains 70% by mass of Al2O3..What is the maximum mass of aluminium metal that could be obtained from 200kg of
mm = molar mass
am = atomic mass
200 kg x (2*am Al/mm Al2O3) x 0.70 = ? g Al
oops
That's kg not g.
To find the molar mass of bauxite (AlO3.H2O), we need to sum up the atomic masses of all the atoms in its chemical formula. Let's break it down:
Al: aluminum atom's atomic mass = 27 g/mol
O: oxygen atom's atomic mass = 16 g/mol
H: hydrogen atom's atomic mass = 1 g/mol
The formula unit AlO3.H2O consists of one aluminum atom, three oxygen atoms, and two hydrogen atoms. Therefore, the molar mass can be calculated as follows:
Molar mass of AlO3.H2O = (1 x Al) + (3 x O) + (2 x H) = (1 x 27 g/mol) + (3 x 16 g/mol) + (2 x 1 g/mol) = 102 g/mol
Therefore, the molar mass of bauxite (AlO3.H2O) is 102 g/mol.
Moving on to the second part of your question, we need the percentage by mass of Al2O3 in the bauxite. It is given as 70% by mass. To calculate the mass of Al2O3 in a 200 kg sample of bauxite, we can use the following steps:
Step 1: Calculate the mass of Al2O3
Mass of Al2O3 = (70/100) x 200 kg = 0.7 x 200 kg = 140 kg
Step 2: Convert the mass of Al2O3 to moles
Molar mass of Al2O3 = (2 x Al) + (3 x O) = (2 x 27 g/mol) + (3 x 16 g/mol) = 102 g/mol
Number of moles of Al2O3 = Mass of Al2O3 / Molar mass of Al2O3 = 140 kg / (102 g/mol) = 1372.55 mol
Step 3: Calculate the mass of aluminum (Al) in moles
Since Al2O3 and Al have a 2:1 molar ratio, the number of moles of aluminum will be half that of Al2O3.
Number of moles of Al = (1/2) x Number of moles of Al2O3 = (1/2) x 1372.55 mol = 686.275 mol
Step 4: Calculate the mass of aluminum (Al)
Molar mass of Al = 27 g/mol
Mass of Al = Number of moles of Al x Molar mass of Al = 686.275 mol x 27 g/mol = 18,549.225 g
Therefore, the maximum mass of aluminum that can be obtained from a 200 kg sample of bauxite is 18,549.225 grams (or 18.549225 kg).