Considering the definition of empirical formula, the correct answer is the second option: the empirical formula is Al₂O₃.
Definition of empirical formula
The empirical formula is the simplest expression to represent a chemical compound, which indicates the elements that are present and the minimum proportion in whole numbers that exist between its atoms, that is, the subscripts of chemical formulas are reduced to the most integers. small as possible.
Empirical formula in this case
Assuming a 100 grams sample, the percentages match the grams in the sample. So you have 53 grams of Al and 47 grams of O.
Then it is possible to calculate the number of moles of each atom in the molecule, taking into account the corresponding molar mass:
Al: [tex]\frac{53 grams}{27 \frac{grams}{mole} }[/tex]= 1.9629 moles
O: [tex]\frac{47 grams}{16 \frac{grams}{mole} }[/tex]= 2.9375 moles
The empirical formula must be expressed using whole number relationships, for this the numbers of moles are divided by the smallest result of those obtained. In this case:
Al: [tex]\frac{1.9629 moles}{1.9629 moles}[/tex]= 1
O: [tex]\frac{2.9375 moles}{1.9629 moles}[/tex]≅ 1.5
You cannot have a decimal subscript, so you will multiply our answers by a factor of 2 to get to a whole number:
Al: 1× 2= 2
O: 1.5× 2= 3
Therefore the Al:O mole ratio is 2: 3
Finally, the correct answer is the second option: the empirical formula is Al₂O₃.
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