Considering the definition of empirical formula, the empirical formula is Co₁S₁O₃= CoSO₃.
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.
In this case, in first place you need to convert the number of grams given into percentage as follow:
Cobalt (Co): [tex]\frac{0.884g}{2.086 g}x100 =[/tex] 42.38 %
Sulfur (S): [tex]\frac{0.482g}{2.086 g} =[/tex] 23.11%
Oxygen (O): [tex]\frac{0.720g}{2.086 g} =[/tex] 34.52%
Assuming a 100 grams sample, the percentages match the grams in the sample. So you have 42.38 grams of cobalt, 23.11 grams of sulfur and 34.52 grams of oxygen.
Then it is possible to calculate the number of moles of each atom in the molecule, taking into account the corresponding molar mass:
Cobalt (Co): [tex]\frac{42.38g}{58.93 \frac{g}{mole} } =[/tex] 0.72 moles
Sulfur (S): [tex]\frac{23.11g}{32.06 \frac{g}{mole} } =[/tex] 0.72 moles
Oxygen (O):[tex]\frac{34.52g}{16 \frac{g}{mole} } =[/tex] 2.16 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:
Cobalt (Co): [tex]\frac{0.72 moles}{0.72 moles } =[/tex] 1
Sulfur (S): [tex]\frac{0.72 moles}{0.72 moles } =[/tex] 1
Oxygen (O): [tex]\frac{2.16 moles}{0.72 moles } =[/tex] 3
Therefore the Co: S: O mole ratio is 1: 1: 3
Finally, the empirical formula is Co₁S₁O₃= CoSO₃.
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