Answer:
To determine the empirical formula of a compound, we need to know the relative amounts of each element in the compound. Given the masses of iron and sulfur, we can calculate the number of moles of each element present:
moles of iron = 39.27 g / 55.85 g/mol = 0.703 mol
moles of sulfur = 33.77 g / 32.06 g/mol = 1.053 mol
We can then find the ratio of these moles by dividing both by the smallest number of moles (0.703):
0.703 mol Fe : 1.053 mol S
0.667 Fe : 1.000 S
This ratio indicates that there are approximately 0.667 atoms of iron for every 1 atom of sulfur in the compound.
To convert this ratio to a whole-number ratio of atoms, we need to multiply by a factor that will give us whole numbers. We can do this by dividing both sides of the ratio by the smallest number of atoms:
0.667 Fe : 1.000 S
0.667/0.667 Fe : 1.000/0.667 S
1.000 Fe : 1.498 S
This gives us a ratio of approximately 1 atom of iron for every 1.498 atoms of sulfur. To get a whole-number ratio, we can multiply both sides by 2:
2.000 Fe : 2.996 S
Rounding to the nearest whole number, we get a ratio of:
2 Fe : 3 S
Therefore, the empirical formula of the compound is Fe2S3.