Determining the Number of Sulfur Atoms in Iron(III) Sulfide

Iron(III) sulfide (Fe2S3) is a compound with a complex structure, and to fully understand its composition, we need to determine the number of sulfur atoms it contains in a given mass. This article will guide you through the process of how to calculate it.

Step 1: Determine the Molar Mass of Iron(III) Sulfide

The first step is to figure out the molar mass of iron(III) sulfide, which is key to solving the problem. The formula for iron(III) sulfide is Fe2S3, where Fe represents iron and S stands for sulfur.

Calculating Molar Mass

To calculate the molar mass of Fe2S3, we need the atomic masses of iron (Fe) and sulfur (S). From the periodic table, we can see that:

Iron (Fe) has a molar mass of approximately 55.85 g/mol. Sulfur (S) has a molar mass of approximately 32.07 g/mol.

The formula weight of Fe2S3 is calculated as follows:

Formula weight of Fe2S3 2 x Molar mass of Fe 3 x Molar mass of S

Substituting the atomic masses:

Formula weight of Fe2S3 2 x 55.85 g/mol 3 x 32.07 g/mol

Performing the calculation:

Formula weight of Fe2S3 111.70 g/mol 96.21 g/mol 207.91 g/mol

Step 2: Calculate the Number of Moles of Iron(III) Sulfide

Once we have the molar mass, we can determine the number of moles of iron(III) sulfide in 62 g. The formula is:

Number of moles Mass / Molar mass

Substituting the values:

Number of moles of Fe2S3 62 g / 207.91 g/mol ≈ 0.298 mol

Step 3: Determine the Number of Moles of Sulfur

Since each formula unit of iron(III) sulfide (Fe2S3) contains 3 sulfur atoms, the number of moles of sulfur can be calculated as:

Moles of S Moles of Fe2S3 x 3 mol S/mol Fe2S3

Substituting the values:

Moles of S 0.298 mol Fe2S3 x 3 mol S/mol Fe2S3 ≈ 0.894 mol S

Step 4: Convert Moles of Sulfur to Atoms

Finally, to convert moles of sulfur to atoms, we use Avogadro's number (6.022 x 1023 atoms/mol). The formula is:

Number of atoms of S Moles of S x 6.022 x 1023 atoms/mol

Substituting the values:

Number of atoms of S 0.894 mol S x 6.022 x 1023 atoms/mol ≈ 5.375 x 1023 atoms

Therefore, there are approximately 5.38 x 1023 atoms of sulfur in 62 g of iron(III) sulfide Fe2S3.

Advanced Calculations

An alternative approach to the calculation is to simplify the problem by first finding the formula weight of iron(III) sulfide and then determining the number of moles of iron(III) sulfide in 62 g:

Step 1: Formula weight of Fe2S3 2 x 55.845 g/mol 3 x 32.06 g/mol 207.87 g/mol

Step 2: Number of moles of Fe2S3 62 g / 207.87 g/mol ≈ 0.30 mol

Step 3: Total number of molecules of Fe2S3 Avogadro's number x 0.30 mol

Total number of molecules of Fe2S3 6.022 x 1023 atoms/mol x 0.30 mol ≈ 1.8066 x 1023 molecules

Step 4: Total number of sulfur atoms 1.8066 x 1023 molecules x 3 atoms/sulfur atom 5.4198 x 1023 sulfur atoms

Conclusion

This calculation allows us to accurately determine the number of sulfur atoms in a given mass of iron(III) sulfide, which can be a crucial piece of information in various scientific and industrial applications. Understanding these steps can help researchers and engineers in fields such as materials science and analytical chemistry.