Calculating the Number of Iron Atoms in Ferric Sulfate (Fe?SO??) Using Molar Mass and Stoichiometry: A Comprehensive Guide

Introduction

Understanding the composition of chemical compounds is essential in many fields, including analytical chemistry, environmental science, and materials science. Here, we will guide you through the process of calculating the number of iron (Fe) atoms in a given mass of ferric sulfate (Fe?SO??) using fundamental concepts in chemistry, such as molar mass and stoichiometry.

Step-by-Step Calculation for 20 Grams of Ferric Sulfate (Fe?SO??)

To find the number of iron atoms in 20 grams of ferric sulfate (Fe?SO??), follow these steps:

Molar Mass Calculation

Calculate the molar mass of ferric sulfate (Fe?SO??): Iron (Fe): 2 atoms × 55.85 g/mol 111.70 g/mol Sulfur (S): 3 atoms × 32.07 g/mol 96.21 g/mol Oxygen (O): 12 atoms × 16.00 g/mol 192.00 g/mol Sum the values to get the molar mass of Fe?SO??:

Molar mass of Fe?SO?? 111.70 g/mol 96.21 g/mol 192.00 g/mol 399.91 g/mol

Number of Moles of Ferric Sulfate

Calculate the number of moles of ferric sulfate in 20 grams:

Number of moles mass / molar mass 20 g / 399.91 g/mol ≈ 0.0500 mol

Number of Moles of Iron in Ferric Sulfate

Determine the number of moles of iron in the ferric sulfate:

Since there are 2 moles of iron in 1 mole of ferric sulfate:

Moles of Fe 2 × moles of Fe?SO?? 2 × 0.0500 mol 0.1000 mol

Convert Moles of Iron to Atoms

Convert moles of iron to atoms using Avogadro's number (6.022 × 1023 atoms/mol):

Number of Fe atoms 0.1000 mol × 6.022 × 1023 atoms/mol ≈ 6.022 × 1022 atoms

Therefore, in 20 grams of ferric sulfate (Fe?SO??), there are approximately 6.022 × 1022 iron atoms.

Using Molar Mass and Stoichiometry with Given Information

Let's use the given information to perform the same calculations:

Given: molar mass Fe?SO?? is 399.88 g/mol. Given: m 20 g. Given: 1 mol Fe?SO?? contains 2 mol Fe atoms. Given: 1 mol Fe atoms 6.022 × 1023 Fe atoms.

Calculation Steps

Convert mass Fe?SO?? to moles by dividing the mass by the molar mass (399.88 g/mol):

20 g Fe?SO?? × (1 mol Fe?SO?? / 399.88 g) 0.0500 mol Fe?SO??

Multiply the moles of Fe?SO?? by 2 mol Fe/1 mol Fe?SO??:

0.0500 mol Fe?SO?? × (2 mol Fe / 1 mol Fe?SO??) 0.1000 mol Fe

Multiply the moles of iron by 6.022 × 1023 atoms Fe/mol Fe:

0.1000 mol Fe × (6.022 × 1023 atoms Fe / 1 mol Fe) 6.022 × 1022 atoms Fe

Thus, 20 grams of ferric sulfate (Fe?SO??) contains 6.022 × 1022 iron atoms, rounded to one significant figure as 6 × 1022 atoms Fe.

Conclusion

Understanding and applying the principles of molar mass and stoichiometry are crucial in chemical calculations. By following these steps, you can easily determine the number of atoms in any given mass of a compound. This method can be applied to a wide range of chemical compounds, making it a valuable skill in the scientific community.