To determine the empirical formula of a compound given its percentage composition by mass, follow these detailed steps.
### Step 1: Percentages to Masses
We'll assume we have 100 grams of the compound. This assumption simplifies our calculations because the percentages can be directly converted to grams:
- Iron (Fe): 36.76 grams
- Sulfur (S): 21.11 grams
- Oxygen (O): 42.13 grams
### Step 2: Masses to Moles
Next, we need to convert these masses to moles by dividing by the respective atomic masses of the elements:
- Molar mass of Iron ([tex]\(Fe\)[/tex]) = 55.845 g/mol
- Molar mass of Sulfur ([tex]\(S\)[/tex]) = 32.06 g/mol
- Molar mass of Oxygen ([tex]\(O\)[/tex]) = 16.00 g/mol
#### Calculate moles of each element:
- Moles of Iron ([tex]\(Fe\)[/tex]):
[tex]\[
\frac{36.76 \text{ g}}{55.845 \text{ g/mol}} \approx 0.65825 \text{ moles}
\][/tex]
- Moles of Sulfur ([tex]\(S\)[/tex]):
[tex]\[
\frac{21.11 \text{ g}}{32.06 \text{ g/mol}} \approx 0.65845 \text{ moles}
\][/tex]
- Moles of Oxygen ([tex]\(O\)[/tex]):
[tex]\[
\frac{42.13 \text{ g}}{16.00 \text{ g/mol}} \approx 2.63313 \text{ moles}
\][/tex]
### Step 3: Simplest Mole Ratio
To find the simplest whole number ratio of the moles of the elements, we divide each mole value by the smallest number of moles we calculated:
- The smallest number of moles is approximately 0.65825.
#### Calculate ratios:
- Ratio for Iron ([tex]\(Fe\)[/tex]):
[tex]\[
\frac{0.65825}{0.65825} = 1.0
\][/tex]
- Ratio for Sulfur ([tex]\(S\)[/tex]):
[tex]\[
\frac{0.65845}{0.65825} \approx 1.0003
\][/tex]
- Ratio for Oxygen ([tex]\(O\)[/tex]):
[tex]\[
\frac{2.63313}{0.65825} \approx 4.0002
\][/tex]
### Step 4: Approximately Whole Numbers
The calculated ratios:
- Ratio for Iron ([tex]\(Fe\)[/tex]) ≈ 1
- Ratio for Sulfur ([tex]\(S\)[/tex]) ≈ 1
- Ratio for Oxygen ([tex]\(O\)[/tex]) ≈ 4
These ratios are very close to whole numbers, which means we can round them to the nearest whole number without significant loss of accuracy.
### Step 5: Write the Empirical Formula
Finally, combining these whole number ratios, we determine the empirical formula:
The empirical formula of the compound is [tex]\( \text{Fe}_1 \text{S}_1 \text{O}_4 \)[/tex], which can be simplified as [tex]\( \text{FeSO}_4 \)[/tex].
Therefore, the empirical formula is FeSO[tex]$_4$[/tex].
