To determine the empirical formula of the compound, let’s go through the detailed step-by-step process of converting the percentage composition to moles and then finding the simplest whole number ratio.
### Step 1: Convert Percentage to Moles
We start by converting the percentage composition of each element into moles. This is done by dividing the percentage by the atomic mass of each element.
1. Iron (Fe):
[tex]\[
\text{Moles of Fe} = \frac{36.76}{55.845} = 0.6582505148177993
\][/tex]
2. Sulfur (S):
[tex]\[
\text{Moles of S} = \frac{21.11}{32.06} = 0.6584529008109794
\][/tex]
3. Oxygen (O):
[tex]\[
\text{Moles of O} = \frac{42.13}{16.00} = 2.633125
\][/tex]
### Step 2: Normalize the Moles
Next, we find the element with the smallest number of moles and divide the mole values of each element by this smallest number to get the simplest whole number ratio.
The smallest number of moles is for iron (Fe), which is approximately 0.6582.
1. Ratio of Fe:
[tex]\[
\frac{0.6582505148177993}{0.6582505148177993} = 1.0
\][/tex]
2. Ratio of S:
[tex]\[
\frac{0.6584529008109794}{0.6582505148177993} = 1.000307460440401 \approx 1
\][/tex]
3. Ratio of O:
[tex]\[
\frac{2.633125}{0.6582505148177993} = 4.0001867689064206 \approx 4
\][/tex]
Thus, we obtain the ratio of Fe : S : O as 1 : 1 : 4.
### Step 3: Write the Empirical Formula
The empirical formula of the compound is based on these whole number ratios:
[tex]\[
\text{Fe}_1\text{S}_1\text{O}_4
\][/tex]
This can be simplified to:
[tex]\[
\text{FeSO}_4
\][/tex]
So, the correct answer is:
Fe, S, 4.
