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What is the empirical formula?

A compound is used to treat iron deficiency in people. It contains [tex]36.76\%[/tex] iron, [tex]21.11\%[/tex] sulfur, and [tex]42.13\%[/tex] oxygen. The empirical formula is [tex]\text{Fe} \, \square \, \text{S} \, \square \, \text{O} \, \square[/tex].



Answer :

GinnyAnswer
To determine the empirical formula of the compound, we follow these steps:

1. Determine the mass percentages of each element in the compound:
- Iron (Fe): [tex]\( 36.76\% \)[/tex]
- Sulfur (S): [tex]\( 21.11\% \)[/tex]
- Oxygen (O): [tex]\( 42.13\% \)[/tex]

2. Convert these mass percentages into moles of each element:
- The atomic mass of Fe is [tex]\( 55.85 \)[/tex] g/mol.
- The atomic mass of S is [tex]\( 32.07 \)[/tex] g/mol.
- The atomic mass of O is [tex]\( 16.00 \)[/tex] g/mol.

To find the number of moles of each element:

- Moles of Fe = [tex]\( \frac{36.76}{55.85} \approx 0.658 \)[/tex]
- Moles of S = [tex]\( \frac{21.11}{32.07} \approx 0.658 \)[/tex]
- Moles of O = [tex]\( \frac{42.13}{16.00} \approx 2.633 \)[/tex]

3. Determine the simplest ratio of the moles of each element:
- To find the simplest ratio, divide the moles of each element by the smallest number of moles calculated:

The smallest number of moles is approximately [tex]\(0.658\)[/tex].

- Ratio of Fe = [tex]\( \frac{0.658}{0.658} \approx 1 \)[/tex]
- Ratio of S = [tex]\( \frac{0.658}{0.658} \approx 1 \)[/tex]
- Ratio of O = [tex]\( \frac{2.633}{0.658} \approx 4 \)[/tex]

4. Write the empirical formula:
- The empirical formula is written using the ratios of the elements:

Therefore, the empirical formula is Fe[tex]\(\mathbf{1}\)[/tex]S[tex]\(\mathbf{1}\)[/tex]O[tex]\(\mathbf{4}\)[/tex].

So, the complete empirical formula is Fe[tex]\(\mathbf{1}\)[/tex]S[tex]\(\mathbf{1}\)[/tex]O[tex]\(\mathbf{4}\)[/tex].

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