Answer :
The simplest ratio of iron to sulfur is [tex]1:2[/tex]. The empirical equation is [tex]FeS_2[/tex].
We must convert the mass percentages to moles in order to determine the empirical formula. Given that pyrite is composed of [tex]46.5\%[/tex] iron and [tex]53.5\%[/tex] sulfur, we follow these steps:
Convert mass percentages to grams (assume [tex]100[/tex] grams of pyrite):
- Iron: [tex]46.5 grams[/tex]
- Sulfur: [tex]53.5 grams[/tex]
Convert grams to moles using atomic masses (Iron: [tex]55.85 g/mol[/tex], Sulfur: 3[tex]2.07 g/mol[/tex]):
- Moles of Iron: [tex]\frac{46.5 \, \text{g}}{55.85 \, \text{g/mol}} \approx 0.833 \, \text{moles}[/tex]
- Moles of Sulfur: [tex]\frac{53.5 \, \text{g}}{32.07 \, \text{g/mol}} \approx 1.669 \, \text{moles}[/tex]
Divide the moles by the smallest number of moles to find the simplest ratio:
- Moles of Iron: [tex]\frac{0.833}{0.833} \approx 1[/tex]
- Moles of Sulfur:[tex]\frac{1.669}{0.833} \approx 2[/tex]
Hence, the empirical formula is [tex]FeS_2[/tex].
The empirical formula for pyrite is FeS2.
HOW TO CALCULATE EMPIRICAL FORMULA:
- The empirical formula represents the simplest whole number ratio of constituents element of a compound. The empirical formula of pyrite can be calculated as follows:
46.5 mass % Fe = 46.5g of Fe
53.5 mass % S = 53.5g of S
- Next, we divide each element's mass value by its molar mass
Fe = 46.5g ÷ 56g/mol = 0.83mol
S = 53.5g ÷ 32g/mol = 1.67mol
- Next, we divide each mole value by the smallest (0.83mol)
Fe = 0.83mol ÷ 0.83 = 1
S = 1.67mol ÷ 0.83 = 2.014
Approximately, the ratio of Fe to S is 1:2. Therefore, the empirical formula of pyrite is FeS2.
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