To determine the empirical formula of the compound in question, we will follow these steps:
1. Determine the number of moles of each element:
- Given percentages:
- Silicon (Si): 46.8%
- Oxygen (O): 53.2%
- Molar masses:
- Silicon (Si): approximately 28.085 g/mol
- Oxygen (O): approximately 15.999 g/mol
- Assume we have 100 grams of the compound. Therefore:
- Mass of Si = 46.8 grams
- Mass of O = 53.2 grams
- Calculate the moles of each element:
[tex]\[
\text{Moles of Si} = \frac{\text{Mass of Si}}{\text{Molar mass of Si}} = \frac{46.8}{28.085} \approx 1.667
\][/tex]
[tex]\[
\text{Moles of O} = \frac{\text{Mass of O}}{\text{Molar mass of O}} = \frac{53.2}{15.999} \approx 3.325
\][/tex]
2. Determine the simplest mole ratio:
- To find the simplest ratio, we divide the moles of each element by the smallest number of moles calculated:
[tex]\[
\text{Ratio of Si} = \frac{1.667}{1.667} = 1
\][/tex]
[tex]\[
\text{Ratio of O} = \frac{3.325}{1.667} \approx 1.995 \approx 2
\][/tex]
3. Write the empirical formula:
- The ratio of Si to O is 1:2.
- Therefore, the empirical formula is [tex]\(SiO_2\)[/tex].
Given the choices:
A. [tex]\(SiO_2\)[/tex]
B. [tex]\(SiO_3\)[/tex]
C. [tex]\(Si_2O_3\)[/tex]
D. [tex]\(Si_2O\)[/tex]
The correct answer is A. [tex]\(SiO_2\)[/tex].
