To determine the empirical formula of a compound containing silicon (Si) and oxygen (O) with given mass percentages, we'll follow these steps:
1. Find the masses of each element based on a 100g sample:
- For Si: [tex]\(46.8\)[/tex] grams
- For O: [tex]\(53.2\)[/tex] grams
2. Convert the mass of each element to moles by using their atomic masses:
- The atomic mass of Si is [tex]\(28.085 \text{ g/mol}\)[/tex].
- The atomic mass of O is [tex]\(16.00 \text{ g/mol}\)[/tex].
Calculate the moles of each element:
[tex]\[
\text{Moles of Si} = \frac{46.8 \text{ g}}{28.085 \text{ g/mol}} \approx 1.667 \text{ moles}
\][/tex]
[tex]\[
\text{Moles of O} = \frac{53.2 \text{ g}}{16.00 \text{ g/mol}} \approx 3.325 \text{ moles}
\][/tex]
3. Determine the simplest whole number ratio of the moles of each element:
- We find the ratio of Si to O by dividing the moles of each element by the smallest number of moles calculated.
The smallest number of moles here is for Si:
[tex]\[
\text{Ratio of Si} = \frac{1.667}{1.667} = 1
\][/tex]
[tex]\[
\text{Ratio of O} = \frac{3.325}{1.667} \approx 2
\][/tex]
4. Write the empirical formula:
- The simplest whole number ratio of Si to O is 1:2.
Therefore, the empirical formula for the compound is [tex]\( \text{SiO}_2 \)[/tex].
The correct answer is:
C. [tex]\( \text{SiO}_2 \)[/tex]
