To determine the molecular formula, we need to:
1. Calculate the molar amounts of each element using their respective masses and atomic weights.
2. Find the simplest whole number ratio of these elements.
3. Adjust this ratio to account for the given molecular weight of the compound.
Here are the steps:
1. Calculate the number of moles of each element:
- Carbon (C):
Atomic weight of carbon = 12 g/mol.
Moles of carbon = [tex]\( \frac{196.01 \text{ grams}}{12 \text{ g/mol}} \approx 16.33 \text{ moles} \)[/tex].
- Hydrogen (H):
Atomic weight of hydrogen = 1 g/mol.
Moles of hydrogen = [tex]\( \frac{41.14 \text{ grams}}{1 \text{ g/mol}} = 41.14 \text{ moles} \)[/tex].
- Oxygen (O):
Atomic weight of oxygen = 16 g/mol.
Moles of oxygen = [tex]\( \frac{130.56 \text{ grams}}{16 \text{ g/mol}} \approx 8.16 \text{ moles} \)[/tex].
- Silicon (Si):
Atomic weight of silicon = 28 g/mol.
Moles of silicon = [tex]\( \frac{57.29 \text{ grams}}{28 \text{ g/mol}} \approx 2.05 \text{ moles} \)[/tex].
2. Find the simplest whole number ratio:
The ratio of moles roughly simplifies to:
- Carbon: [tex]\( C = 16.33 \)[/tex]
- Hydrogen: [tex]\( H = 41.14 \)[/tex]
- Oxygen: [tex]\( O = 8.16 \)[/tex]
- Silicon: [tex]\( Si = 2.05 \)[/tex]
To approach finding the simplest integer ratio, we compare.
The smallest number is 2.05. If we divide all the moles by 2.05:
- [tex]\( \frac{16.33}{2.05} \approx 8 \)[/tex]
- [tex]\( \frac{41.14}{2.05} \approx 20 \)[/tex]
- [tex]\( \frac{8.16}{2.05} \approx 4 \)[/tex]
- [tex]\( \frac{2.05}{2.05} = 1 \)[/tex]
Thus, the empirical formula is approximated to [tex]\( C_8H_{20}O_4Si \)[/tex].
3. Compare with given options:
Given that none of the empirical reductions matches a formula closer to reality, and by further understanding, you match it to [tex]\( C_8H_{20}O_4Si \)[/tex].
Therefore, the correct answer is:
D. [tex]$C_8H_{20}O_4Si$[/tex]
