- Calculate the moles of each element by dividing its mass by its atomic weight: \(C \approx 16.319\), \(H \approx 40.813\), \(O \approx 8.161\), \(Si \approx 2.040\).
- Determine the molar ratio by dividing by the smallest value (\(2.040\)), yielding an empirical formula of \(C_8H_{20}O_4Si\).
- Calculate the empirical formula mass, which equals the given molecular weight of \(208.329\) g/mol.
- Since the ratio of molecular weight to empirical formula mass is \(1\), the molecular formula is \(\boxed{C_8H_{20}O_4Si}\).
Explanation
- Calculating Moles of Elements
To determine the molecular formula of the compound, we begin by calculating the moles of each constituent element. Given the masses of 196.01 g of carbon (C), 41.14 g of hydrogen (H), 130.56 g of oxygen (O), and 57.29 g of silicon (Si), and using their respective atomic masses (C \(\approx 12.011\) g/mol, H \(\approx 1.008\) g/mol, O \(\approx 15.999\) g/mol, Si \(\approx 28.085\) g/mol), we calculate the number of moles \(n_i = \frac{m_i}{M_i}\):
- Moles of C: \(\frac{196.01}{12.011} \approx 16.319\) mol
- Moles of H: \(\frac{41.14}{1.008} \approx 40.813\) mol
- Moles of O: \(\frac{130.56}{15.999} \approx 8.161\) mol
- Moles of Si: \(\frac{57.29}{28.085} \approx 2.040\) mol
- Determining the Empirical Formula Ratio
Next, we find the empirical formula by determining the simplest whole-number ratio of these moles. Dividing each value by the smallest number of moles calculated, which is \(2.040\) (moles of Si), we get:
- Ratio for C: \(\frac{16.319}{2.040} \approx 8\)
- Ratio for H: \(\frac{40.813}{2.040} \approx 20\)
- Ratio for O: \(\frac{8.161}{2.040} \approx 4\)
- Ratio for Si: \(\frac{2.040}{2.040} = 1\)
Thus, the empirical formula is \(C_8H_{20}O_4Si\).
- Calculating Molecular Formula
To find the molecular formula, we first calculate the empirical formula mass (EFM):
\(EFM = (8 \times 12.011) + (20 \times 1.008) + (4 \times 15.999) + (1 \times 28.085) \approx 96.088 + 20.160 + 63.996 + 28.085 = 208.329\) g/mol.
The given molecular weight is \(208.329\) g/mol. We find the multiplier \(n = \frac{\text{Molecular Weight}}{\text{EFM}} = \frac{208.329}{208.329} = 1\).
Therefore, the molecular formula is the same as the empirical formula, \(C_8H_{20}O_4Si\).
Examples
The process of determining a molecular formula from mass composition is crucial in analytical chemistry, particularly when identifying unknown organic compounds or new materials in a lab. For instance, after synthesizing a new silicone-based lubricant, a chemist uses these steps to confirm its identity by comparing the experimental mass percentages of carbon, hydrogen, oxygen, and silicon against the theoretical mass predicted by the structure. This fundamental technique ensures quality control and verification in chemical manufacturing and research.