To determine the molecular formula of a compound, we need to follow these steps:
1. Calculate the molar mass of the empirical formula:
The empirical formula given is [tex]\( C_2H_5O_2 \)[/tex].
- Molar mass of Carbon (C): 12.01 g/mol
- Molar mass of Hydrogen (H): 1.008 g/mol
- Molar mass of Oxygen (O): 16.00 g/mol
First, we calculate the molar mass for [tex]\( C_2H_5O_2 \)[/tex]:
[tex]\[
\text{Molar mass of } C_2H_5O_2 = (2 \times 12.01) + (5 \times 1.008) + (2 \times 16.00)
\][/tex]
[tex]\[
= 24.02 + 5.04 + 32.00 = 61.06 \, \text{g/mol}
\][/tex]
2. Determine the ratio of the compound’s molar mass to the empirical formula’s molar mass:
The molar mass of the compound provided is 122.11 g/mol. Thus we find the ratio:
[tex]\[
\text{Ratio} = \frac{\text{Compound's molar mass}}{\text{Empirical formula's molar mass}} = \frac{122.11}{61.06} \approx 2.00
\][/tex]
3. Determine the molecular formula by multiplying the subscripts in the empirical formula by the ratio:
The empirical formula is [tex]\( C_2H_5O_2 \)[/tex], and the ratio is approximately 2. So, multiply each subscript in the empirical formula by this ratio:
- Carbon atoms: [tex]\( 2 \times 2 = 4 \)[/tex]
- Hydrogen atoms: [tex]\( 5 \times 2 = 10 \)[/tex]
- Oxygen atoms: [tex]\( 2 \times 2 = 4 \)[/tex]
Therefore, the molecular formula is [tex]\( C_4H_{10}O_4 \)[/tex].
4. Match the determined molecular formula with the given options:
Among the provided options, the one that matches [tex]\( C_4H_{10}O_4 \)[/tex] is:
[tex]\[ C_4H_{10}O_4 \][/tex]
Thus, the molecular formula of the compound is [tex]\( C_4H_{10}O_4 \)[/tex].
