To determine the molecular formula of a compound given its empirical formula and molecular mass, follow these detailed steps:
1. Understand the Empirical Formula: The empirical formula of the compound is [tex]\(CH_2O\)[/tex]. This formula shows the simplest whole-number ratio of atoms in the compound. Specifically, it has 1 carbon (C), 2 hydrogen (H), and 1 oxygen (O) atom.
2. Calculate the Empirical Formula Mass: The empirical formula mass is the sum of the atomic masses of all the atoms in the empirical formula:
- Carbon (C) has an atomic mass of approximately 12 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1 g/mol.
- Oxygen (O) has an atomic mass of approximately 16 g/mol.
Therefore, the empirical formula mass of [tex]\(CH_2O\)[/tex] is:
[tex]\[
12 \,(\text{from C}) + 2 \times 1 \, (\text{from H}) + 16 \,(\text{from O}) = 12 + 2 + 16 = 30 \, \text{g/mol}
\][/tex]
3. Determine the Molecular Mass: The molecular mass of the compound is given as 180 g/mol.
4. Calculate the Ratio of Molecular Mass to Empirical Formula Mass:
[tex]\[
\text{Ratio} = \frac{\text{Molecular mass}}{\text{Empirical formula mass}} = \frac{180}{30} = 6
\][/tex]
5. Determine the Molecular Formula: The molecular formula is obtained by multiplying each subscript in the empirical formula by this ratio. Since the empirical formula is [tex]\(CH_2O\)[/tex], multiply each subscript by 6:
[tex]\[
\text{Molecular formula} = C_{1 \times 6}H_{2 \times 6}O_{1 \times 6} = C_6H_{12}O_6
\][/tex]
Therefore, the molecular formula of the compound is [tex]\(C_6H_{12}O_6\)[/tex].
Among the given choices, the correct answer is:
(iii) [tex]\(C_6H_{12}O_6\)[/tex].
