To determine the molecular formula of a compound given its empirical formula and molar mass, follow these steps:
### Step 1: Calculate the molar mass of the empirical formula
The empirical formula provided is [tex]\( \text{CH}_2 \)[/tex].
To find the molar mass of the empirical formula:
- The atomic mass of Carbon (C) is approximately [tex]\( 12.01 \, \text{g/mol} \)[/tex].
- The atomic mass of Hydrogen (H) is approximately [tex]\( 1.008 \, \text{g/mol} \)[/tex].
Calculate the molar mass of [tex]\( \text{CH}_2 \)[/tex]:
[tex]\[ \text{Empirical formula weight} = (12.01 \times 1) + (1.008 \times 2) = 12.01 + 2.016 = 14.026 \, \text{g/mol} \][/tex]
### Step 2: Find the ratio of the molar mass of the molecular formula to the empirical formula mass
The given molar mass of the compound is [tex]\( 140.1 \, \text{g/mol} \)[/tex].
To find the ratio (or multiple) [tex]\( n \)[/tex]:
[tex]\[ n = \frac{\text{Molar mass of compound}}{\text{Empirical formula weight}} = \frac{140.1}{14.026} \approx 10 \][/tex]
### Step 3: Determine the molecular formula
Multiply the subscripts of each element in the empirical formula by this ratio (or multiple). The empirical formula is [tex]\( \text{CH}_2 \)[/tex].
Calculate the molecular formula:
- For Carbon (C):
[tex]\[ 1 \times 10 = 10 \][/tex]
- For Hydrogen (H):
[tex]\[ 2 \times 10 = 20 \][/tex]
Thus, the molecular formula of the compound is [tex]\( \text{C}_{10}\text{H}_{20} \)[/tex].
### Conclusion:
The molecular formula of the compound, given the empirical formula [tex]\( \text{CH}_2 \)[/tex] and a molar mass of [tex]\( 140.1 \, \text{g/mol} \)[/tex], is [tex]\( \text{C}_{10}\text{H}_{20} \)[/tex].
So, the correct choice is:
[tex]$ \boxed{C_{10}H_{20}} $[/tex]
