A compound with the empirical formula CH2 has a molar mass of 84 g/mol. What is the molecular formula for this compound?
The correct answer and explanation is:
To find the molecular formula of a compound given its empirical formula and molar mass, follow these steps:
Step 1: Determine the molar mass of the empirical formula
The empirical formula is CH₂, which means it contains one carbon (C) atom and two hydrogen (H) atoms. The atomic masses of carbon and hydrogen are:
- Carbon (C): 12 g/mol
- Hydrogen (H): 1 g/mol
The molar mass of the empirical formula CH₂ is calculated by adding the atomic masses of each element: Molar mass of CH2=(12 g/mol)+(2×1 g/mol)=12 g/mol+2 g/mol=14 g/mol\text{Molar mass of CH}_2 = (12 \, \text{g/mol}) + (2 \times 1 \, \text{g/mol}) = 12 \, \text{g/mol} + 2 \, \text{g/mol} = 14 \, \text{g/mol}
Step 2: Divide the molar mass of the compound by the molar mass of the empirical formula
The given molar mass of the compound is 84 g/mol. To find how many empirical formula units are present in the molecular formula, divide the molar mass of the compound by the molar mass of the empirical formula: Number of units=Molar mass of the compoundMolar mass of the empirical formula=84 g/mol14 g/mol=6\text{Number of units} = \frac{\text{Molar mass of the compound}}{\text{Molar mass of the empirical formula}} = \frac{84 \, \text{g/mol}}{14 \, \text{g/mol}} = 6
Step 3: Multiply the empirical formula by the number of units
Now that we know there are 6 empirical formula units in the molecular formula, multiply each element in the empirical formula by 6: Molecular formula=(CH2)×6=C6H12\text{Molecular formula} = (C H_2) \times 6 = C_6 H_{12}
Conclusion
The molecular formula of the compound is C₆H₁₂.
This means the compound consists of 6 carbon atoms and 12 hydrogen atoms. The empirical formula (CH₂) represents the simplest ratio of elements in the compound, and the molecular formula shows the actual number of atoms in one molecule of the compound.