The molar mass of a compound is 148 g/mol and its empirical formula is c4h10o. What is the molecular formula of this compound?
The Correct Answer and Explanation is :
To determine the molecular formula of a compound, we need to use the molar mass of the compound and its empirical formula. The empirical formula represents the simplest whole number ratio of the elements in the compound, while the molecular formula shows the actual number of atoms of each element in the compound.
Step 1: Determine the Molar Mass of the Empirical Formula
The empirical formula of the compound is ( C_4H_{10}O ). To calculate its molar mass, sum the atomic masses of each element:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
- Oxygen (O): 16.00 g/mol
So, the molar mass of the empirical formula ( C_4H_{10}O ) is:
[
(4 \times 12.01 \, \text{g/mol}) + (10 \times 1.008 \, \text{g/mol}) + (1 \times 16.00 \, \text{g/mol}) = 48.04 \, \text{g/mol} + 10.08 \, \text{g/mol} + 16.00 \, \text{g/mol} = 74.12 \, \text{g/mol}
]
Step 2: Calculate the Factor to Multiply the Empirical Formula
The molar mass of the compound is given as 148 g/mol. To find the factor by which we need to multiply the empirical formula, divide the molar mass of the compound by the molar mass of the empirical formula:
[
\frac{\text{Molar mass of compound}}{\text{Molar mass of empirical formula}} = \frac{148 \, \text{g/mol}}{74.12 \, \text{g/mol}} = 2
]
Step 3: Determine the Molecular Formula
To get the molecular formula, multiply the subscripts in the empirical formula by the factor (2):
[
(C_4H_{10}O) \times 2 = C_8H_{20}O_2
]
Thus, the molecular formula of the compound is ( C_8H_{20}O_2 ).
Conclusion
The molecular formula of the compound is ( C_8H_{20}O_2 ). This formula represents the actual number of atoms of each element in the molecule, which is twice the number of atoms in the empirical formula.