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 the compound, we need to compare the molar mass of the compound with the molar mass of its empirical formula. The empirical formula is the simplest ratio of the elements in the compound, while the molecular formula represents the actual number of atoms of each element in a molecule of the compound. Here’s the step-by-step approach:
Step 1: Calculate the molar mass of the empirical formula
The empirical formula is given as ( C_4H_{10}O ). To calculate the molar mass of the empirical formula, we add up the atomic masses of each element:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
- Oxygen (O): 16.00 g/mol
Now, calculate the molar mass of ( C_4H_{10}O ):
[
\text{Molar mass of } C_4H_{10}O = (4 \times 12.01) + (10 \times 1.008) + (1 \times 16.00)
]
[
= 48.04 + 10.08 + 16.00 = 74.12 \, \text{g/mol}
]
So, the molar mass of the empirical formula ( C_4H_{10}O ) is 74.12 g/mol.
Step 2: Find the ratio of the molar mass of the compound to the molar mass of the empirical formula
The molar mass of the compound is given as 148 g/mol. To find the ratio of the molecular formula to the empirical formula, divide the molar mass of the compound by the molar mass of the empirical formula:
[
\text{Ratio} = \frac{\text{Molar mass of compound}}{\text{Molar mass of empirical formula}} = \frac{148}{74.12} \approx 2
]
Step 3: Determine the molecular formula
Since the ratio is approximately 2, this means the molecular formula is twice the empirical formula. Multiply the subscripts in the empirical formula by 2:
[
\text{Molecular formula} = (C_4H_{10}O) \times 2 = C_8H_{20}O_2
]
Conclusion:
The molecular formula of the compound is ( C_8H_{20}O_2 ).
Explanation:
- The empirical formula ( C_4H_{10}O ) represents the simplest whole-number ratio of the elements in the compound.
- The molecular formula represents the actual number of atoms in a molecule of the compound, and we determined this by comparing the molar mass of the empirical formula with the molar mass of the compound. Since the molar mass of the compound is exactly twice that of the empirical formula, the molecular formula is ( C_8H_{20}O_2 ).