A compound has an empirical formula of CHN. What is the molecular formula, if it’s molar mass is 135.13 g/mol? (C=12.01 amu, H=1.008 amu, N= 14.01)
The Correct Answer and Explanation is:
To find the molecular formula of a compound with the empirical formula CHN and a molar mass of 135.13 g/mol, we first need to determine the molar mass of the empirical formula.
Step 1: Calculate the Molar Mass of the Empirical Formula
The empirical formula CHN consists of one carbon (C), one hydrogen (H), and one nitrogen (N). The molar mass can be calculated by summing the atomic masses of the constituent elements:
- Carbon (C): 1 × 12.01 amu = 12.01 g/mol
- Hydrogen (H): 1 × 1.008 amu = 1.008 g/mol
- Nitrogen (N): 1 × 14.01 amu = 14.01 g/mol
Now, we add these values together:
[
\text{Molar mass of CHN} = 12.01 + 1.008 + 14.01 = 27.028 \text{ g/mol}
]
Step 2: Determine the Ratio of Molecular Mass to Empirical Mass
Next, we need to determine how many times the empirical formula fits into the molecular formula by dividing the molar mass of the compound by the molar mass of the empirical formula:
[
\text{n} = \frac{\text{Molar mass of compound}}{\text{Molar mass of empirical formula}} = \frac{135.13 \text{ g/mol}}{27.028 \text{ g/mol}} \approx 5
]
Step 3: Calculate the Molecular Formula
The value of ( n ) indicates that the molecular formula contains five times the number of each atom in the empirical formula. Therefore, we multiply each subscript in the empirical formula CHN by 5:
- C: ( 1 \times 5 = 5 )
- H: ( 1 \times 5 = 5 )
- N: ( 1 \times 5 = 5 )
Thus, the molecular formula is:
[
\text{Molecular Formula} = C_5H_5N_5
]
Conclusion
The molecular formula ( C_5H_5N_5 ) indicates that the compound contains five carbon atoms, five hydrogen atoms, and five nitrogen atoms. This formula reflects the actual number of atoms in one molecule of the compound, while the empirical formula ( CHN ) provides the simplest whole-number ratio of the elements present. By determining the relationship between the empirical and molecular formulas through molar mass, we have successfully identified the molecular formula of the compound.