An organic compound contains 53.1% Carbon, 6.2% Hydrogen, 12.4% Nitrogen, and 28.3% Oxygen by mass. What is…

To solve this problem, we need to follow two main steps: first, find the empirical formula, and second, use the vapour density to find the molecular formula.

Step 1: Find the Empirical Formula

We calculate the mole ratio of each element by dividing the percentage composition by the relative atomic mass.

• Carbon (C): $53.1 / 12 = 4.425$
• Hydrogen (H): $6.2 / 1 = 6.2$
• Nitrogen (N): $12.4 / 14 = 0.886$
• Oxygen (O): $28.3 / 16 = 1.769$

Now, divide each result by the smallest value ($0.886$):

• C: $4.425 / 0.886 \approx 5$
• H: $6.2 / 0.886 \approx 7$
• N: $0.886 / 0.886 = 1$
• O: $1.769 / 0.886 \approx 2$

The empirical formula is C$_5$H$_7$NO$_2$.

Step 2: Find the Molecular Formula

The relationship between molecular mass and vapour density is: Molecular Mass = 2 × Vapour Density

• Molecular Mass = $2 \times 56.5 = 113$

Now, calculate the mass of the empirical formula (C$_5$H$_7$NO$_2$):

• $(5 \times 12) + (7 \times 1) + (1 \times 14) + (2 \times 16)$
• $60 + 7 + 14 + 32 = 113$

Since the empirical formula mass ($113$) is equal to the molecular mass ($113$), the molecular formula is the same as the empirical formula.

Conclusion

The molecular formula is C$_5$H$_7$NO$_2$.

Exam Tip: Always remember that Vapour Density is only for gases or volatile liquids. If the question gives you Vapour Density, the molecular mass is always double that value. Don't waste time looking for other formulas!