A compound contains 40.0% C, 6.7% H 53.3% O. If the molecular mass of the compound is 180, its molecular formula is [C =12, H =1,O]

To find the molecular formula of the compound, we follow these steps:

1. Determine the Empirical Formula

First, we assume a 100g sample of the compound. This means we have:

• Carbon (C): 40.0g
• Hydrogen (H): 6.7g
• Oxygen (O): 53.3g

Next, divide each mass by its relative atomic mass to find the number of moles:

• Moles of C: $40.0 / 12 = 3.33$
• Moles of H: $6.7 / 1 = 6.7$
• Moles of O: $53.3 / 16 = 3.33$

Now, divide each value by the smallest number of moles (3.33) to get the simplest ratio:

• C: $3.33 / 3.33 = 1$
• H: $6.7 / 3.33 \approx 2$
• O: $3.33 / 3.33 = 1$

The empirical formula is $CH_2O$.

2. Calculate the Empirical Formula Mass

Using the atomic masses ($C=12, H=1, O=16$):

• Empirical Mass = $12 + (2 \times 1) + 16 = 30$

3. Find the Molecular Formula

The relationship between the molecular formula and the empirical formula is: $\text{Molecular Formula} = (\text{Empirical Formula})_n$ Where $n = \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}}$

• $n = 180 / 30 = 6$

Now, multiply the empirical formula ($CH_2O$) by $n=6$:

• $C_{(1 \times 6)} H_{(2 \times 6)} O_{(1 \times 6)} = \mathbf{C_6H_{12}O_6}$

Conclusion

Comparing our result to the options provided, the correct molecular formula is $C_6H_{12}O_6$.

Exam Tip: Always remember that the empirical formula represents the simplest ratio of atoms, while the molecular formula represents the actual number of atoms in one molecule. If you are ever stuck, you can quickly check the options by calculating their molar masses—the one that equals 180 is likely your answer!