A compound contains 40.0% carbon, 6.7% hydrogen and 53.3% oxygen. If the molar mass of the compound is 180. Find the molecular formula. [H = 1, C = 12, O = 16]

To find the molecular formula of this compound, we follow a systematic two-part process: finding the empirical formula first, and then determining the molecular formula.

Step 1: Determine the Empirical Formula

Assume we have 100g of the compound. This means we have:

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

Next, divide each mass by the respective 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 result by the smallest value (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$_2$O.

Step 2: Determine the Molecular Formula

The empirical formula mass of CH$_2$O is: $(12 \times 1) + (1 \times 2) + (16 \times 1) = 12 + 2 + 16 = 30$

We use the formula: $\text{Molecular Formula} = (\text{Empirical Formula})_n$ Where $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$

$n = \frac{180}{30} = 6$

Now, multiply the subscripts in the empirical formula by $n$ (which is 6):

• C: $1 \times 6 = 6$
• H: $2 \times 6 = 12$
• O: $1 \times 6 = 6$

The molecular formula is C$_6$H$_{12}$O$_6$.

Conclusion

Comparing our result to the given options, the correct choice is C.

Exam Tip: Always remember that the empirical formula represents the simplest ratio, while the molecular formula represents the actual number of atoms in a molecule. If you are ever stuck, you can quickly check the options by calculating their molar masses; only the correct molecular formula will match the molar mass provided in the question (180).