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: first, finding the empirical formula, and then finding the molecular formula.

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 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 result (which is 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. Determine the Molecular Formula

The molecular formula is a multiple ($n$) of the empirical formula. We use the formula: $n = \text{Molar Mass} / \text{Empirical Formula Mass}$

• Empirical Formula Mass ($CH_2O$): $(12 \times 1) + (1 \times 2) + (16 \times 1) = 12 + 2 + 16 = 30$
• $n$: $180 / 30 = 6$

Now, multiply the empirical formula by $n$: Molecular Formula $= 6 \times (CH_2O) = \mathbf{C_6H_{12}O_6}$

Conclusion

Comparing our result to the options provided: A. $CH_2O$ (This is the empirical formula) B. $C_3H_6O_3$ C. $C_6H_{12}O_6$ D. $C_6H_{12}O_3$

The correct option is C.

Exam Tip: When calculating the mole ratio, if you get a decimal like 1.5, multiply all values by 2 to get whole numbers. If you get 1.33, multiply by 3. In this question, the values were very close to whole numbers, making it straightforward!