Question

A gaseous compound having carbon, hydrogen and oxygen was burnt in the presence of oxygen. After combustion, 1 volume of the gaseous compound produces 2 volumes of CO\(_2\) and 2 volumes of steam. Determine the molecular formula of the compound, if all the volumes were measured under the same conditions of pressure and temperature.

• A. C\(_2\)H\(_4\)O\(_2\)
• B. C\(_3\)H\(_6\)O\(_3\)
• C. C\(_4\)H\(_8\)O\(_2\)
• D. C\(_5\)H\(_{10}\)O\(_3\)

Hint:

For problems involving gas volumes, always use Avogadro's hypothesis to directly relate volume ratios to mole ratios, simplifying the determination of the molecular formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Avogadro's hypothesis states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules. Therefore, the volume ratio is equivalent to the mole ratio.

Step 2: Detailed Explanation:
Let the molecular formula be C\(_x\)H\(_y\)O\(_z\). The balanced combustion equation is: \[ \text{C}_x\text{H}_y\text{O}_z + \text{O}_2 \rightarrow x\text{CO}_2 + \frac{y}{2}\text{H}_2\text{O} \] From the given volume data (1 vol compound : 2 vol CO\(_2\) : 2 vol steam): • Number of carbon atoms: \(x = 2\) (from 2 volumes of CO\(_2\)). • Number of hydrogen atoms: \(\frac{y}{2} = 2 \Rightarrow y = 4\) (from 2 volumes of steam). • Number of oxygen atoms: From the products, total oxygen atoms = \(2x + \frac{y}{2} = 4 + 2 = 6\). Oxygen from O\(_2\) is 4 atoms, so the compound must provide 2 oxygen atoms. Thus \(z = 2\). Therefore, the molecular formula is C\(_2\)H\(_4\)O\(_2\).

Step 3: Final Answer:
The molecular formula is C\(_2\)H\(_4\)O\(_2\), which corresponds to option (A).