When a hydrocarbon A undergoes combustion in the presence of air, it requires 9.5 equivalents of oxygen and produces 3 equivalents of water. What is the molecular formula of A?

Some Basic Concepts of Chemistry PYQ — JEE Main 2023 · 29 Jan · Shift 2 · Q6 with Solution

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Correct answer: C

Let the hydrocarbon be $\mathrm{C_xH_y}$ .
Write the combustion reaction: $\mathrm{C_xH_y + \left(x+\frac{y}{4}\right)O_2 \rightarrow xCO_2 + \frac{y}{2}H_2O}$
Use the given data about water formed: It produces $3$ equivalents of water.

In combustion stoichiometry, moles of water formed are: $\frac{y}{2} = 3$ Hence, $y = 6$
Use the given oxygen requirement: It requires $9.5$ equivalents of oxygen, so: $x + \frac{y}{4} = 9.5$ Substituting $y=6$ : $x + \frac{6}{4} = 9.5$ $x + 1.5 = 9.5$ $x = 8$
Therefore, the molecular formula is $\boxed{\mathrm{C_8H_6}}$
Check with options:
- A: $\mathrm{C_9H_6}$ gives oxygen needed $=9+\frac{6}{4}=10.5$ ❌
- B: $\mathrm{C_6H_6}$ gives oxygen needed $=6+\frac{6}{4}=7.5$ ❌
- C: $\mathrm{C_8H_6}$ gives oxygen needed $=8+\frac{6}{4}=9.5$ and water $=\frac{6}{2}=3$ ✅
- D: $\mathrm{C_9H_9}$ gives water $=\frac{9}{2}=4.5$ ❌

So the correct option is C.