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?

Solution

Chemistry ma’am · 4 steps

Water gives you the hydrogens first, then the oxygen count hands you the carbons.

1. Balanced combustion. Take the hydrocarbon as CₓH_y. Each C becomes one CO₂ and every 2 H become one H₂O. Counting oxygen atoms on the right, you need x + y/4 moles of O₂ per mole of A.

   CₓH_y + (x + y/4)O₂ → x CO₂ + y/2 H₂O

2. Hydrogen from water. 3 moles of water per mole of A means y/2 = 3, so y = 6.
3. Carbon from oxygen. Now x + 6/4 = 9.5, which gives x + 1.5 = 9.5 and so x = 8.

   Option	H₂O formed, y/2	O₂ needed, x + y/4
   (a) C₉H₆	3	10.5
   (b) C₆H₆	3	7.5
   (c) C₈H₆	3	9.5
   (d) C₉H₉	4.5	11.25

4. So. Only C₈H₆ matches both numbers, so the answer is (c).

The idea to keep. For CₓH_y burning, O₂ needed is x + y/4 and water formed is y/2. Solve for y from water first, then x from oxygen.

Answer from the NTA final answer key. Solution by PrepWiser.