If a rocket runs on a fuel (C₁₅H₃₀) and liquid oxygen, the weight of oxygen required and CO₂ released for every litre of fuel respectively are :
(Given : density of the fuel is 0.756 g/mL)

Solution

Chemistry ma’am · 4 steps

Turn the litre into grams with the density first, then let the balanced equation do the rest.

1. Mass to moles. One litre of fuel is 1000 mL, so its mass is 1000 × 0.756 = 756 g. The molar mass of C₁₅H₃₀ is 15 × 12 + 30 × 1 = 210 g mol⁻¹, so the fuel is 756/210 = 3.6 mol.

   C₁₅H₃₀ + 45/2 O₂ → 15CO₂ + 15H₂O

2. Oxygen needed. Each mole of fuel needs 22.5 mol of O₂. That gives 3.6 × 22.5 = 81 mol of O₂, which is 81 × 32 = 2592 g.
3. Carbon dioxide released. Each mole of fuel gives 15 mol of CO₂. That gives 3.6 × 15 = 54 mol of CO₂, which is 54 × 44 = 2376 g.
4. So. The oxygen needed is 2592 g and the CO₂ released is 2376 g, in that order. That is option (c).

The idea to keep. When a question gives a volume of liquid, convert it to mass with the density before anything else. Equations only work in moles, never in litres of liquid.

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