How many kg of water does an airplane produce after burning a kg of kerosene?

Answer

Dear Gerard,

This is fairly easy to calculate based on the formula you indicate yourself, there you see that after the reaction 10 times as many molecules of water have been formed as there were originally molecules “kerosene” (C9H20). We now only need to find out how many molecules of kerosene are present in 1 kg. This can be easily calculated via the molecular mass.

The molecular mass for C9H20 = 9*12.011 + 20*1.008 = 128,259 grams/mol (the molecular masses can be found in any periodic table) from which we learn that 1000 / 128,259 = 7,797 moles of kerosene are present in 1 kg. Conversion gives 10x as many molecules of water, so 77.97 moles of water. Now we still need to know the molecular mass of water: 2*1.008 + 1* 15.999 = 18.015 gram/mol. This yields for the number of moles of water: 77.97 mole * 18.015 gram/mol = 1405 gram (or 1.405 kg).

So 1 kg of kerosene gives rise to 1.4 kg of water.

However, we should make a small remark here, namely kerosene is not a pure substance but a mixture of different hydrocarbons (C9H20 is only one of them) with 6 to 16 carbon atoms per molecule. Had we used a “different kerosene” molecule in the combustion reaction, a different amount of water would also be found: eg

2 C12H26 + 37 O2 –> 26H2O + 24 CO2

In this case we get 13 molecules of water for every kerosene molecule (now with molecular mass = 170.34 g/mol) and the mass of water becomes 1.375 kg … or 30 grams less.

If we look at the entire range of hydrocarbons that occur in kerosene (C6H14 to C16H34), we find quantities of water that vary from 1,352 kg to 1,463 kg. Thus, for a mixture, the mass of water obtained will be between 1.35 and 1.46 kg.

Danny Vanpoucke