Moist air is lighter than dry air

The title of today's post seems both self explanatory, in that we observe clouds to rise and counter intuitive in that when we add something to something else we expect it to get heavier.  So what's happening? We need three pieces of science knowledge to explain this: Avogadro's hypothesis; an understanding of the composition of air; and the concept of atomic weight.

Avogadro's Hypothesis states that equal volumes of gas at the same temperature and pressure contain the same number of molecules, regardless of the chemical composition of the gas. [1] Specifically that number is 602,214,150,000,000,000,000,000 (over 602 sextillion) molecules of gas in 22.4 litres of gas at a temperature of 0°C, and 1 atmosphere of pressure.  The number will vary depending on the temperature and the pressure.



Dry air is composed of four elements.  Nitrogen (78.08 %) in a two atom molecular form known as di-nitrogen.  This is a nitrogen atom bound to another nitrogen atom with three chemical bonds, it is so strongly bound together it effectively functions as an inert gas for most of the time. Oxygen (21%) in a two atom molecular form known as di-oxygen, an inert gas Argon (1%) which because it is an 'inert gas' would be present as single atoms.  Finally, there are trace amounts of other gases including carbon dioxide.

Atomic weight.  The weight of a molecule is determined by the weight of its constituent atoms, and the weight of the constituent atom is determined by the number of protons and neutrons in the nucleus, electrons are virtually weightless, protons and neutron have the same weight.  Hydrogen is the lightest atom, it contains one proton and no neutrons and therefore has an atomic weight of 1. Nitrogen has seven protons and seven neutrons and therefore an atomic weight of 14. Oxygen has eight protons and eight neutrons and therefore an atomic weight of 16.

Di-nitrogen and di-oxygen together make up 99% of the weight of a parcel of air so I will only consider the weight of these two elements.  Suffice to say that carbon di-oxide is heavier than both of these molecules.  Di-nitrogen has a weight of 14 + 14 = 28, di-oxygen has a weight of 16 + 16 = 32. Water is made of two hydrogen atoms and one oxygen atom and therefore has a weight of 1 + 1 + 16 = 18.

Given Avogadro's Hypothesis that the number of molecules is constant, for every molecule of water 'added' to dry air, one molecule of di-nitogren or di-oxygen will need to be subtracted.  This would be a weight saving of 10 in the case of di-nitogren, and a weight saving of 14 in the case of di-oxygen and therefore moist air is lighter than dry.

Therefore clouds can rise and the hydrologic cycle can exist.

[1] http://www.chemistry.co.nz/avogadro.htm accessed May 31, 2015.