At this stage you could argue: “It doesn’t make any difference that water molecules are lighter than those of oxygen and nitrogen. The water molecules are being added to the oxygen and hydrogen in the air, which makes it heavier.”
You’d be wrong. To see why, we need to go back to 1811 and the work of the Italian scientist Count Lorenzo Romano Amedeo Carlo Avogadro (1776-1856), who hypothesized that equal volumes of gasses at the same temperature and pressure contain equal numbers of molecules.
His hypothesis took a while to be confirmed and accepted by scientists, but by 1860 Avogadro’s law was a bedrock of chemistry as it still is.
In other words, when water molecules evaporate into a cubic foot of air an equal number of other molecules will leave that particular cubic foot of air. Remember, we’re talking about air that can freely move in the atmosphere, it’s not sealed in a bottle.
Each molecule of water that evaporates into a particular parcel of air as vapor will replace a molecule of either nitrogen or oxygen, which account for roughly 99 percent of the air’s gasses. Nitrogen in the air (with two atoms in each molecule) has a molecular weight of 28 and the oxygen molecules (also two atoms per molecule) a molecular weight of 32.
Water vapor molecules, which are one oxygen atom with a weight of 16 and two hydrogen atoms each with a weight of 1, add up to a molecular weight of 18, which is much lighter than the nitrogen and oxygen they displace when they evaporate into air.