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I've read that when water vapor enters the atmosphere, the vapor molecules push the oxygen and nitrogen molecules out of the way and occupy their space.
But if water vapor molecules are lighter than oxygen and nitrogen molecules, then how do their molecules push them away? On what factors depends a gas pushing another gas away?
There is a lot of free space in air, not need of pushing anything away. Just to get into the picture, at normal conditions, molecules of air typically freely fly along a path several hundred times their size, until they hit other molecules.(higher tens of nm)
Imagine a large gym where is flying and bouncing 200 volleyballs, and you just add 6 basketballs. Do they need to push volleyballs away ? No, the do not.
What happens, when the molecule counts per volume increases, is the increase of pressure and the gas expansion. If you had 2 reservoirs of dry air, each 20 °C with the pressure 100 kPa, and if you let evaporate some water in one of them (while keeping the temperature), its pressure would increase. If they were interconnected, its content would partially expand to the other until pressures got equal.
Ať the given T and p, gas contains (idealized,with small error ) the same number of molecules, regardless of gas.(Avogadro law). If a molecule has a lower mass, the gas has lower density:
$$\rho=\frac{pM}{RT}$$
Air with vapor expands to have the same pressure as the surrounding air, so numbers decrease to value according to p and T.
Total number of molecules per unit volume is $\frac NV =\frac {N_\mathrm{A}.pV}{RT}\frac 1V=\frac {N_\mathrm{A}.p}{RT}$
Perhaps all started with misunderstood replacement. If you add 10 mmol of air molecules to 1 mol of air molecules do they replace them? The same for 10 mmol of water molecules.
This schematic illustration may help (not in the scale):
At the same temperature and pressure, assuming ideal gas behavior, there is the same average space per a single molecule of a gas, regardless of the type of this molecule ($\ce{N2}$, $\ce{O2}$, $\ce{CO2}$, $\ce{H2O}$, $\ce{CH4}$,...)
..A.....A.....A.....A.. | ..A.....A.....A.....A..
..A..W..A.....A..W..A.. -->| ..A.....A.....A.....A..
..A.....W.....A.....A.....W.....A..| ..A.....A.....A.....A..
Think of this as a meteorological question, not as chemistry.
Suppose some area of the Earth, perhaps 30 km square, has say 10 billion tonnes of air above it. If it is over a wet (ocean) or moist (jungle) area and some water evaporates into it, say a few hundred million tonnes of water vapour. The air will now have a mass that is several percent higher than it was before; its original mass plus the mass of the water.
The weight of that increased mass of air over any small area will be increased by several percent, increasing the air pressure (which is normally, and somewhat amazingly, over 10 tonnes per square metre). In terms of weather, that is called a high pressure area. Very large high pressure areas are marked with an "H" on weather maps.
The surrounding dry air will still have its original lower pressure, and so air will flow from the higher pressure area into the lower pressure area, creating wind.
In the above map, the huge high over Idaho can be seen pushing the blue-coloured front to the south and east. Similarly, the low over Wisconsin is allowing the red front to move northward.
(The colours indicate that the moving air is relatively colder or warmer than the air in the area they are moving into. The black lines are isobars, indicating lines with the same air pressure along them, as indicate by their numbers.)
The original 10 billion tonnes of air that was over the original area will spread out, so that over any one spot there will be a little less of the original air than there was before.
This results in the phenomenon that the question refers to as "pushing the oxygen and nitrogen molecules out of the way".
Water molecules leaving a surface have a momentum directed away from the surface. This momentum of the added molecules results in an increase in pressure of the air mass. The air expands against the surrounding atmosphere increasing the volume. The collisions with other molecules push them away until pressures [almost] equalize. Since the molecular weight of water is lower than air the overall density of the air mass decreases. Surrounding more dense air is pulled down by gravity forcing the less dense air upwards where it adiabatically cools by expanding against the lower pressure air etc. Contrary to popular usage convection is caused by gravity affecting air density variations not by pressure differences, no gravity there is no convection. Convection is directional with gravity; pressure is exerted in every direction causing air masses to expand or contract until pressures equalize, resulting in changes in density. To answer the original question the air molecules are pushed outwards by the greater number of collisions with the greater number of molecules in the air with the water molecules [higher pressure]. Temperature is also involved since higher water temperature both increases evaporation and raises the temperature of the air both of which raise the pressure increasing the rate of expansion and the decrease in density that increases convection and results in hurricanes over the tropical oceans.
