dry air or moist air?
Dry air.
For each H2O molecule (at. wt. 16+1+1=18), either a N2 molecule (at. wt.14+14=28) or an O2 molecule (at. wt. 16+16=32) is displaced, reducing the combined weight of the mixture.
The key principle here is called Avagadro’s Law.
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Avogadro’s law states that, “equal volumes of all gases, at the same temperature and pressure, have the same number of molecules”.
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So if you have a cubic foot of air, and you add some water vapor to it, the pressure inside that cubic foot of air is going to go up. Since your cubic foot of air isn’t in any kind of container, the increased pressure is just going to push some of the air out into the air around that cubic foot of air, equalizing the pressure. So, as long as you end up with the same pressure and temperature, you’ve got the same number of molecules inside that cubic foot of air.
The air on earth is roughly 78 percent nitrogen in the form of N2 molecules, roughly 21 percent oxygen in the form of O2 molecules, and roughly 1 percent other stuff (argon, carbon dioxide, helium, etc). So most likely, your water molecules are going to be pushing out either nitrogen or oxygen molecules.
And so what you end up with is exactly what excavating (for a mind) posted. When you add a water molecule, you mostly push out either a nitrogen molecule (78 percent of the time) or an oxygen molecule (21 percent of the time). Since nitrogen molecules and oxygen molecules both weigh more than water molecules, the air with the water molecules ends up weighing less.
In case you are wondering where excavating (for a mind)'s numbers come from, it’s this:
Nitrogen molecules - two nitrogen atoms with an atomic weight of 14 each, for a total of 28.
Oxygen molecules - two oxygen atoms with an atomic weight of 16 each, for a total of 32.
Water molecules - one oxygen atom with an atomic weight of 16, plus two hydrogen atoms with an atomic weight of 1 each, for a total of 18.
Avogadro’s Law: Avogadro’s law states that, “equal volumes of all gases, at the same temperature and pressure, have the same number of molecules”.
Is there some simple “intuitive” explanation of why this is true?
which is heavier: a pound of lead or a pound of feathers?
Certainly. The pressure on the container is due to the collisions of the speeding gas molecules with the walls. The pressure P must be proportional to the number of molecules n that hit the walls per cm^2 per second times the momentum p of each molecule. The momentum is equal to the mass m of the molecules times their velocity v. The number that hit the wall per cm^2 per second is given by the density r of the gas (in molecules per cm^3) times the velocity v. (Imagine a column of gas molecules that are all going to strike the same 1 cm^2 patch of wall in the next second. The length of this column is v in cm/s, i.e. if v = 10 cm/s then all the molecules in a column 10 cm long will hit the wall in the next second. The number of molecules in this column is the volume of the column, v, times the numer density r.)
So to sum up, P = k n p = k (r v)(m v) = k r m v^2, with k some constant.
Now m v^2 is just proportional to the average kinetic energy of the gas molecules. Equipartition tells us that must be proportional to the temperature. That is, m v^2 = k’ T, with k’ some other constant.
That means P = k" r T, with k" some third constant. Rearranging, we find r = k’‘’ P/T with k’‘’ yet another constant. That is, the number density is proportional to the pressure and inversely proportional to the temperature – the mass of the molecules has disappeared, which means at the same temperature and pressure, you must have the same number of molecules per cm^3, regardless of the identity of the gas.
In words, I guess we could say that the pressure depends on the density and how hard the molecules strike the walls. You might think heavier molecules would hit harder, but of course they’re also moving more slowly at the same temperature, and the two effects just cancel out, so that the oomph with which the molecules strike the wall turns out to depend only on the temperature. That means the pressure depends only on the number density (molecules per cm^3) and the temperature, which in turn means the number density depends only on the pressure and temperature.
So basically, it comes down to the fact that temperature is a function of kinetic energy, which depends on mass, and cancels out the mass that is part of momentum that is used to calculate pressure. There’s no simple reason that the mass drops out other than it just does. What you’re left with is the ideal gas law equation, saying that the product of the pressure and volume is proportional to the product of the number of molecules and the absolute temperature of the molecules (which is proportional to their average kinetic energy). So for a given temperature, pressure, and volume, the same number of molecules are present.
That’s an ideal gas law, which holds well at low pressures where molecules are generally far apart. If you crank the pressure up high enough, intermolecular forces will cause the relationship to break down. I believe the corrections for standard conditions are well known, but I’m not sure what their order of magnitude is.
“Simple and intuitive” is a relative concept. The argument above is simple, if you think about it hard enough, except for the equipartition theorem, which took decades and the genius of both Maxwell and Boltzmann to establish.