The average composition of the atmosphere is 78% nitrogen, 21% oxygen, and 1% “o

Question

The average composition of the atmosphere is 78% nitrogen, 21% oxygen, and 1% “others” including water vapor and other gases. However, the percentage of water vapor (a gas) varies between ~0% to 4% in the atmosphere. Avogadro stated long ago that ‘equal volumes of all gases, at the same temperature and pressure, have the same number of molecules’. What this means is that an air mass with lots of water vapor (H2O) will have less nitrogen (N2) and oxygen (O2) molecules than a drier air mass would (if we assume equal volumes, temperatures, and pressures for both).

a. The molar weight of water vapor is about 18g per mole, while the molar weight of dry air is about 29g per mole since most of it is the N2 (28g/mole) and O2 (32g/mole). If a moist air mass and a dry air mass of equivalent volumes were at the same temperature and pressure, which air mass would be denser?

b. If these two air masses have the same dimensions and collide with one another at the surface, which air mass would be forced to rise and why?

Explanation / Answer

a) Modified form of ideal gas law can be given as, PM = dRT, where, P=Pressure, M = average molecular weight and d = density, R is gas constant and T is temperature.

Now since the molecular mass of water molecule is less than the dry air's average molecular mass and since number of moles at same pressure, temperature and volume can not be different, reduced molecular mass of water will decrease overall average molecular mass of moist air.

As per modified idea gas law if P and T are constant, density becomes directly proportional to average molecular mass. Now since, molecular mass of moist air is less than molecular mass of dry air and since density is proportional to molecular weight we will have density of moist air as less than the density of dry air.

b) Now if these air masses collide with each other and since dry air mass is more denser than the moist air mass, for same dimension dense dry air mass will have more weight which will lead to it sinking more as compared to lighter moist air mass which will be forced to rise.

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