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Re: Density of gas mixture



On Tue, 20 Jul 1999, John Cooper wrote:

On Tue, 20 Jul 1999, Alvin V. Flores wrote:

dry air is actually denser than moist air, contrary to what majority of
our clients thought. in one particular session, i encountered a teacher
who was quite hard to convince. kindly provide me with a thorough
explanation.

For a 'perfect' gas mixture, P = (Sum n) RT/V.
But Density = (Sum n*FW)/V
Since the formula weights of water, N2 and O2 are .018, .028 and .032,
replacing the latter two with water results in a lower density at
constant temperature and total pressure.

Dry air is *not* necessarily denser than moist air. It is *if* you are
comparing gases at the same temperature and pressure. Most beginners
don't not recognize this, and why do we expect them to? Consider the
following problem:

If you take a closed container of water and dry air, the water will
evaporate into the dry air, making it moist. Does the moist air have a
lower density than the dry air that was there before? Hmmm...as the water
evaporates, the number of molecules in the air portion increases, but the
volume of air increases as the volume of liquid water decreases, and the
temperature decreases due to evaporational cooling, and...

In the atmosphere, on the other hand, the air tends toward equilibrium
with its neighbor air, so that an increase in water vapor leads to an
increase in pressure which leads to an expansion of the air into
surrounding areas. The assumption is that the volume will expand (in
order to keep the pressure the same) and so for a given volume the water
vapor *replaces* part of the dry air rather than *adding* to the dry air.
Since water vapor has a lower mass/molecule than N2, O2 and A, the average
mass/molecule decreases.

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| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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