### Re: Why the number of molecules a constant, under same external conditions ?

Date: Fri Apr 19 01:27:40 2002
Posted By: In Koo Kim, Grad student, Physical Chemistry, Harvard
Area of science: Chemistry
ID: 1017836832.Ch
Message:
```
In fact, given a constant temperature, pressure, and volume, the
number of molecules (or moles) is not constant for different gases.
You may have been told this in introductory chemistry, however, this
is only an approximation based on the ideal gas law.  Real gases
have inter and intra-molecular forces (fugacity, viscosity, mass
volume, etc) that make the ideal gas approximation fail at high
pressures and temperatures.

However, given conditions that do not violate the assumptions of the
ideal gas law, the number of molecules per unit volume (also called
number density) for different type molecules can be considered
constant.  You were on the right track about the "lighter" molecules
moving faster and 'heavier" molecules moving slower, effectively
exerting the same force per unit area.

Now the average kinetic (translational) energy is found by the
temperature of the gas.  I pause here because it's more complicated
depending on whether you're talking about monoatomic or
polyatomic gases.  If you want the full 9 yards, I refer you to Paul
Atkin's Physical Chemistry textbook.  Anyway, since the temperature
is the same for two gases, the average KE is the same.  It's roughly
equal to kt (k is Boltzmann's constant in units of J/K).  k is equal to nR
so:
E= nRT
n=E/RT
Now recall the ideal gas law:
PV = nRT
so E = PV
or P = E/V
So for gasses, pressure can be thought of as a gauge of how much
energy there is in a given volume.  Since two gases of the same
temperature have the same energy, if they occupy the same volume,
they must also have the same pressure.

```

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