MadSci Network: Chemistry

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

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 
E= nRT
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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