Ask A Scientist Chemistry Archive

name         Cameron M.
status       educator
age          30s

Question -   When discussing air molecules, which are close and which are far apart - cold and 
warm.  I realize that they spread apart the further away from the earth they are and that is a 
cooler area.  That would imply that cold are farther apart and warm are closer.  However, it 
has been explained that cold air molecules are close together hence having more pressure, and 
warm air molecules are farther apart allowing space for water vapor / humidity.  Which is 
it?
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The mean free path of a gas particle is given by the formula:
L (meters) = [R/2^1/2*pi*d^2*Na]* T/P
where R = gas constant, pi = 3.14159, d = mean diameter of the gas particle,
Na = Avagodro's number = 6x10^23, T = temperature in kelvins,
and P = pressure. All of the quantities in the [square brackets] are fixed by the boundary 
conditions of the
particular gas you choose to analyze. For an ideal gas PV=nRT so the
quantity T/P = V/nR =1/D where D= molar density of the gas in which case the mean free path
is:
L (meters) = [1/(2^1/2*pi*d^2*Na)] / D
The excellent web site for most any question in physics:
 http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html#c2
lets you work out various combinations of all the inputs to the equation for L.

Vince Calder
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