Answer 1:
First of all, let me point out that the speeds
of the individual molecules in a gas range over
many possible speeds. So we need to discuss out
answers in terms of average or mean speeds
or "most probable speeds" or RMS speeds.
This question is in the field of
thermodynamics (thermo > temperature
induced & dynamic > motion or change over time)
and the question can be answered using the
kinetic theory of gases. The equation is:
Average kinetic energy (KE) = 1.5kT
with the following definitions:
k = Boltzmann's constant (he discovered
this relationship and published it)
T = the temperature of the gas.
KE = 1/2 * mv^{2}
This equation relies on a number of assumptions:
1) the gas is not overly compressed such that
the molecules it is made of do not hit each other
very often
2) the molecules do not lose energy when they do
hit each other (they don't break up or deform)
3) modeling their motion on Newton's laws of
motion is close enough for us (and it is plenty
accurate)
4) the molecules are moving randomly in direction
(you are in a closed container with no wind or
convection).
So all that really matters is what the
temperature of the gas is and what the gas is made
of. Furthermore, you can use some statistical
methods to get an idea of what the spread in
velocities of a large group of molecules (your
gas) would be  this is called the Maxwell
speed distribution curve.
The following link addresses these issues in
depth, even including a java script calculator to
allow you to figure out the speeds you want to
know based on your inputs:
speed calculator
Using this speed calculator, I found the
approximate answer for dry air at room temperature
to be around 1,000 miles per hour (yes, we are
talking about speeds exceeding the speed of
sound.)
Thanks for asking
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