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 * mv²
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.)