## Derivation of Average Speed of Gaseous Molecules

We can start by analyzing equation #15 from the Derivation of Ideal Gas Law below:

Because we want to derive the equation to the speed of gaseous molecules, the most important factor come to mind is the speed v_{x}. Therefore, the equation will be

1.

Canceling out from both side we get:

2.

Since R = N_{a}k.

3.

Finally, to calculate the avarage speed we find v_{rms}(Root Meean Square of Speed).

**4.**

M = N_{a}m in the equation above is the mass of one mole of molecules (the molecular mass).

* The gas constant R must be expressed in correct units for the situation in which it is being used. In the ideal gas equation where pv=nRT, it is logical to use units (L)(atm)/(mol)(K).

*In regard to speed, however, energy unit must be taken into account. Therefore, it is more appropriate to to convert it to (J)/(mol)(K).

**A. **

Please be careful with this. The RMS speed IS NOT equivalent to the average speed. In fact, the RMS speed will always be greater than the average speed.