Velocities of gas molecules

Average Velocity :

As per kinetic theory of gases, each molecule is moving with altogether different velocity. Let ‘ n ‘ molecules be present in a given mass of gas, each one moving with velocity v1, v2, v3… vn. The average velocity or Uav = average of all such velocity terms.

Root Mean Square Velocity :

The root mean square velocity of a molecule can be obtained by using the formula

Vrms =

If we have to calculate the root-mean-square velocity of oxygen molecules at room temperature, 25°C

Vrms =

= 481.2 m/s

So an oxygen molecule travels through the air at 481.2 m/s which is 1726 km/h, much faster than a jetliner can fly and faster than that of most rifle bullets.

The very high speed of gas molecules under normal room conditions would indicate that a gas molecule would travel across a room almost instantly. In fact, gas molecules do not do so. If a small sample of a very odorous (and poisonous) gas, H2S is released in one corner of a room, our noses will not detect it in another corner of the room for several minutes unless the air is vigorously stirred by a mechanical fan. The slow diffusion of gas molecules which are moving very quickly occurs because the gas molecules travel only short distances in straight lines before they are deflected in a new direction by collision with other gas molecules.

The distance any single molecule travels between collisions will vary from very short to very long distances, but the average distance that a molecule travels between collisions in a gas can be calculated. This distance is called the mean free path of the gas molecules. If the root-mean-square velocity is divided by the mean free path of the gas molecules, the result will be the number of collisions one molecule undergoes per second. This number is called the collision frequency of the gas molecules.

The postulates of the kinetic molecular theory of gases permit the calculation of the mean free path of gas molecules. The gas molecules are visualized as small hard spheres. Without going into the mathmatical detail; as the temperature rises the mean free path increases; it also rises as the pressure decreases, and as the size of the molecules decrease. Diffusion takes place slowly because even though molecules are moving very fast, they travel only short distances in any one straight line.

Most Probable Velocity :

It is the velocity which is possessed by maximum no. of molecules.

Vmp =    

Kinetic Energy of Gas :

As per kinetic equation PV =

For 1 mole m × n = Molecular Mass (M)

∴ PV =     or    

Also    

Where     is the Boltzmann constant

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