# Molecular Velocity

**Molecular Velocities**

In kinetic theory of gas the velocity of molecules is expressed in the following three terms

(i) *Root-mean square velocity or R.M.S. Velocity:*

It may be defined as, “The square root of the mean value of the squares of the velocities of all molecules”. It is denoted by u. If are the velocities for n molecules, then

(ii) *The average velocity* is the arithmetic mean of the velocities of all molecules. It is denoted by v and is given by the following equation:

[

Average velocity (v) = 0.9213 x R. M. S. velocity (u)

(iii) *The most probable velocity* is the velocity possessed by maximum number of molecules of the gas at a given temperature. It is denoted by and is given by the following equation:

(since M= mN)

Or,

These three velocities are related to each other as:

Y : v : = 1.0 : 0.9213 : 0.8177

= 1.0 : 1.128 : 1.224 so

Maxwell’s distribution of velocities

**Example 1**: Calculate the root mean square velocity of nitrogen molecule at N.T.P.

*Solution*: According to kinetic gas equation:

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