# Molecular Speed Formula

According to Kinetic Molecular Theory of Gases, it explains that gas particles are in continuous motion and exhibit ideally elastic collisions. Gas particles are found in a constant state of random motion and particles always travel in a straight line until and unless they collide with another particle. It also explains that the average kinetic energy of a group of gas particles is directly proportional to temperature. In an ideal gas condition, the speed associated with a group of molecules can be found.

As per the Kinetic Molecular Theory of Gases, Kinetic energy is given by

$$\begin{array}{l}KE=\frac{1}{2}mv^{2}\end{array}$$

The root-mean-square speed or molecular speed measures the average speed of particles in gas and is given by

$$\begin{array}{l}v=\sqrt{\frac{3RT}{m}}\end{array}$$

Where:

V = molecular speed of the particle

T = Temperature in Kelvin

m: molar mass of the compound

R = Ideal gas constant (8.314 kg*m2/s2*mol*K)

## Solved Example OnÂ Molecular Speed Formula

Example 1: A temperature of the container full of particles with molar mass 2 gr/mol is 900K. Calculate the speed of those particles if they are not reacting with each other?

Solution:

Given

m=Â 2 gr/mol

T = 900 K

$$\begin{array}{l}v=\sqrt{\frac{3RT}{m}}\end{array}$$

v =Â âˆš(3 Ã— 8.314 Ã— 900)/2

v =Â âˆš(22447.8)/2

v =Â âˆš11223.9

v = 105.9 m/s

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