Sections 5.24 - 5.25: Average Speed of Gas Particles

E_T = ½ mv² Average Translational Kinetic Energy

m = mass of particle

v = average speed

“The speed of gaseous particles is inversely proportional to the square root of the molar mass at constant Temperature, T”. Hence, the higher the molar mass, the lower the average speed of that molecule at constant temperature, T.

Now we can also compare the average speed for particles of a given gas at two different temperatures, T₁ and T₂.

“The average speed of same gas molecules is directly proportional to the square root of the absolute temperature.”

Example 1: Calculate the average speed of O₂ molecules at 25.00 ^oC.

v_O2 = 482 m/s

Example 2: Consider the following gases: He, Cl ₂, CH₄, and NH₃. Rank the average speeds of this gases at the same temperature T.

The lower the molar mass, the higher the average speed.

Hence, Helium has the lowest molar mass and the highest average speed.