Speed of Gas Basics

This is the equation you need to use (We derived this equation in class - get someone's notes or see me):

v = √(3RT/M)

Some necessary information:

R = 8.31 J mol¯¹ K¯¹

M = the molar mass of the substance, expressed in kilograms

Example Problem #1: What is the ratio of the average velocity of krypton gas atoms to that of nitrogen molecules at the same temperature and pressure?

Solution path one:

1) Let us determine the velocity of Kr atoms at 273 K:

v = √(3RT/M)

v = √[[(3) (8.31447) (273)] / (0.083798)]

v = 285 m/s

2) Let us determine the velocity of N₂ atoms at 273 K:

v = √(3RT/M)

v = √[[(3) (8.31447) (273)] / (0.028014)]

v = 493 m/s

3) Let us expresss the ratio both ways:

N₂ : Kr ratio = 493 / 285 = 1.73 to 1

Kr : N₂ ratio = 285 / 493 = 0.578 to 1

Example Problem #2: At the same temperature, which molecule travels faster, O₂ or N₂? How much faster?

Solution:

1) Oxygen velocity @ 273 K:

v = √(3RT/M)

v = √[[(3) (8.31447) (273)] / (0.0159994)]

v = 652.4 m/s

2) Nitrogen velocity @ 273 K:

v = √(3RT/M)

v = √[[(3) (8.31447) (273)] / (0.028014)]

v = 493 m/s

3) Nitrogen moves faster. How much faster?

652.4 / 493 = 1.3233

Nitrogen moves slightly more than 1.3 times as fast as oxygen, at the same temperature.