Gases

Molecular Effusion and Diffusion

Kinetic-molecular theory stated that

• Thus, at a given temperature, to different gases (e.g. He vs. Xe) will have the same average kinetic energy
• The lighter gas has a much lower mass, but the same kinetic energy, therefore its rms velocity (u) must be higher than that of the heavier gas

where M is the molar mass

Example

Calculate the rms speed, u, of an N₂ molecule at room temperature (25°C)

T = (25+273)°K = 298°K

M = 28 g/mol = 0.028 kg/mol

R = 8.314 J/mol °K = 8.314 kg m²/s² mol °K

Note: this is equal to 1,150 miles/hour!

The rate of escape of a gas through a tiny pore or pinhole in its container.

• Latex is a porous material (tiny pores), from which balloons are made
• Helium balloons seem to deflate faster than those we fill with air (blow up by mouth)

The effusion rate, r, has been found to be inversely proportional to the square root of its molar mass:

and a lighter gas will effuse more rapidly than a heavy gas:

• The only way for a gas to effuse, is for a molecule to collide with the pore or pinhole (and escape)
• The number of such collisions will increase as the speed of the molecules increases

• Similarly to effusion, diffusion is faster for light molecules than for heavy ones
• The relative rates of diffusion of two molecules is given by the equation

• The speed of molecules is quite high, however...

• Due to the density of molecules comprising the atmosphere, collisions occur about 10¹⁰ (i.e. 10 billion) times per second
• Due to these collisions, the direction of a molecule of gas in the atmosphere is constantly changing

The average distance traveled by a molecule between collisions is the mean free path

• The higher the density of gas, the smaller the mean free path (more likelyhood of a collision)
• At sea level the mean free path is about 60 nm
• At 100 km altitude the atmosphere is less dense, and the mean free path is about 0.1 m (about 1 million times longer than at sea level)

1996 Michael Blaber