**Gases**

Molecular Effusion and Diffusion

Molecular Effusion and Diffusion

Kinetic-molecular theory stated that

The average kinetic energy of molecules is proportional to absolute temperature

- 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 N

T = (25+273)°K = 298°K

*M* = 28 g/mol = 0.028 kg/mol

R = 8.314 J/mol °K = 8.314 kg m^{2}/s^{2} mol °K

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

Effusion

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:

Basis of effusion

- 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

Diffusion: the spread of one substance through space, or though a second substance (such as the atmosphere)

Diffusion and Mean Free Path

- 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...

the rates of diffusion are slower than molecular speeds due to molecular collisions

- Due to the density of molecules comprising the atmosphere, collisions occur about 10
^{10}(i.e.) times per second*10 billion* - 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*