# How would you compare diffusion with effusion?

Jul 13, 2017

Here's my interpretation.

#### Explanation:

Diffusion is when a substance disperses evenly throughout a medium; i.e. a perfume dispersing its scent through a room:

Effusion is when a substance "escapes" through a (tiny) opening; i.e. helium in a balloon escaping through the balloon's rubber network:

We can infer that the rates of diffusion and effusion of a gas depend on the speed of the particles.

In the effusion image, we notice that $\text{He}$ effuses faster than ${\text{C"_2"H"_4"O}}_{2}$....but why?

Graham's law of effusion (or diffusion) explains this:

$\frac{{r}_{1}}{{r}_{2}} = \sqrt{\frac{{M}_{2}}{{M}_{1}}}$

where

• $\frac{{r}_{1}}{{r}_{2}}$ is the ratio of the rates of effusion of a gas 1 and a gas 2

• ${M}_{1}$ and ${M}_{2}$ are the molar masses of gases 1 and 2

This equation tells us that

The rate of effusion (and diffusion) of a gas is inversely proportional to the square root of its molar mass.

Therefore, the lower the mass of a gas, the higher its rate of effusion and the higher its speed.

This makes intuitive sense, as a gas with less mass should move faster than a gas with more mass.

In terms of rates and speeds, effusion and diffusion are quite similar.

The difference between the two is that diffusion is the spreading out of a substance within a dispersing medium, and effusion is when a substance escapes through a tiny pinhole, or other hole.

Another way to differentiate between diffusion and effusion is to imagine effusion as motion of particles through a hole one-dimensionally (i.e. $\pm x$), and diffusion allows for all three dimensions (i.e. $\pm x , \pm y , \pm z$).

$\uparrow$ Credit Truong-Son N. for this addition $\uparrow$