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Chemistry Textbook

Effusion and Diffusion of Gases

By the end of this section, you will be able to:
  • Define and explain effusion and diffusion
  • State Graham’s law and use it to compute relevant gas properties

If you have ever been in a room when a piping hot pizza was delivered, you have been made aware of the fact that gaseous molecules can quickly spread throughout a room, as evidenced by the pleasant aroma that soon reaches your nose. Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be hundreds of times the diameter of the molecule

Diffusion

Diffusion is how a gas disperses through space and is the result of the random motion as illustrated in Figure  6.13. The gas follows the postulates of the Kinetic Molecular Theory, moving like a classical particle and changing directions every time there is a collision. The gaseous atoms or molecules are, of course, unaware of any concentration gradient, they simply move randomly—regions of higher concentration have more particles than regions of lower concentrations, and so a net movement of species from high to low concentration areas takes place. 

LINK TO LEARNING

The following video provides a good illustration of the Diffusion and Effusion processes.

https://www.youtube.com/embed/_oLPBnhOCjM

Effusion

A process involving movement of gaseous species similar to diffusion is effusion, the escape of gas molecules through a tiny hole such as a pinhole in a balloon into a vacuum (Figure 6.13). Although diffusion and effusion rates both depend on the molar mass of the gas involved, their rates are not equal; however, the ratios of their rates are the same.

This figure contains two cylindrical containers which are oriented horizontally. The first is labeled “Diffusion.” In this container, approximately 25 purple and 25 green circles are shown, evenly distributed throughout the container. “Trails” behind some of the circles indicate motion. In the second container, which is labeled “Effusion,” a boundary layer is evident across the center of the cylindrical container, dividing the cylinder into two halves. A black arrow is drawn pointing through this boundary from left to right. To the left of the boundary, approximately 16 green circles and 20 purple circles are shown again with motion indicated by “trails” behind some of the circles. To the right of the boundary, only 4 purple and 16 green circles are shown.
Figure 6.13 Diffusion involves the unrestricted dispersal of molecules throughout space due to their random motion. When this process is restricted to passage of molecules through very small openings in a physical barrier, the process is called effusion.

If a mixture of gases is placed in a container with porous walls, the gases effuse through the small openings in the walls. The lighter gases pass through the small openings more rapidly (at a higher rate) than the heavier ones (Figure 6.13). In 1832, Thomas Graham studied the rates of effusion of different gases and formulated Graham’s law of effusion: The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles:

rate of effusion∝1ℳrate of effusion∝1ℳ

This means that if two gases A and B are at the same temperature and pressure, the ratio of their effusion rates is inversely proportional to the ratio of the square roots of the masses of their particles:

rate of effusion of Arate of effusion of B=ℳBℳArate of effusion of Arate of effusion of B=ℳBℳA

Key Equations:

  • rate of diffusion=amount of gas passing through an areaunit of timerate of diffusion=amount of gas passing through an areaunit of time
  • rate of effusion of gas Arate of effusion of gas B=mBmA=ℳBℳArate of effusion of gas Arate of effusion of gas B=mBmA=ℳBℳA