9.6 Diffusion & Effusion

Diffusion & Effusion

The process by which gas molecules spread out in response to a concentration gradient is diffusion. Heavier molecules diffuse slowly than lighter molecules.

The process by which a gas escapes from its container through a tiny hole into an evacuated space. In 1846 Thomas Graham examined this process and concluded that the effusion rate is the number of moles (or molecules) of gas effusing per unit time. Since density is directly proportional to molar mass, we state Graham’s law of effusion:

Figure 9.66 Scientist Graham

Ref: commons.wikimedia.org/

Ref: commons.wikimedia.org/

Diffusion: random motion with direction

Diffusion refers to the transport of matter through a concentration gradient; the rule is that substances move (or tend to move) from regions of higher concentration to those of lower concentration. The diffusion of tea out of a teabag into water, or of perfume from a person, are common examples; we would not expect to see either process happening in reverse!

Figure 9.67 Diffusion of Gas

 Figure 9.68 Diffusion of Gas

https://www.quora.com/What-chemical-equations-is-the-formation-reaction-of-NH4Cl-s

The white “smoke” consists of tiny particles of solid ammonium chloride, formed when hydrogen chloride and ammonia gas diffuse into the air from their concentrated aqueous solutions in the reagent bottles.

HCl + NH₃ → NH₄ Cl(s)

Figure 9.69 Diffusion of Gases

When the stopcock is opened, random motions cause each gas to diffuse into the other container.

After diffusion is complete (bottom), individual molecules of both kinds continue to pass between the flasks in both directions.

It might at first seem strange that the random motions of molecules can lead to a completely predictable (i.e., non-random) drift in their ultimate distribution. The key to this apparent paradox is the distinction between an individual and the population. Although we can say nothing about the fate of an individual molecule, the behavior of a large collection (“population”) of molecules is subject to the laws of statistics. This is exactly analogous to the manner in which insurance actuarial tables can accurately predict the average longevity of people at a given age, but provide no information on the fate of any single person.

Understanding effusion and Graham’s law

If a tiny hole is made in the wall of a vessel containing a gas, then the rate at which gas molecules leak out of the container will be proportional to the number of molecules that collide with unit area of the wall per second, and thus with the rms-average velocity of the gas molecules. This process, when carried out under idealized conditions, is known as effusion.

Figure 9.70 Effusion of Gas

Around 1830, the English chemist Thomas Graham (1805-1869) discovered that the relative rates at which two different gases, at the same temperature and pressure, will effuse through identical openings is inversely proportional to the square root of its molar mass.

Graham’s law, as this relation is known, is a simple consequence of the square-root relation between the velocity of a body and its kinetic energy.

According to the kinetic molecular theory, the molecules of two gases at the same temperature will possess the same average kinetic energy. If v₁ and v₂ are the average velocities of the two kinds of molecules, then at any given temperature ke₁ = ke₂ and

or, in terms of molar masses M,

Thus the average velocity of the lighter molecules must be greater than those of the heavier molecules, and the ratio of these velocities will be given by the inverse ratio of square roots of the molecular weights.

Although Graham’s law applies exactly only when a gas diffuses into a vacuum, the law gives useful estimates of relative diffusion rates under more practical conditions, and it provides insight into a wide range of phenomena that depend on the relative average velocities of molecules of different masses.

The effusion of a gas is inversely proportional to the square of its molar mass. Graham’s law can be used to determine the molar mass of an unknown gas.

Because of the presence of many other gas molecules, diffusion rates are much lower than effusion rate.

Diffusion can also occur in liquids. However, liquid molecules are very close to each other and attractive force is stronger, therefore collisions are more frequent. Diffusion is much slower in liquid than diffusion in gases.

Figure 9.71 Effusion of Gases

Ref: commons.wikimedia.org/

The kinetic molecular theory explains that at a given temperature and pressure, the gas with the lower molar mass effuse faster because the most probable speed of its molecules is higher, therefore more molecules escape per unit time.

Problem Example

Figure 9.72 Effusion of Gases

Ref: commons.wikimedia.org/

The glass tube shown above has cotton plugs inserted at either end. The plug on the left is moistened with a few drops of aqueous ammonia, from which NH₃ gas slowly escapes. The plug on the right is similarly moisted with a strong solution of hydrochloric acid, from which gaseous HCl escapes. The gases diffuse in opposite directions within the tube; at the point where they meet, they combine to form solid ammonium chloride, which appears first as a white fog and then begins to coat the inside of the tube.

NH₃(g) + HCl(g) → NH₄Cl(s)

a) In what part of the tube (left, right, center) will the NH₄Cl first be observed?

b) If the distance between the two ends of the tube is 100 cm, how many cm from the left end of the tube will the NH₄Cl first form?

Solution:

a) The lighter ammonia molecules will diffuse more rapidly, so the point where the two gases meet will be somewhere in the right half of the tube.

b) The ratio of the diffusion velocities of ammonia (v₁)and hydrogen chloride (v₂) can be estimated from Graham’s law:

We can therefore assign relative velocities of the two gases as v₁ = 1.46 and v₂ = 1. Clearly, the meeting point will be directly proportional to v₁. It will, in fact, be proportional to the ratio v₁/(v₁+v₂)*:

*In order to see how this ratio was deduced, consider what would happen in the three special cases in which v₁=0, v₂=0, and v₁=v₂, for which the distances (from the left end) would be 0, 50, and 100 cm, respectively. It should be clear that the simpler ratio v₁/v₂ would lead to absurd results.

Note that the above calculation is only an estimate. Graham’s law is strictly valid only under special conditions, the most important one being that no other gases are present. Contrary to what is written in some textbooks and is often taught, Graham’s law does not accurately predict the relative rates of escape of the different components of a gaseous mixture into the outside air, nor does it give the rates at which two gases will diffuse through another gas such as air. See Misuse of Graham’s Laws by Stephen J. Hawkes, J. Chem. Education 1993 70(10) 836-837

Here is the video on Graham’s law experiment:

Graham’s Law of Effusion – Proven

Practice problem:

1. A mixture of He and CH₄ are placed in an effusion apparatus. Calculate the ratio of their effusion rates.

2. If it takes 1.25 min for 0.010 mol of He to effuse, how long will it take for the same amount of ethane CH₄ to effuse?

Ans: 1. 2:1

1. 2.50 min