Diffusion and Brownian Motion

Diffusion is the spreading of particles from a region of higher concentration to a region of lower concentration through random motion, and Brownian motion is the random, jerky movement of small visible particles caused by collisions with fast-moving molecules of the fluid around them. In brief: a drop of ink spreads through still water by diffusion, and pollen grains in water jiggle under a microscope because of Brownian motion; both give evidence that matter is made of moving particles.

Both phenomena arise from the same cause, which is the constant random motion of particles. Diffusion is a net movement that evens out concentrations, and Brownian motion is what the movement of a single larger particle looks like. This article explains each process, describes the factors that change the rate of diffusion, explains the classic ammonia and hydrogen chloride experiment, includes a worked calculation and gives the history of Brown, Einstein and Perrin.

What is diffusion?

Particles in gases and liquids move randomly. If a region has many particles of a substance and a neighboring region has few, more particles will move from the crowded region to the empty one than the other way round, simply because there are more of them. The result is a net movement from high concentration to low concentration, which continues until the particles are spread evenly. Individual particles keep moving, but there is no net change.

Diffusion needs no stirring or flow. It works best in gases and is slow in liquids. In solids it is extremely slow, though it does occur at high temperatures. It is the reason why the smell of baking bread reaches the other end of a room, or why a drop of food coloring slowly colors a glass of water.

What is Brownian motion?

When you look at fine smoke particles in air or tiny pollen fragments in water through a microscope, you see them move in a zigzag path. The particles are much bigger than molecules, but they are hit from all sides by molecules of the surrounding fluid. At any moment, the hits from one side are slightly stronger than from the other, so the particle is pushed in a random direction.

The movement never stops and gets stronger when the temperature is higher, or when the particle is smaller. Brownian motion is direct visible evidence for the existence and constant motion of molecules.

What affects the rate of diffusion?

The ammonia and hydrogen chloride experiment

This classic experiment shows that lighter particles diffuse faster.

1. Place a plug of cotton wool soaked in concentrated ammonia solution at one end of a long, dry glass tube, and a plug soaked in concentrated hydrochloric acid at the other end. Seal both ends with stoppers.
2. Ammonia gas (NH₃) and hydrogen chloride gas (HCl) diffuse along the tube from opposite ends.
3. Where they meet, they react to form a white ring of solid ammonium chloride: NH₃ + HCl → NH₄Cl.
4. The ring forms closer to the hydrochloric acid end, which shows that ammonia travelled farther in the same time. Ammonia particles are lighter than hydrogen chloride particles.

This work should be done in a fume cupboard or well-ventilated room with eye protection, because both substances are irritants.

Worked example: where do the gases meet?

Graham’s law says that the rates of diffusion of two gases are inversely proportional to the square roots of their molar masses: rate₁ ÷ rate₂ = √(M₂ ÷ M₁).

1. Molar masses. NH₃ = 14 + 3 = 17 g/mol. HCl = 1 + 35.5 = 36.5 g/mol.
2. Ratio of speeds. rate(NH₃) ÷ rate(HCl) = √(36.5 ÷ 17) = √2.147 = 1.465.
3. Distances. In the same time, the distances are in the same ratio: d(NH₃) ÷ d(HCl) = 1.465. For a tube of 100 cm, d(NH₃) + d(HCl) = 100 cm.
4. Solve. d(HCl) = 100 ÷ (1 + 1.465) = 40.6 cm, and d(NH₃) = 100 − 40.6 = 59.4 cm.

The white ring forms about 59 cm from the ammonia end and about 41 cm from the hydrochloric acid end. In real experiments, the ring may be slightly displaced because the gases are not ideal and the gases collide with air in the tube.

Where does diffusion matter?

• Breathing: oxygen diffuses from the air in the lungs into the blood, and carbon dioxide diffuses the other way.
• Plants: carbon dioxide diffuses into leaves through tiny pores.
• Smell: odor molecules diffuse from a source to your nose.
• Industry: uranium isotopes were once separated by differences in diffusion rates through porous barriers.
• Cooking and medicine: flavors spread in soup, and drugs diffuse through tissues.

How were Brownian motion and diffusion explained?

In 1827 the Scottish botanist Robert Brown observed pollen grains moving in water under a microscope. He first thought that the motion was a sign of life, but he saw the same movement in dust and other non-living particles. In 1855 Adolf Fick described diffusion mathematically, and in 1905 Albert Einstein predicted the size of Brownian displacement from molecular collisions. Jean Perrin measured these displacements carefully around 1908 and obtained values of Avogadro’s number that matched other methods, and he received the Nobel Prize in Physics in 1926.

Which mistakes are common?

Mistake 1: Thinking that particles stop moving when concentrations are equal

They keep moving, but there is no net movement in either direction.

Mistake 2: Saying that the particles are pushed by a force

Diffusion results from random motion, not from a force that points down the concentration gradient.

Mistake 3: Believing that Brownian motion is caused by the pollen being alive

Non-living particles also show it. The cause is collisions with fluid molecules.

Mistake 4: Expecting diffusion to be fast over long distances

Diffusion is fast for short distances but slow for long ones. Without air currents, a smell may take minutes to cross a large room.