diffusion, in chemistry, the spontaneous migration of substances from regions where their concentration is high to regions where their concentration is low. Diffusion is important in many life processes. It occurs, for example, across the alveolar membrane of the lung, which separates the carbon-dioxide-rich blood from the oxygen-rich air. Oxygen diffuses across the membrane and becomes dissolved in the blood; carbon dioxide diffuses across the membrane into the air.

The spontaneous redistribution of a substance is due to the random motion of the molecules (or atoms or ions) of the substance. Because of the random nature of the motion of molecules, the rate of diffusion of molecules out of any region in a substance is proportional to the concentration of molecules in that region, and the rate of diffusion into the region is proportional to the concentration of molecules in the surrounding regions. Thus, while molecules continuously flow both into and out of all regions, the net flow is from regions of higher concentration to regions of lower concentration. Generally, the greater the difference in concentration, the faster the diffusion.

Since an increase in temperature represents an increase in the average molecular speed, diffusion occurs faster at higher temperatures. At any given temperature, small, light molecules (such as H2, hydrogen gas) diffuse faster than larger, more massive molecules (such as N2, nitrogen gas) because they are traveling faster, on the average (see heat; kinetic-molecular theory of gases). According to Graham's law (for Thomas Graham), the rate at which a gas diffuses is inversely proportional to the square root of the density of the gas.

Diffusion often masks gravitational effects. For example, if a relatively dense gas (such as CO2, carbon dioxide) is introduced at the bottom of a vessel containing a less dense gas (such as H2, hydrogen gas), the dense gas will diffuse upward and the less dense gas will diffuse downward. It is true, however, that at equilibrium the two gases will not be uniformly mixed. There will be some variation in the density and composition of the gas mixture; at the top of the vessel the gas mixture will be slightly less concentrated, and there will be a slight preponderance of molecules of the less dense gas. These differences, which are due to gravity, are almost impossible to measure in the laboratory, although they interact with other factors in determining the distribution of gases in planetary atmosphere.

Diffusion is not confined to gases; it can take place with matter in any state. For example, salt diffuses (dissolves) into water; water diffuses (evaporates) into the air. It is even possible for a solid to diffuse into another solid; e.g., gold will diffuse into lead, although at room temperature this diffusion is very slow. Generally, gases diffuse much faster than liquids, and liquids much faster than solids. Diffusion may take place through a semipermeable membrane, which allows some, but not all, substances to pass. In solutions, when the liquid solvent passes through the membrane but the solute (dissolved solid) is retained, the process is called osmosis. Diffusion of a solute across a membrane is called dialysis, especially when some solutes pass and others are retained.

Diffusion is the net movement of particles (typically molecules) from an area of high concentration to an area of low concentration by uncoordinated random movement. In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually lead to complete mixing.

Diffusion is part of transport phenomena. Of the material transport mechanisms, diffusion is known as a slow one. Molecular diffusion is generally superimposed on, and often masked by, other transport phenomena such as convection, which tend to be much faster. However, the slowness of diffusion can be the reason for its importance: diffusion is often encountered as a step in a sequence of events, and the velocity of the whole chain of events is that of the slowest step. For example, the rate at which a chemical reaction progresses can be entirely limited by the rate of diffusion of reactants/products to/from the place where the reaction occurs.

The speed of diffusion can be approximately illustrated as follows (at room temperature)

  • in gas: 100 mm per minute
  • in liquid: 0.5 mm per minute
  • in solid: 0.0001 mm per minute


Diffusion is driven by random thermal motion of molecules.

Diffusion is a statistical phenomenon in that the chance of a molecule "jumping" from one volume to another depends on the number of molecules in the first volume, so molecules in volumes which have a relatively high initial concentration tend to disperse to less concentrated areas until a balance of exchange (equilibrium) is reached.

Einstein relation

Fick's law (empirical) can be derived by noting that the flux due to diffusion only can depend on the chemical potential, and taking this potential to be that of an ideal gas. This last step is justified because the final stage of a spreading concentration may be described as an ideal gas. The result is

mathbf{J} (mathbf{r} , t) = - frac{kT}{gamma}mathbf{nabla} c (mathbf{r}, t),

where gamma is the drag coefficient (the inverse of the mobility). The Einstein relation follows directly to be

D = frac{kT}{gamma},

which is the most general expression for the diffusion coefficient, not referring to any microscopic model.

Entropy and diffusion

Diffusion increases the entropy of a system. In other words, diffusion is a spontaneous and irreversible process. Something can spread out by diffusing, but it won't spontaneously 'suck back in'. Thermodynamically, diffusion is a process to lower the free energy of the system, to increase the entropy. That is, diffusion is driven by gradients of the chemical potential rather than gradients of the chemical concentration, implying that diffusion, under certain circumstances, may occur against a concentration gradient.

In biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids through cell membranes.

Non equilibrium system

Because diffusion is a transport process of particles, the system in which it takes place is a non equilibrium system (i.e. it is not at rest yet). For this reason thermodynamics and statistical mechanics are of little to no use in describing diffusion. However, there might occur so-called quasi-steady states where the diffusion process does not change in time. As the name suggests, this process is a fake equilibrium since the system is still evolving.

Types of diffusion

The spreading of any quantity that can be described by the diffusion equation or a random walk model (e.g. concentration, heat, momentum, ideas, price) can be called diffusion. Some of the most important examples are listed below.

Metabolism and respiration rely in part upon diffusion in addition to bulk or active processes. For example, in the alveoli of mammalian lungs, due to differences in partial pressures across the alveolar-capillary membrane, oxygen diffuses into the blood and carbon dioxide diffuses out. Lungs contain a large surface area to facilitate this gas exchange process.

Experiments to demonstrate diffusion

Diffusion is easy to observe, but care must be taken to avoid a mixture of diffusion and other transport phenomena.

It can be demonstrated with a wide glass tubed paper, two corks, some cotton wool soaked in ammonia solution and some red litmus paper. By corking the two ends of the wide glass tube and plugging the wet cotton wool with one of the corks, and litmus paper can be hung with a thread within the tube. It will be observed that the red litmus papers turn blue.

This is because the ammonia molecules travel by diffusion from the higher concentration in the cotton wool to the lower concentration in the rest of the glass tube. As the ammonia solution is alkaline, the red litmus papers turn blue. By changing the concentration of ammonia, the rate of color change of the litmus papers can be changed.

Another simpler way to demonstrate diffusion is to drop a drop of ink by dropper into a glass of water. One can see the ink spreads slowly from the initial region where the ink first encountered the water surface, to everywhere in the glass. This is because the dye molecules in the ink diffuses from the high concentration region to other lower concentration regions.


  • Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. Dover.

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