Diffusion in Gases and Liquids

Diffusion in gases and liquids is a basic physical event whereby molecules move down gradients of concentration, temperature, or pressure. It has many useful and important applications, and helps to explain many natural phenomena.

Overview

"To diffuse" means to spread out, or to scatter. Diffusion is the process of spreading out, or scattering. In the fields of physics and chemistry, the major types of diffusion are molecular diffusion, thermal diffusion, forced diffusion, and eddy diffusion. Molecular diffusion refers to a special phenomenon whereby molecules of a substance, in the absence of any other influencing factors, move from an area of relatively high concentration to an area of lesser concentration.

If a drop of colored solution (for example, ink) is placed in a container of still liquid (for example, water) and allowed to stand undisturbed, the color is observed to spread slowly throughout the liquid. Although the process may require a significant amount of time, eventually a uniform solution will result.

This phenomenon is not restricted to two liquids. A similar result will occur if, for example, a small quantity of table salt is placed in the bottom of a container of undisturbed, liquid water. After sufficient time has elapsed, a uniform saltwater solution will be found in the container. When a gas is placed in a closed container, and then a second gas is introduced, a uniform mixture of the two gases eventually will be observed.

Common to these and all other examples of molecular diffusion is the fact that the atoms or molecules of the introduced substance have moved from an area of initially high concentration (the point at which they were introduced) to an area of lower concentration (the surrounding fluid or gas). Questions naturally arise as to the nature of the force that causes this movement, and the reason for the movement proceeding in the direction of decreasing concentration. In order to understand these phenomena, it is necessary to know that all atoms and molecules (even those of solids) are in continuous, chaotic motion. The atoms or molecules of a gas move in random directions, colliding with one another and the walls of their container. There is a much more restricted movement by the atoms or molecules of a solid, since they are bound to one another. The random molecular movement possible in a liquid is intermediate to that in gases and solids. The movement of these particles means that they possess kinetic energy (the energy of motion). The motion itself is called thermal motion. Molecular diffusion is a direct consequence of the thermal motion of molecules.

Given a closed vessel with a mixture of fluids (liquids or gases), the quantity of molecules of any of the component fluids that will move in any observed direction away from a selected starting point within the fluid mixture is proportional to the concentration (number per unit volume) of the component at the starting point. When all areas within the vessel have equal concentrations of the component fluid, (that is, there is already a uniform concentration present within the vessel), there will be equal numbers of the component's molecules moving in all directions (a condition known as dynamic equilibrium); and, on average, no regional changes in concentration will occur. The result is different whenever a change in concentration of the component exists in a particular direction (in which case we say that a concentration gradient exists in the given direction). Because there are always more molecules per unit volume in the area of higher concentration than in the area of lower concentration, more molecules (on average) will be moving at any instant from the high concentration zone into the low concentration zone compared to the number of molecules moving (at that instant) in the opposite direction.

Therefore, there will be a net movement of molecules in the direction of their decreasing concentration.

As the name implies, thermal motion is related to the temperature of a substance. In fact, temperature is a way of quantifying the amount of thermal motion exhibited by the atoms or molecules of a substance: The higher the temperature, the greater is the thermal motion of the particles (the faster is their random motion).

One of the characteristics of molecular diffusion is that it occurs at a faster rate when the temperature of the substance is higher. This is predictable in view of the nature of thermal motion and the definition of diffusion. The characteristic can easily be demonstrated with two containers, one filled with cold and the other with hot water, and a small quantity of table salt.

The salt will become uniformly distributed in the hot water more quickly than in the cold water.

Therefore, scientists say that the rate of diffusion depends on the temperature.

Another characteristic of diffusion is that its rate is proportional to the size of the concentration gradient existing across the area (customarily, one square centimeter) over which the diffusion is to occur. When the concentration gradient is large, the rate of diffusion will be higher than when the gradient is small.

This explains the observation that agitating, or stirring, the initial mixture can dramatically speed the mixing process. The agitation accomplishes this by bringing together parts of the mixture that may have quite large concentration differences, thereby speeding the rate of diffusion.

The size of the barrier, or reference plane, across which molecules are to diffuse also influences the rate at which the molecular diffusion will occur. For example, the time required for X grams of molecule R to diffuse across a 1-square-centimeter barrier is three times longer than the time needed for the same amount of R to cross a 3-square-centimeter barrier. In fact, the time required to transfer X grams of molecule R across a barrier that is N square centimeters is N times the time required to transfer the same amount of R across a 1-square-centimeter barrier.

A third important characteristic of diffusion is that its rate is affected by the size of the diffusing molecules. At any given temperature, smaller molecules move faster than larger molecules. Therefore, if the concentration gradients in several containers of fluid are equally large, and if the temperatures are also equal, the container whose diffusing molecules are the smallest will display the highest rate of diffusion, and will be the first whose contents reach a state of dynamic equilibrium.

The phenomenon of diffusion resembles that of thermal conductivity. While diffusion will result in uniformity of composition, thermal conductivity results in uniformity of temperature. The similarity is not coincidental but results from the fact that both phenomena, according to kinetic theory, are caused by the thermal motion of molecules. Both are known as transport phenomena.

Thermal diffusion may result when a temperature gradient (difference in temperature between different positions) exists within a mixture of fluids, whereupon one of the components of the mixture moves (relative to the entire mixture) in the direction of decreasing temperature.

Thermal diffusion rates are greater for larger temperature gradients and for larger areas through which the diffusion may occur. Unless the temperature gradient is very large, however, thermal diffusion is usually negligible compared to molecular diffusion.

Forced diffusion occurs when an outside force (for example, a pressure, or an electrical field) causes movements by the molecules similar to molecular diffusion, except that the molecules now move down the gradient of the force (pressure, or electrical field) instead of down a concentration gradient. The rate of forced diffusion is proportional to the size of the gradient of the force. As before, temperature and molecular properties influence the rate of diffusion.

The flow of fluids may be described as being either laminar or turbulent. Laminar flow is characterized by smooth streamlines running parallel to the surface over which the flow occurs, while turbulent flow exhibits localized areas of eddies (small whirlpools or flows of current running contrary to the main current). Eddies will appear as a result of sufficiently high speeds of fluid flow past a surface, or (even at relatively low speeds) because of sufficiently large irregularities on the surface over which the flow occurs. Whereas material movements caused by concentration gradients and consequent molecular diffusion take place during laminar flow, there is rapid mixing occurring during turbulent flow as a result of the whirlpool action of the eddies in the fluid. The latter process is thus termed eddy diffusion (or turbulent diffusion).

The rate of eddy diffusion is proportional to the speed and size of the eddies as well as to the concentration gradient. Because of the great complexity involved in precisely describing the characteristics of eddies, this is the most poorly understood of the diffusions.

Applications

Diffusion can be exploited in a number of ways, ranging from biochemical studies to industrial, chemical, and medical applications. The fact that molecules can move down a concentration gradient as a result of their thermal energy of motion helps to simplify what would otherwise be very complicated procedures.

One application of diffusion is the determination of the molecular weight of a large molecule. This is a question that frequently arises in biochemical as well as organic chemistry laboratories. The weight can be rather difficult to discover when the exact structure of the molecule is unknown. The method to be described works best for molecules with a molecular weight in the range of 20,000 to 200,000 as is often the case for polymer molecules.

The technique requires the use of a membrane that permits passage of small liquid molecules but prevents passage of the larger polymer molecules dissolved in the liquid. In this situation, the liquid is referred to as the solvent, and the polymer is the solute. The membrane, referred to as a semipermeable membrane, functions in this selective manner as a result of the size of miniature holes, or pores, that are distributed across its surface, permitting only the relatively small solvent molecules to pass across the membrane.

When the semipermeable membrane is arranged in such a way that it separates two solutions, one containing the large polymer molecules and the other containing only pure solvent, there will be a concentration gradient of the solvent across the membrane. The solution of pure solvent will be the area of higher solvent concentration (100 percent solvent). Since only the small solvent molecules can pass through the membrane's pores, the result will be the movement (diffusion) of solvent from the side of higher solvent concentration into the area of lower solvent concentration (which also contains the polymer molecules). Such a process is referred to as osmosis.

As osmosis proceeds, the volume (and thus the pressure), will increase on the side of the membrane containing the polymer. Measurements of the pressure increase across the semipermeable membrane can be used to calculate the molecular weight of the solute (polymer) molecules.

The technique known as gel filtration is another example of applied diffusion. This method can separate a mixture of polymer molecules of various size. The technique is based on the fact that the assorted polymer molecules have differing abilities to penetrate the pores of a gel structure. The larger the polymer molecule, the slower it can diffuse through the gel. After a period of time, the polymer molecules become separated according to their size.

In the United States alone, more than three million people suffer from some kidney disorder. Malfunctioning kidneys do not perform their normal regulation of the solute concentrations of a person's blood. This can cause many substances to accumulate in the bloodstream to toxic levels, with possible resultant development of nausea, fatigue, memory loss, organ failure, and even death. To restore the proper solute concentrations, a kidney dialysis machine can be used. Because these machines perform a function similar to that of the kidneys, they are often referred to as artificial kidneys.

The principle of dialysis is based on the separation of substances (by molecular diffusion) across a semipermeable membrane that separates two solutions of differing concentrations. In hemodialysis, one of the solutions is the patient's blood, diverted out of the person's circulatory system and into the dialysis machine, and the other is the dialysis fluid, containing a variety of salts, nutrients, and other substances. The dialysis fluid establishes the correct concentration gradients with the blood flowing on the other side of the membrane. The concentration gradients cause the substances that are at too high a concentration in the blood to diffuse down the concentration gradients and into the dialysis fluid, while the important large protein molecules of the blood, and the blood's cells, are too large to pass through the pores in the membrane, thereby remaining in the blood. If necessary, important nutrient molecules can be permitted to diffuse from the dialysis fluid, down their concentration gradients, into the patient's blood. After passing through the artificial kidney, the blood is returned to the patient's circulatory system.

Indeed, molecular diffusion makes possible life as we know it. All living cells in plants and animals require particular gas molecules in order to perform the chemical reactions that sustain life. For example, humans are aerobic (oxygen-requiring) animals. Our cells all require a continuous supply of oxygen molecules to complete the reactions of aerobic respiration, which provide the energy necessary for life. Since the cells are continuously using the oxygen present inside of them, the concentration of internal oxygen remains lower than its external concentration. As a result, there exists an oxygen concentration gradient between the extracellular environment (with a high oxygen concentration) and the intracellular environment (low oxygen concentration). Therefore, the oxygen needed for intracellular chemical reactions enters the cells by means of molecular diffusion down a concentration gradient.

Simultaneously, our cells produce carbon dioxide as a waste product of aerobic respiration. The continuous production of carbon dioxide inside the cells produces a carbon dioxide concentration gradient: There is a higher concentration of carbon dioxide inside the cells than there is in the extracellular environment. Thus, carbon dioxide diffuses out of the cells, down a concentration gradient. Molecular diffusion not only brings oxygen into our cells, but it also removes the potentially toxic waste product carbon dioxide.

Context

The discovery of the molecular diffusion of gases is attributed to John Dalton of Manchester, England, in 1801. Because of the difficulty of making accurate measurements, it was not until 1833 that Thomas Graham was able to formulate what has become known as Graham's law, which relates the rate at which a gas diffuses to the molecular weight of the gas molecules.

Further research by Graham, culminating in 1854, helped to explain osmosis. He had found that solutions of small molecules could pass through a sheet of parchment, while solutions of larger molecules were unable to pass through the submicroscopic pores of the sheet. Then he noted that the solution of large molecules, when separated from a solution of pure water by a parchment sheet, increased in volume as water passed across the sheet and into the solution of large molecules (the phenomenon of osmosis). Graham also performed pioneering studies of the diffusion of gases through septa, and of the principle of dialysis (whereby a solution of large and small solutes can have the smaller solutes separated from the larger ones because of the greater diffusibility of the smaller molecules through a semipermeable membrane).

The Dutch scientist Jacobus Hendricus van't Hoff further developed the understanding of osmosis into a more modern form in 1886. He used the principles of thermodynamics to find precise relationships between osmotic pressure and changes in the freezing point of a solution, and between osmotic pressure and vapor pressure.

By the last decades of the twentieth century, advances in computers and numerical techniques made it possible to begin to unravel the extremely complex nature of eddy diffusion.

Previously, the crude approximations that were possible necessarily limited greatly the range of scientists' understanding of eddy phenomena.

Diffusion in gases and liquids is a fundamental phenomenon that permits living organisms to survive, and it occurs in a variety of physical systems, as well. It has been utilized by scientists to perform many complicated procedures, to develop industrial applications, and to explain relationships between various, seemingly unrelated physical phenomenon. Without knowledge of its existence and properties, not only would many of the procedures (such as dialysis for patients with diseased kidneys) be impossible to perform, but a basic understanding of many physical events and their interrelationships would not exist.

Principal terms

CONCENTRATION: the number of molecules of a substance per unit volume

GRADIENT: a gradation with distance in the rate of change of a physical quantity, such as temperature, concentration, or pressure

KINETIC ENERGY: the energy of an object that results from its motion

SOLUTE: something dissolved in solution

SOLVENT: that which dissolves or can dissolve another substance

THERMAL MOTION: the motion of molecules that occurs as a consequence of their temperature

Bibliography

De Duve, Christian. A GUIDED TOUR OF THE LIVING CELL. Vol. 1. New York: W. H. Freeman, 1984. This volume of the SCIENTIFIC AMERICAN books series provides an easy reading level for advanced high school or beginning college readers. As is usual with this series, there are superb illustrations and the subject treatment is excellent. Consult chapter 3 for information about diffusion in living systems.

Mascetta, Joseph A. CHEMISTRY THE EASY WAY. New York: Barrons, 1989. This book is intended for high school or beginning college students with a nontechnical background. Consult chapter 5 (about gases) for an easy-to-understand discussion of diffusion. There are good diagrams and an adequate index.

Matta, Michael S., and A. C. Wilbraham. ATOMS, MOLECULES, AND LIFE. Menlo Park, Calif.: Benjamin/Cummings, 1981. Another book for advanced high school or beginning college readers. The text presents very clear explanations of diffusion, osmosis, osmotic pressure, and dialysis. The diagrams are very simple but convey the content adequately. Use the index to find text references for the topics mentioned.

Rogers, Eric M. PHYSICS FOR THE INQUIRING MIND. Princeton, N.J.: Princeton University Press, 1960. The level of this book is appropriate for advanced high school or beginning college readers. It illustrates many applications of diffusion and uses a problem-oriented approach to show how knowledge of a topic can be used for the solution of problems. The index can direct the reader to those portions of the book dealing with diffusion.

Starr, Cecie, and Ralph Taggart. BIOLOGY: THE UNITY AND DIVERSITY OF LIFE. 5th ed. Belmont, Calif.: Wadsworth, 1989. This introductory text for advanced high school or beginning college students provides an easy-to-understand description of diffusion and the many occurrences of it in living systems. The relevant parts of the text are best found by consulting the extensive index. It has many excellent illustrations and a good glossary.

The Behavior of Gases

Solutes and Precipitates

Laws of Thermodynamics