Molecular Kinetic Theory: History, Postulates And Examples

The molecular kinetic theory is one that seeks to explain the experimental observations of gases from a microscopic perspective. That is, it tries to associate the nature and behavior of the gaseous particles with the physical characteristics of the gas as a fluid; explain the macroscopic from the microscopic.

Gases have always been of interest to scientists because of their properties. They occupy the entire volume of the container in which they are found, being able to be completely compressed without their content opposing the least resistance; and if the temperature increases, the container begins to expand, and may even crack.

Many of these properties and behaviors are summarized in the ideal gas laws. However, they consider the gas as a whole and not as a collection of millions of particles scattered in space; furthermore, it does not provide, based on pressure, volume and temperature data, further information regarding how these particles move.

It is thus then that the molecular kinetic theory (TCM), proposes to visualize them as mobile spheres (upper image). These spheres collide with each other and the walls arbitrarily, and maintain a linear trajectory. However, when the temperature decreases and the pressure increases, the trajectory of the spheres becomes curved.

A gas, according to TCM, should behave like the spheres in the first frame of the image. But, by cooling and increasing the pressure on them, their behavior is far from ideal. They are then real gases, close to undergoing liquefaction and thus pass to the liquid phase.

Under these conditions, the interactions between the spheres become more important, to the point that their velocities momentarily slow down. The closer they are to liquefaction, the more curvy their trajectories become (inset on the right), and their collisions are less energetic.

History

Daniel Bernoulli

The idea of ​​these spheres, better called atoms, had already been considered by the Roman philosopher Lucretius; not for gases, but for solid, static objects. On the other hand, in 1738 Daniel Bernoulli applied the atomic vision to gases and liquids by imagining them as disordered spheres moving in all directions.

His work, however, violated the laws of physics at the time; a body could not move eternally, so it was impossible to think that a set of atoms and molecules would collide with each other without losing their energy; that is, the existence of elastic collisions was not possible.

Rudolf clausius

A century later, other authors reinforced TCM with a model where the gaseous particles moved in only one direction. Rudolf Clausius, however, compiled his results and assembled a more complete model of TCM with which he sought to explain the ideal gas laws demonstrated by Boyle, Charles, Dalton, and Avogadro.

James Clerk Maxwell and Ludwig Boltzmann

In 1859, James Clerk Maxwell proposed that gaseous particles exhibit a range of speeds at a given temperature, and that a set of these can be considered by means of an average molecular speed.

Then in 1871 Ludwig Boltzmann connected existing ideas with entropy, and how gas thermodynamically always tends to occupy as much space as possible in a homogeneous and spontaneous way.

Postulates of molecular kinetic theory

To consider gas from its particles, a model is necessary in which certain postulates or assumptions are fulfilled; postulates that logically must be able to predict and explain (as faithfully as possible) macroscopic and experimental observations. That said, the TCM postulates are mentioned and described.

The volume of the gaseous particles is negligible

In a container filled with gaseous particles, these disperse and move away from each other in all corners. If for a moment they could all be brought together at a specific point in the container, without liquefaction, it would be observed that they only occupy a negligible portion of the volume of the container.

It means that the container, even if it contains millions of gaseous particles, is actually more empty than full (volume-void ratio much less than 1); therefore, if its barriers allow it, it and the gas within it can be compressed abruptly; since in the end the particles are very small, as is their volume.

The image above accurately illustrates the above, using a bluish-colored gas.

The attractive forces between the particles are zero

The gaseous particles inside the container collide with each other without enough time for their interactions to gain strength; even less when what mainly surrounds them is molecular vacuum. An immediate consequence of this is that their linear paths allow them to completely encompass the volume of the container.

If this were not the case, a container with a “bizarre” and “labyrinthine” shape would have humid regions as a result of gas condensation; instead, the particles travel around the container in full freedom, without the force of their interactions stopping them.

The linear trajectories of the upper image (A.) demonstrate this postulate; while if the trajectories are curved (B.), it shows that there are interactions that cannot be ignored between the particles.

Gaseous particles are always in motion

From the first two postulates, the fact that the gas particles never stop moving also converges. Once blurred in the container, they collide with each other and with its walls, with a force and speed directly proportional to the absolute temperature; this force is, pressure.

If the gaseous particles stopped moving for an instant, “tongues of smoke” would be witnessed inside the container, emerging from nowhere, with enough time to arrange themselves in a vacuum and give random shapes.

Collisions between the particles and the walls of the container are elastic

If only elastic collisions between the gaseous particles and the walls of the container predominate inside the container, condensation of the gas will never occur (as long as the physical conditions do not change); or what is the same as saying that they never rest and are always colliding.

This is because in elastic collisions there is no net loss of kinetic energy; a particle collides with the wall and bounces at the same speed. If a particle when colliding slows down, the other accelerates, without producing heat or sound that dissipates the kinetic energy of either of them.

Kinetic energy does not remain constant

The movement of the particles is random and chaotic, so that they do not all have the same speed; as happens, for example, on a highway or in a crowd. Some are more energetic and travel faster, while others are slow, waiting for a collision to speed them up.

To describe its speed, it is then necessary to calculate an average; and with this, the average kinetic energy of the gaseous particles or molecules is obtained in turn. As the kinetic energy of all the particles is constantly changing, the averaging allows better control of the data and can be worked with greater reliability.

Average kinetic energy is equal to a given temperature for all gases

The average molecular kinetic energy (EC mp ) in a container changes with temperature. The higher the temperature, the higher the energy will be. Because it is an average, there may be particles or gases that have higher or lower energy than this value; some faster and some slower, respectively.

It can be shown mathematically that EC mp depends exclusively on temperature. This means that no matter what the gas is, its mass or molecular structure, its EC mp will be the same at a temperature T and will only vary if it increases or decreases. Of all the postulates, this is perhaps the most relevant.

And what about the average molecular speed? Unlike the EC mp , the molecular mass does influence the speed. The heavier the gas particle or molecule, it is natural to expect it to move more slowly.

Examples

Here are some brief examples of how TCM has managed to explain the ideal gas laws. Although not addressed, other phenomena, such as diffusion and effusion of gases, can also be explained with TCM.

Boyle’s Law

If the volume of the container is compressed at constant temperature, the distance that the gaseous particles must travel to collide with the walls decreases; which is equal to an increase in the frequency of such collisions, resulting in greater pressure. As the temperature remains constant, EC mp is also constant.

Charles Law

If you increase T, EC mp will increase. The gaseous particles will move faster and will collide more times with the walls of the container; the pressure increases.

If the walls are flexible, able to expand, their area will become larger and the pressure will drop until it becomes constant; and as a result, the volume will also increase.

Dalton’s Law

If several liters of different gases were added to a spacious container, coming from smaller containers, its total internal pressure would be equal to the sum of the partial pressures exerted by each type of gas separately.

Why? Because all gases begin to collide with each other and to disperse homogeneously; the interactions between them are zero, and the vacuum predominates in the container (TCM postulates), so it is as if each gas were alone, exerting its pressure individually without the interference of the other gases.

References

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