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The Kinetic Theory of Matter

The kinetic theory of matter recognizes that matter is composed of very small particles (ions, atoms and molecules) whose different pattern of arrangements and motions result in the different possible states in which matter can occur. It also explains the properties of these states.

The kinetic theory of gases explains the empirical laws (i.e. Boyle’s law, Charles’ law, Graham’s law of diffusion, Dalton’s law of partial pressure and Avogadro’s law), which govern the behavior of gases.

The theory is based on the following assumptions about perfect or ideal gases (these are gases whose behaviors can be explained by the kinetic theory - they have no real existence):

- Gases are composed of discrete particles called molecules which are in rapid, random motion, moving at high speed in straight lines - this is the reason gases can diffuse very rapidly.

- The molecules are so small, and at low pressures are so far apart, such that on the average, the actual volume of their molecules is negligible compared with the volume of their container

- this is the reason gases do not have fixed volume, but take up the volume of the container in which they are kept.

- The molecules exert no force of attraction or repulsion upon one another. I.e., the molecules are independent of each other - this is the reason gases do not have definite shape.

- Upon collision with one another, or with any surface, they rebound without any loss in the total kinetic energy of the system. In other words, the molecular collisions are perfectly elastic.

- The pressure of the gas results from the impacts of the molecules upon the walls of the containing vessel. The pressure exerted by a gas confined within a fixed volume is proportional to nE_k , i.e., the number of molecules per unit volume (n) times their average kinetic energy (E_k).

- The average kinetic energy of all the molecules is assumed to be directly proportional to the absolute temperature of the gas. This means that molecules of different gases at the same temperature have the same average kinetic energy. The kinetic energy of a moving molecule, like that of any moving object, is the energy associated with its motion.

The quantity of kinetic energy such a molecule possesses is equal to the work it is capable of performing in being brought to a rest, and is given by the expression:

E_k = 1/2 mu²

where m is its mass and u its velocity

Note: at ordinary temperature and pressure, real gases approximately fulfill the above assumptions.

The three properties of gases that are especially important are diffusibility, thermal expansion and compressibility.

All gases are characterized by diffusibility, but the rates at which different gases diffuse depend on their molecular weights.

When heated, gases expand to a much greater extent than do solids or liquids- all gases tend to behave alike in this respect. In comparison with solids and liquids, gases are very easily compressed - all gases tend to behave alike in this regard also. These properties, as well as the empirical laws governing the behavior of gases can be explained by the kinetic theory.

Diffusion is a phenomenon whereby particles of a substance move from an area of high concentration into an area of low concentration - gases diffuse rapidly. For example, if a small quantity of an odorous gas, e.g. hydrogen sulphide, is released at one point of a room, the smell soon gets to all parts of the room. This (diffusion), can be explained using the kinetic theory of gases.

From the assumptions of the theory, we have that:

I. Gases are made of discrete particles called molecules, and not a single piece. If they were made of a single piece, then, the smell of the hydrogen sulphide would not pervade the whole room at the same time, but would probably be perceived at one corner of the room at a time.

II. The molecules are relatively far apart and are in rapid, random motion, moving at high speeds in straight lines. The spontaneous diffusion of hydrogen sulphide and air into each other is the result of molecules of each kind moving into the spaces between the molecules of the other kind.

This account for the smell getting to every part of the room in a couple of minutes after the release.

Compressibility of gases can be explained from the assumption of the kinetic theory, which states that a gas consists of particles that are separated from one another by large spaces. Based on this, it is therefore easy to bring the molecules closer together (i.e. compressed) when the volume of the container is reduced.

Reduction in volume leads to decrease in temperature (according to Charles’ law, V α T). Hence, compression of gases results in a drop of temperature in the system - the kinetic energy of the system also drops.

Expansion of gases can be explained by the kinetic theory from the assumptions which state that:

1. Gases are in constant rapid motion, moving at great speeds, occupying the volume of the container.

2. The average kinetic energy of all the molecules is assumed to be directly proportional to the absolute temperature of the gas. The greater the average kinetic energy of gas molecules, the greater they are able to move and occupy more volume. Therefore, at higher temperatures, gases obtain higher kinetic energy, and thus expand (or occupy large volumes).

The kinetic theory of gases explain Charles’ law thus:

I. Gases, due to their molecules been very far apart, do not have appreciable volumes, but occupy the volume of the vessel in which they are kept - the greater or higher their molecules are able to move in the vessel, the more volume they occupy, and vice versa.

II. Gaseous molecules are able to move or expand because they possess kinetic energy. Their average kinetic energy is directly proportional to the absolute temperature. I.e., the higher the temperature, the greater the average kinetic energy, and the more volume they occupy, and vice versa. In general, we can sum-up the explanation this way: since the volume which gas molecules occupy is directly dependent upon their movement, which in turn is directly dependent upon their kinetic energy, and which in turn is directly dependent on the absolute temperature, it goes to prove that the volume is directly proportional to its absolute temperature at constant pressure – Charles’ law (V α T).

Note: Another way Charles’ law can be expressed is: that the volume is directly proportional to the average kinetic energy of the gas molecules at constant pressure.

Boyle’s law gives an inverse relationship between the volume of a fixed mass of gas and its pressure at constant temperature. I.e., V α 1/P. The kinetic theory explains the law as follows: From the assumptions of the kinetic theory of gases, the pressure exerted by a gas is due to the collisions between the gas molecules and the walls of the vessel. Hence, the greater the rate of collision, the greater the pressure.

At lower volumes, molecules are closer to one another, thus they collide more frequently with the walls of the container, leading to increase in pressure. The reverse would occur if volumes were increased. Therefore, the relationship between volumes and pressures of a gas at constant temperature is an inverse one as given by Boyle’s law.

Dalton’s law of partial pressure can be explained from the assumption which states that there is no attraction between gas molecules. Therefore, in a mixture of gases, each kind of molecule strikes the walls of the container the same number of times per second, and with the same force, as if it were the only kind of molecule present.

Thus, the partial pressure of a gas is not changed by the presence of other gases. Each partial pressure is proportional to the number of molecules of that species present, and the total pressure exerted by the mixture of gases is the sum of the pressures exerted by the individual components.

Graham’s law of diffusion can be explained from the assumption which states that the average kinetic energy of gas molecules is directly proportional to the absolute temperature - molecules of different gases at the same temperature have the same kinetic energy. This means that molecules of one kind, A, must have velocities (or rate of diffusion) that are different from velocities (or rate of diffusion) of molecules of another gas, B, unless they have the same masses.

Mathematically, if

½ m_Au²_A = ½ m_Bu²_B

and u²_A/u²_B = m_B/m_A

So that u_A/u_B = √m_B/m_A

or R_A/R_B = √m_B/m_A

 For example, a methane molecule (molecular weight, 16), A, has a mass one fourth as great as the mass of a sulphur(IV) oxide molecule (molecular weight, 64), B. If

m_B/m_A = 4

u_A/u_B = √4 = 2

or u_A = 2 x u_B

The methane molecules have an average velocity twice that of the sulphur(IV) oxide molecules. Thus, the kinetic theory shows why methane diffuses twice as fast as sulphur(IV) oxide, and why , in general, different gases diffuse at rates that vary inversely with the square roots of their molecular weights or densities. 

Avogadro’s law can be explained from the assumptions:

1. The average kinetic energy of gas molecules is proportional to the absolute temperature. Hence, at the same temperature, the average kinetic energy of two different gases are the same.

2. The pressure exerted by a gas confined within a fixed volume is proportional to nE_k , i.e., the number of molecules per unit volume times their average kinetic energy. Therefore, if two gases are at the same temperature, then E_k (the average kinetic energy per molecule) is the same for both gases, and if the two gases are also exerting the same pressure, then nE_k is the same for the two gases.

Thus, if two gases are at the same temperature and pressure, n must be the same for both. The number of molecules per unit volume is the same - i.e., equal volumes of different gases contain the same number of molecules if they are at the same temperature and pressure.  

Related Tutorials

Limitations of the Kinetic Theory
Application of the Kinetic Theory of Matter
Deviations from Ideal Gas Behavior
Effect of Collisions on Pressures