The similar behavior of all gases suggests that they have the same structure. For example, since gases are easily compressible, the distance between their molecules should be much larger than the size of the molecules themselves, and given that the gases quickly occupy the volume provided to them completely, it means that their constituent particles are in constant motion. In molecular kinetic theory, the basic equation for ideal gases relates macroscopic thermodynamic quantities that determine its state.
General description of gas theory
The basic equation for ideal gases in molecular kinetic theory is derived from the idea that gases are composed of small particles (molecules) that are constantly moving. Under equal conditions, the molecules of two different gases move with different average speeds. This speed also varies with temperature; as it increases, the molecules accelerate their movement.
The temperature of ideal gases in molecular kinetic theory is a measure of the average energy of molecules that are assumed to be completely elastic. The molecules are in constant motion, collide with each other and bounce elastically. If you throw the ball on asphalt, it will bounce off of it, however, with each such bounce its height will become less and less, that is, the ball will lose energy, which means that its rebound from asphalt is not absolutely elastic. According to the basic equation of ideal gases, gas molecules in molecular kinetic theory do not lose energy in a collision.
As soon as changes occur in such macroscopic parameters as temperature and pressure, knowledge of the peculiarities of the motion of molecules can explain the behavior of gases. At specific temperature and pressure, the same average number of molecules for an arbitrary gas is contained in the same volume. This fact is a postulate for the basic equation in the kinetic-molecular theory of ideal gases.
Brownian motion
For the first time, the peculiarities of particle motion in gases and liquids were observed by the Scot Robert Brown in 1827. In his observations, solid particles that were suspended in a gas or in a liquid made random zigzag motions.
Brown found that the smaller the size of the suspended particle, or the higher the temperature of the gas or liquid, the more clearly these chaotic movements appear.
The Brownian motion indicated that the molecules that make up the liquid and gaseous bodies are in constant chaotic movement. These representations and observations took shape in the kinetic theory of matter, the basic postulates of which are as follows:
- Molecules are in constant motion.
- Heat is a sign of the movement of molecules.
Molecular Kinetic Gas Theory
After Robert Boyle discovered a simple experimental law on the behavior of gases in 1661, he tried to create an ideal theory of motion in them, which was subsequently developed by Bernoulli, Joel, Clausius and Einstein. This doctrine, called molecular kinetic theory for an ideal gas, explains the macroscopic experimental behavior of matter through its microscopic analysis.
The following postulates are introduced in this theory:
- Gas is a conglomerate of particles (molecules and atoms) that obey the Newtonian laws of mechanics. In this ideal gas, intermolecular interactions can be neglected, that is, each molecule is absolutely independent of its other elements.
- A huge number of molecules move randomly, and the distances between them far exceed their size.
- Between the molecules in the gas, there are no forces other than elastic interactions in the collision of molecules with the walls of the vessel or with each other.
- At any moment in time, every gas molecule has a speed that is different from the speed of other molecules, so their kinetic energies are different, however, the average parameter of the entire set of elements in a substance is proportional to the absolute temperature of the gas.
Basic thermodynamic quantities
The following macroscopic characteristics are included in the basic equation for ideal gases in molecular kinetic theory:
- Pressure. The nature of this quantity consists in the constant bombardment by the molecules of the walls of the vessel and the surface of any body that is placed in the gas.
- Temperature. This value should be understood as the measure of motion of gas particles, the higher it is, the more restless the particles behave.
- Volume. By it is meant the region of space in which the gas molecules are located.
Microscopic explanation of gas behavior
It is reasonable to assume that if the distances between the gas particles are relatively large, then there are no force interactions between them, with the exception of random elastic collisions. Since they are elastic, the kinetic energy of the entire system is conserved.
According to the laws of classical mechanics, between collisions, gas particles move uniformly and rectilinearly, while the free motion time is much longer than the collision periods.
The basic postulates of the MKT make it possible to establish the basic equation for ideal gases in molecular-kinetic theory, the predictions of which are in good agreement with experimental observations.
Statistics and MKT
The macroscopic parameters that are observed experimentally, for example, pressure and temperature, are averaged values for all gas molecules, therefore, to describe them, it is necessary to use statistical analysis.
The observed pressure is the result of impacts of millions and billions on the walls of a vessel of gas molecules. In this case, the resulting force is directed perpendicular to the wall, since all other forces in other directions cancel each other out.
Temperature is a measure of the kinetic average energy of gas particles. Note that the average particle velocity in a gas is higher than that in a liquid.
Statistical representations of MKT allow us to calculate the number of particles making up a gas under given conditions, that is, under known conditions: pressure, temperature, and volume.
The equation of state for an ideal gas
If we apply the MKT postulates for an ideal gas, we can obtain the following expression: PV = nRT, where V, P, T, n, R are the volume, pressure, gas temperature, amount of substance, and the gas constant is universal, respectively. This expression is called the basic equation for ideal gases in molecular-kinetic theory. The amount of substance n is expressed in special units - mol. One mole is such a parameter that contains 6.023 * 10 23 particles, this value is the Avogadro number, which is named after the famous Italian scientist. The universal gas constant is equal to the product of the Boltzmann constant and the Avogadro number, that is, R = 6.023 * 10 23 * 1.38 * 10 -23 = 8.31 J / (mol * K).
Ideal gas volume and pressure
The equation, the main one in MKT (molecular kinetic theory), says that the product of pressure by volume is a constant if the amount of substance and the temperature of the gas do not change. From here we get a special case of the basic equation of state - the Boyle-Mariotte law: P 1 V 1 = P 2 V 2 , that is, for any isothermal process of an ideal gas, the pressure of the occupied volume is inversely proportional.
Gay Lussac Laws and Gas Temperature
The basic equation of MKT also allows us to establish the relationship between temperature and volume during the isobaric process, that is, which occurs with constant pressure. In this case, the expression V 1 / T 1 = V 2 / T 2 is obtained. This expression is called the first Gay-Lussac law.
Now, if we assume that the volume remains constant for an ideal gas, from the main MKT equation we get P 1 / T 1 = P 2 / T 2 , such a process is called isochoric, and the expression is called the second Gay-Lussac law.
In both Gay-Lussac laws, the absolute temperature of the gas is in direct proportion to volume or pressure.
Real gases
The basic MKT equation of an ideal gas in physics gives good results for all real gases under normal conditions, that is, at temperatures close to room temperature and at pressures close to atmospheric. At higher values of these thermodynamic quantities, the behavior of gases begins to differ from ideal, since weak van der Waals interactions between gas molecules appear.
For the case of real gases, the interactions of molecules in which cannot be neglected, the equation of state was generalized. It has the form: (P + an 2 / V 2 ) (V-nb) = nRT, where a and b are the van der Waals constants for a particular gas.