5.7:
Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules
The observations of different gas properties, as expressed by the various gas laws derived by Boyle, Charles, Gay-Lussac, and Avogadro, follow conceptually from kinetic molecular theory.
The pressure exerted by a gas results from the impact of constantly moving particles on the walls of its container.
Decreasing the volume of the container, while keeping the number of moles and temperature constant, brings the gas particles closer together, reducing their interparticle spacing.
In this smaller volume, the density of the gas and collision frequency — the frequency of molecule-wall collisions — increases. Therefore, the pressure exerted by the gas increases. The inverse relationship between pressure and volume is given by Boyle’s law.
Adding more moles of gas to the container at constant temperature increases the gas density, and hence, the collision frequency.
To maintain the initial pressure, the volume must expand. This direct relationship between volume and moles is given by Avogadro’s law.
Now, consider the number of moles is kept constant and the temperature is raised. Because the average kinetic energy of gas particles increases proportionally with temperature, the particles collide more frequently and forcefully.
If the volume is held constant while the temperature is increased, the density of the gas and the collision frequency increases, and hence the pressure will also increase. The direct relationship between pressure and temperature is given by Gay-Lussac’s law.
If, on the other hand, the pressure must remain constant along with a constant number of moles, then a rise in temperature must be accompanied by an increase in volume to spread the collisions out over a greater surface area. This direct relationship between volume and temperature is given by Charles’s law.
Finally, according to kinetic molecular theory, gas particles do not attract or repel one another. In a mixture of different gases, the components act independently and their individual pressures remain unaffected by the presence of another gas.
The total pressure of the mixture is, therefore, the sum of individual partial pressures. This is Dalton’s law.
5.7:
Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules
The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws (Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, and Dalton’s laws) can be derived from the assumptions of the KMT, which have led chemists to believe that the assumptions of the theory accurately represent the properties of gas molecules.
The Kinetic Molecular Theory Explains the Behavior of Gases
Recalling that gas pressure is exerted by rapidly moving gas molecules and depends directly on the number of molecules hitting a unit area of the wall per unit of time, the KMT conceptually explains the behavior of a gas as follows:
- Gay-Lussac’s law: If the temperature is increased, the average speed and kinetic energy of the gas molecules increase. If the volume is held constant, the increased speed of the gas molecules results in more frequent and more forceful collisions with the walls of the container, therefore increasing the pressure. This is also termed as Amontons’s law.
- Charles’s law: If the temperature of a gas is increased, constant pressure may be maintained only if the volume occupied by the gas increases. This will result in greater average distances traveled by the molecules to reach the container walls, as well as increased wall surface area. These conditions will decrease both the frequency of molecule-wall collisions and the number of collisions per unit area, the combined effects of which balance the effect of increased collision forces due to the greater kinetic energy at the higher temperature.
- Boyle’s law: If the gas volume is decreased, the container wall area decreases, and the molecule-wall collision frequency increases, both of which increase the pressure exerted by the gas.
- Avogadro’s law: At constant pressure and temperature, the frequency and force of molecule-wall collisions are constant. Under such conditions, increasing the number of gaseous molecules will require a proportional increase in the container volume in order to yield a decrease in the number of collisions per unit area to compensate for the increased frequency of collisions.
- Dalton’s law: Because of the large distances between them, the molecules of one gas in a mixture bombard the container walls with the same frequency, whether other gases are present or not, and the total pressure of a gas mixture equals the sum of the (partial) pressures of the individual gases.
This text is adapted from Openstax, Chemistry 2e, Section 9.5: The Kinetic-Molecular Theory.