# Kinetic molecular theory relationship between pressure and volume

### Kinetic molecular theory of gases (video) | Khan Academy

Express the five basic assumptions of the Kinetic Molecular Theory of Gases. Charles' Law states that at constant pressure, the volume of a gas increases or decreases by the same This relationship is shown by the following equation. To use Kinetic Molecular Theory to describe the behavior of the macroscopic gas laws. What happens to gas particles when conditions such as pressure and According to this model, most of the volume occupied by a gas is empty . What is the difference between the average speed and root mean. Kinetic molecular theory is a mixture of classical mechanics and statistics. Then the pressure on any one face (the force divided by the area of the face) would of the total kinetic energy of all the molecules divided by the volume of the box. . If the difference between my number and your number is less than or equal to a.

The magnitude of the pressure is related to how hard and how often the molecules strike the wall The "hardness" of the impact of the molecules with the wall will be related to the velocity of the molecules times the mass of the molecules Kinetic Interpretation of Absolute Temperature According to the kinetic molecular theory, the average kinetic energy of an ideal gas is directly proportional to the absolute temperature. Kinetic energy is the energy a body has by virtue of its motion: As the temperature of a gas rises, the average velocity of the molecules will increase; a doubling of the temperature will increase this velocity by a factor of four.

Collisions with the walls of the container will transfer more momentum, and thus more kinetic energy, to the walls. A microscopic picture of the molecules in a gas balls as a specific time. The magnitude of the velocity of each molecule is indicated by the length of the arrow.

If the walls are cooler than the gas, they will get warmer, returning less kinetic energy to the gas, and causing it to cool until thermal equilibrium is reached. We will have more to say about molecular velocities and kinetic energies farther on.

### Kinetic Molecular Theory of Gases - Chemistry LibreTexts

Molecular Speed Although the molecules in a sample of gas have an average kinetic energy and therefore an average speed the individual molecules move at various speeds. Some are moving fast, others relatively slowly Figure 5. At higher temperatures at greater fraction of the molecules are moving at higher speeds Figure 3.

What is the speed velocity of a molecule possessing average kinetic energy? What is the difference between the average speed and root mean square speed of this gas?

## Kinetic Molecular Theory of Gases

Boyle's law is easily explained by the kinetic molecular theory. The pressure of a gas depends on the number of times per second that the molecules strike the surface of the container. If we compress the gas to a smaller volume, the same number of molecules are now acting against a smaller surface area, so the number striking per unit of area, and thus the pressure, is now greater. Kinetic explanation of Charles' law: Kinetic molecular theory states that an increase in temperature raises the average kinetic energy of the molecules.

If the molecules are moving more rapidly but the pressure remains the same, then the molecules must stay farther apart, so that the increase in the rate at which molecules collide with the surface of the container is compensated for by a corresponding increase in the area of this surface as the gas expands. Kinetic explanation of Avogadro's law: If we increase the number of gas molecules in a closed container, more of them will collide with the walls per unit time. If the pressure is to remain constant, the volume must increase in proportion, so that the molecules strike the walls less frequently, and over a larger surface area.

Solve for kinetic energy, K, and Bob's your uncle — we're done. We made some pretty extreme assumptions beyond the four allowed postulates. The big one being that all the molecules were moving with exactly the same speed in one of only three directions. In a real macroscopic box of microscopic molecules, the molecules would be whizzing in all directions, smashing into each other countless times per second, and traveling with all sorts of different velocities.

Turns out, none of this matters. In the middle of the Nineteenth Century roughly — the Scottish physicist James Clerk Maxwell — worked out most of the statistical details.

The Austrian physicist Ludwig Boltzmann extended Maxwell's work in The final theory is known as Maxwell-Boltzmann statistics and it is beyond the scope of this book i. Maxwell-Boltzmann statistics describe the behavior of large numbers of non-interacting particles — particles that interact only briefly when they collide that is, they don't stick together to form a solid, or react chemically in any way, or do anything else to upset their boring behavior.

## Kinetic-Molecular Theory

These particles have momentums and energies that are spread out over a range of values. The proper term is distributed. The symbols on either side of K the are called angle brackets and are used whenever a quantity is averaged over time for a large collection of entites called an ensemble. For an ideal gas, the time-averaged kinetic energy of the molecules is directly proportional to its temperature. We knocked that off in an earlier chapter of this book.