# Kinetic Molecular Theory

The Kinetic Molecular Theory helps us understand how gas molecules behave in a container. Imagine a container filled with pure monatomic helium (He) that has a fixed volume. When we lower the temperature, the pressure inside decreases, affecting the kinetic energy of the gas molecules. Helium molecules are so tiny and far apart that no forces hold them together. This is why the volume of monatomic helium gas is almost negligible.

Monoatomic helium (He) is a great example of a gas molecule that behaves similarly to what the Kinetic Molecular Theory predicts. But what is this theory? Let's find out! In this article, we will define the Kinetic Molecular Theory, discuss its assumptions, and provide examples to help you understand it better.

## What is the Kinetic Molecular theory?

The kinetic molecular theory aims to explain the behavior of gases. Gases that behave ideally are known as ideal gases.

Ideal gases are gases that behave according to the kinetic molecular theory. To learn more about the behavior of ideal gases, check out the article "Ideal Gas Law"!

## Postulates of Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory is based on five assumptions about ideal gases:

1. Gases are made up of tiny particles that are in constant, random motion.
2. These gas particles have kinetic energy, and the amount of kinetic energy depends on the temperature of the gas.
3. The collisions between gas particles are elastic, which means that there is no transfer or loss of energy during the collision.
4. Gas particles are very small and occupy no volume.
5. There are no intermolecular forces (attraction or repulsion) present, so gas particles will move in a straight line until they collide with the walls of the container or other gas particles.

Let's take a closer look at each of these postulates to better understand how the Kinetic Molecular Theory works.

### Postulate 1: Gases are made up of particles that are in constant, random motion.

When we look at the basic properties of gases, we know that gases take the shape and volume of the container, gases can be compressed and they exert a force on the container, this is called pressure.

This pressure is coming from the collisions between the walls and the gas molecules. Inside a container, gas particles move in constant, random, straight-line motion, colliding with the walls of the container and between gas particles. This constant movement prevents gas particles from staying still in one area of the container and helps gas particles to spread throughout the container.

Think about a balloon inflated with helium. After a while, the balloon will start shrinking. This is because the rubber contains very small holes that allow gas molecules to escape. So, when considering gases, we also have to talk about the gas properties of diffusion and effusion.

Diffusion is the movement of a gas mixture from high to low concentration. Diffusion allows gases to mix together!Effusion is the rate at which gas is able to escape through a hole in the container.

And, as you could expect, there is also a law that explains this behavior of gases! This law is called Graham's Law.

Graham's law states that, at a constant temperature and pressure, the rates of effusion of gases are inversely proportional to the square root of their molar masses. In other words, the greater the molar mass, the slower the speed of the gas.

The formula for Graham's Law is:

Where,

r1 = the rate of effusion of gas Ar2 = the rate of effusion of gas BM1 = molar mass of gas AM2 = molar mass of gas B

Which of the following gases will have the highest and the lowest rates of effusion? H2, CO2, and PF5.First of all, we need to calculate the molar masses of each of those gases. Then, we compare their molar masses. The gas with the smaller molar mass will have the greatest rate of effusion, while the heavier gas will have the lowest rate of effusion! So, from the calculated molar masses, we can say that H2 has the highest effusion rate, while PF5 has the lowest rate of effusion!

Let's look at an example that involves calculating the ratio of effusion between two gases, using the formula for graham's law!

Calculate the ratio of the rates of effusion of helium (He) to methane (CH4).First, find the molar masses for He and CH4:Now, we can plug these molar masses into graham's law equation and find the ratio of helium to methane!

Gases also have a very unique sort of speed that is used to describe the collision of gas particles, while considering speed and direction. The average velocity of gas particles is called the root-mean-square speed () and is represented by the following equation:

Where,

R = gas constant (R = 8.3145 J/K·mol)T = temperature of a gas in Kelvin (K)M = molar mass of gas in Kg/mol

What would be the root-mean-square speed of oxygen gas (O2) at 50°C?Notice that we were given the temperature in celsius. First, we need to convert 50°C to Kelvin:Next, calculate the molar mass of O2  in Kg/mol: Finally, we can plug all of these variables into the root-mean-square-velocity equation!

### Postulate 2: Gas particles have kinetic energy.

A typical Maxwell-Boltzmann distribution curve is a bell-shaped curve that shows the distribution of velocities of gas particles at a given temperature. The x-axis represents the velocity of the gas particles, while the y-axis represents the number of particles with a particular velocity.

The curve shows that at any given temperature, there is a range of velocities that the gas particles can have. The highest point of the curve represents the most probable velocity, which is the velocity that the majority of the gas particles have. As you move away from the most probable velocity in either direction, the number of gas particles with that velocity decreases.

Another important concept that you might come across when studying the Maxwell-Boltzmann distribution is the root-mean-square speed. This is the average velocity of the gas particles and is represented by the peak of the curve. The root-mean-square speed increases with temperature, which means that at higher temperatures, gas particles move faster on average.

The area under the curve represents the total number of gas particles, and the area to the right of a certain velocity represents the percentage of gas particles that have that velocity or higher.

Overall, the Maxwell-Boltzmann distribution is a useful tool for understanding how temperature affects the behavior of gas particles and their velocities.

The distribution curve has three different speeds: probable speed, mean speed, and root-mean-square speed. The probable speed shows the largest number of molecules with that speed. The mean speed is the average speed of gas molecules. The root-mean-square speed is the average velocity of gas particles.

Probable speed

Mean speed

Root-mean-square speed

Both temperature and molar mass affect the shape of the distribution curve. When temperature increases, the molecules move with a faster velocity. The higher the velocity, the broader the distribution curve will be. When molar mass increases, the molecules moving at faster velocities decrease. The lower the molar mass, the broader the distribution curve. A broader curve means that there is a larger range for the velocities of the individual gas molecules.

For example, in the distribution curve below, we can see that since He has the smallest molar mass, they have the highest velocity compared to Xe, which is a very heavy gas.

Calculate the most probable speed of F2 molecules at a temperature of 335 K. First, we need to calculate the molar mass of F2 in kg/mol:

### Postulate 3: The collisions between gas particles are elastic.

The third postulate of the kinetic molecular theory states that when gas particles collide, no energy is lost or transferred from one gas particle to another. So, the total kinetic energy before collision will be the same as the total kinetic energy after the collision.

Elastic collisions are collisions where the internal kinetic energy is conserved (no energy is lost).

### Postulate 4: Gas particles are very small so their volume is insignificant.

Inside a container, there is a lot of empty distance so the distance between gas particles is large! (compared to a gas particle)

So, the fourth postulate of the kinetic molecular theory states that ideal gases occupy no volume since their particles are so small compared to the volume in which it is being contained.

### Postulate 5: Gas particles have no attractive or repulsive forces.

According to the kinetic molecular theory, gases contain no intermolecular forces holding them together. This is because the postulates of the kinetic molecular theory state that gas particles are in constant, random, point-like motion and have no intermolecular forces present between gas molecules. This means that the particles are very small and occupy no volume, and the collisions between gas particles are elastic. Therefore, the intermolecular forces that exist between molecules, such as ion-dipole forces, dipole-dipole forces, hydrogen bonding, and London dispersion forces, are not present in gases.

References:

Arbuckle, D., & Albert.io. (2022, March 01). The Ultimate Study Guide to AP® Chemistry. Retrieved April 5, 2022, from https://www.albert.io/blog/ultimate-study-guide-to-ap-chemistry/

Atkins, P. (2017). Atkins' physical chemistry. New York, NY: Oxford University Press.

Hill, J. C., Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C. J., Woodward, P. M., & Stoltzfus, M. (2015). Chemistry: The Central Science, 13th edition. Boston: Pearson.

Moore, J. T., & Langley, R. (2021). McGraw Hill: AP Chemistry, 2022. New York: McGraw-Hill Education.

Zumdahl, S. S., Zumdahl, S. A., & DeCoste, D. J. (2017). Chemistry. Boston, MA: Cengage.

## Kinetic Molecular Theory

What is the Kinetic Molecular Theory?

The Kinetic molecular theory is a theory used to describe the behavior of ideal gases.

Which are the postulates of the kinetic molecular theory?

The postulates of the kinetic molecular theory (KMT) are: Gases are made up of particles that are in constant, random, point-like motion. Gas particles have kinetic energy, and the amount of kinetic energy depends on the temperature of the gas. The collisions between gas particles are elastic, so there is no transfer of energy or loss of energy. Particles are very small so they occupy no volume There are no attraction or repulsion (intermolecular forces) present, so gas particles will move in a straight line until they collide with the walls of the container/other gas particles.

What is the kinetic molecular theory of gases?

The Kinetic molecular theory is a theory used to describe the behavior of ideal gases. The kinetic molecular theory consists of five postulates that describe how ideal gases should behave.

Who proposed kinetic molecular theory?

The kinetic molecular theory was proposed by two scientists, James Clerk Maxwell and Ludwig Boltzmann.

How is condensation explained by the Kinetic molecular theory?

Condensation is the process of turning a gas into a liquid by cooling the temperature. When the temperature decreases, the molecules also slow down and allow the intermolecular forces to infleunce the movement of the gas molecules and convert them into a liquid. The kinetic molecular theory explains condensation because it states that gas particles contain kinetic energy. When the temperature decreases, kinetic energy also decreases.     