Kinetic Theory of Gases, Chemistry tutorial

Introduction:

The kinetic theory of gases was introduced in the late 19th century to describe the observed properties of gases in terms of arbitrary motion of molecules. One of the most significant activities of this theory is that it illustrated that the temperature is proportional to the average kinetic energy of the molecules. Most of the quantities like pressure, diffusion constant and the coefficient of viscosity could be associated to the average velocities, mass and size of the molecules.

The kinetic theory of gases (as well termed as the kinetic-molecular theory) is a law that describes the behavior of a hypothetical ideal gas. This theory illustrates that gases are made up of very small particles in arbitrary and straight line motion. They move quickly and continuously and make collisions by one other and the walls. This was the primary theory to explain gas pressure in terms of collisions by the walls of the container, instead of from static forces which push the molecules apart. Kinetic theory as well describes how the different sizes of particles in a gas can give them dissimilar, individual speeds.

Postulates of kinetic theory of gases:

Kinetic theory makes numerous assumptions in order to describe the reasons gases act the manner they do. According to kinetic theory:

A) Gases comprise of particles in constant, arbitrary motion. They continue in a straight line till they collide by something - generally one other or the walls of their container.

B) Particles are point masses without volume. The particles are very small as compared to the space between them, that we don't consider their size in the ideal gases.

C) No molecular forces are at work. This signifies that there is no repulsion or attraction between the particles.

D) Gas pressure is due to the molecules colliding by the walls of the container. All of such collisions are perfectly elastic, signifying that there is no change in energy of either the particles or the wall on collision. No energy is gained or lost from the collisions.

E) The time it takes to collide is negligible as compared by the time between collisions.

F) Kinetic energy of the gas is a measure of its Kelvin temperature. Individual gas molecules encompass different speeds; however the temperature and kinetic energy of the gas refer to the average of such speeds.

G) Average kinetic energy of the gas particle is directly proportional to the temperature.  The increase in temperature raises the speed in which the gas molecules move.

H) The entire gas at a particular temperature encompasses the similar average kinetic energy.

I) Lighter gas molecules move faster than the heavier molecules.

Thermal Energy:

It will be noted that the temperature of a gas is in reality a measure of its average kinetic energy, and kinetic energy of a particle is associated to its velocity according to the given equation:

KE = 1/2 mv2

Here, KE symbolizes kinetic energy of a particle, 'm' equivalents mass, and v2 is the square of its velocity. As the velocity raises so does the kinetic energy. Obviously the inverse is as well true, that as kinetic energy increases so does the velocity. We can notice from this relationship how a molecule having a higher temperature will be moving faster. The temperature of the system is the average kinetic energy of its particles. Thermal energy is the net kinetic energy of all the particles in a system. Thermal energy, temperature and the speed of a molecule are all directly linked or associated.

Basic Gas Laws:

All the gas laws are based on the properties of gases laid down in the kinetic theory. In order to further comprehend kinetic theory, let us analyze some of its applications.

Boyle's Law:

Boyle's law defines that for the pressure and volume of a gas, whenever one value increases the other decreases, as long as temperature and number of moles remain stable. Boyle's law is sum up by the equation:

PV = k

Here,

'P' is the pressure of the molecules on the container.

'V' is the volume of the container

'k' is a constant.

The value of k for all time stays the same so that P and V differ suitably. For illustration, if pressure increases, 'k' must remain constant and therefore volume will decrease. This is consistent by the predictions of the Boyle's law.

In order to compare a gas where either volume or pressure differ, we can combine the equations P1V1= k and P2V2= k. As 'k' is constant for both the values of volume and pressure,

P1V1=P2V2

Charles' Law:

Charles' law define that the values for volume and temperature of a gas are directly associated. The equation for Charles' law is as follows:

V/T = k

Here,

'V' is the volume of the container

'T' is the temperature of the system in Kelvin

'k' is the constant.

For changes in the temperature and volume, k remains similar.

According to the Charles' law, gases will expand whenever heated. The temperature of a gas is in reality a measure of the average kinetic energy of the particles. As the kinetic energy rises, the particles will move faster and wish for to make more collisions by the container. Though, keep in mind that in order for the law to apply, the pressure should remain constant.

For Charles' Law, we can represent the combined equation:

V1/T1 = V2/T2

The Pressure Law (Gay-Lussac's Law):

The pressure law defines that the values for pressure and temperature of a gas are directly associated. As the temperature of a gas rises, the average speed and kinetic energy of the particles as well. This relationship is represented in the given equation as:

P/T = k

Here, 'P' is the pressure of the particles on the container, 'T' is the temperature in Kelvin and 'k' is a constant. At constant volume, this yields in more collisions and thus greater pressure the container. As the value of 'k' is similar for differing values of temperature and pressure, the pressure law can be represented as:

P1/T1 = P2/T2

Avogadro's Law:

The Avogadro's law defines that the volume of a gas is directly associated to the number of moles of atoms contained in the gas. Equation for the Avogadro's law is:

V/n = k

Here, 'V' is the volume of the container, 'n' is the amount of gas as assessed by the moles of atoms, and 'k' is a constant.

Graham's Law:

a) Diffusion:

Diffusion is a simple method which can be illustrated by the kinetic theory. Whenever you open a bottle of perfume, it can very fast be smelled on the other side of the room. This is due to the reason that the scent particles drift out of the bottle, gas molecules in the air collide by the particles and steadily distribute them all through the air. Diffusion of a gas is the method where the particles of one gas are spread throughout the other gas via molecular motion.

Graham's law of diffusion illustrates the relationship between the diffusion and molar mass.  

Rate of diffusion α 1/√molar mass

b) Effusion:

Effusion is an identical process. Effusion is the method where gas molecules escape from an empty container although a small hole. This is supposed that while a molecule is exiting, there are no collisions on that molecule.

To know how Graham's law of effusion is derived from the kinetic theory, take the equation for the kinetic energy of a gas (avoid rotation).

KE = 1/2 mv2

Root Mean Square (RMS) Speed:

In accordance to the Kinetic Molecular theory, gaseous particles are in the state of constant arbitrary motion; individual particles move at various speeds, constantly colliding and differing directions. We make use of velocity to illustrate the movement of gas particles, thus taking into account both speed and direction.

However the velocity of gaseous particles is continuously changing, the distribution of velocities doesn't change. We can't gauge the velocity of each and every individual particle, therefore we often reason in terms of the particles average behavior. Particles moving in the opposite directions have velocities of opposite signs. As a gas particle are in arbitrary motion, it is plausible that there will be around as many moving in one direction as in the opposite direction, implying that the average velocity for a collection of gas particles equivalents zero; as this value is not helpful, the average of velocities can be found out employing an alternative method.

Via squaring the velocities and taking the square root, we conquer the 'directional' component of velocity and simultaneously get the average velocity of the particle. As the value prohibits the direction of particle, we now refer to the value as the average speed. The root-mean-square speed is the measure of speed of particles in a gas, stated as the square root of the average velocity-squared of the molecules in the gas.

This is represented via the equation: vrms = √3RT/M, here vrms is the root-mean-square of the velocity, 'Mm' is the molar mass of the gas in kilograms per mole, 'R' is the molar gas constant, and 'T' is the temperature in terms of Kelvin.

The root-mean-square speed takes to account both temperature and molecular weight, two factors which directly influence the kinetic energy of a material.

vrms = √3RT/Mm

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