In 1661, Boyle discovered the law that bears his name. By supposing that gasses are made up of small atomic particles, Boyle, Newton, and others attempted to explain the behavior of gasses. More than 150 years later, the true nuclear theory was established.
Assuming that gasses are made of fast-moving atoms or molecules, the kinetic theory of gasses describes how gasses behave. This is conceivable because interatomic interactions, which are short-range forces crucial in solids and liquids, may be ignored in glasses. Maxwell, Boltzmann, and others established the kinetic theory in the nineteenth century. It has been a resounding success.
It is consistent with gas laws and Avogadro’s theory and provides a molecular interpretation of pressure and temperature in a gas. It appropriately explains several gases’ specific heat capacities. It also links quantifiable gas qualities like viscosity, conduction, and diffusion to molecular parameters, resulting in molecule sizes and masses estimations.
In this segment, we learned about the Kinetic theory of gasses, from which many gross features of a gas can be inferred based on a simplified molecular or particle description of the gas. In the nineteenth century, British scientist James Clerk Maxwell and Austrian physicist Ludwig Boltzmann were instrumental in inventing the idea, becoming one of modern science’s most essential notions. We also described all the postulates/assumptions of the Kinetic theory of gasses. Boyle’s law is clearly explained by the kinetic molecular hypothesis. The pressure of a gas is determined by how many molecules it strikes the container’s surface each second. We hope you will find this article informational and fun to read. Stay tuned for more such content!
Source: By A. Greg (Greg L at English Wikipedia) – Own work, Public Domain
A gas sample is composed of molecules. A molecule is the smallest unit with all of the sample’s chemical attributes. The specific behavior of a gas’s considerable number of molecules determines its perceived behavior. The kinetic theory of gases aims to create a model of molecular behavior that will produce the observed behavior of an ideal gas.
At low densities, the assumptions of the kinetic theory are very close to reality. At 0-1 atm and room temperature, the molecular size is 100 times smaller than the typical spacing between molecules. Although actual molecules exert electromagnetic forces on one another, these forces may be overlooked since the shared space is considerable compared to their size. If no lasting deformation is caused, collisions between actual molecules are elastic.
When the temperature isn’t too high, this is true. If the temperature of the walls and the gas temperature are the same, collisions with the walls are elastic.
This assumption will be valid if the gas is left in the container for a long enough time. For the time being, the fact that Newton’s laws can describe the motion of molecules can be dismissed as sheer chance. If the number of molecules is enormous, the last assumption is almost correct. Because there are approximately 61023 molecules per mole, this criterion almost always holds in practice.
Gas kinetic theory is based on the molecular approach, representing matter. A given amount of gas comprises a vast number of molecules in constant random motion (usually on the order of Avogadro’s number). The average distance between molecules under normal pressure and temperature is a factor of or greater than the typical size of a molecule (2 Å). As a result, the molecules’ interactions are insignificant, and we can assume that they travel freely in straight lines following Newton’s first law.
However, they come close to one other on occasion, encounter intermolecular forces, and their velocities alter. Collisions are the name for these kinds of interactions. The molecules collide with one other or with the walls regularly, changing their speeds.
The collisions are thought to be elastic. Based on kinetic theory, we may develop an expression for the pressure of a gas.
We start with the assumption that gas molecules are in a constant state of random motion, interacting with one another and the container’s walls. When the molecules collide within the wall, an elastic collision occurs.
This means that the whole kinetic energy of the system is conserved. As is customary, the total momentum is conserved.
Under the Kinetic theory of gasses, the pressure of an Ideal gas is defined as,
P=(1/3)n m ‾v²
P= Pressure
n= number of molecules per unit volume
‾v 2= mean o d the squared speed
m= mass of the gas
It is called root mean square speed or rms speed, or the square root of mean square speed.
V r ms= √(3ρ/ρ)
=√(3 p V/M)
Example: Find the rms speed of nitrogen at STP. Assume the density of nitrogen is 1.25 kg m-3
Solution:
V r ms= √(3ρ/ρ)
=√(3105 N m-2/1.25 kg m-3 )
= 490 ms-1
The particles move too swiftly at high temperatures for the weak intermolecular interactions to attract them. At low temperatures, however, the molecules move more slowly — so slowly that they become attracted to surrounding molecules.
The kinetic theory of the gasses model assumes that molecules are tiny compared to the distance between them. There are constant and random collisions between the molecules and the container walls as they whiz by. If the molecules move more, the temperature rises.
The kinetic molecular hypothesis clearly explains Boyle's law. The number of times per second that the molecules strike the container's surface determines the pressure of the gas. When we compress a gas to a smaller volume, the same number of molecules now act against a smaller surface area, resulting in a higher number of molecules striking per unit of measurement, hence a higher pressure.