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# Pressure exerted by an ideal gas molecule is given by the expression :

Last updated date: 13th Jul 2024
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Hint: The force that a gas exerts on the walls of its container is described as its pressure. When you blast air into a balloon, it expands because the weight of air molecules on the interior of the balloon is higher than on the outside. a property that governs the direction of mass flow is known as pressure.

According to Kinetic Molecular Theory, gas particles are in continuous motion and have perfectly elastic collisions. Both Charles' and Boyle's Laws can be explained using Kinetic Molecular Theory. The average kinetic energy of a set of gas particles is only proportional to absolute temperature.
In order to understand what has been found experimentally in gases, the Kinetic Theory of Gases has proposed a set of assumptions. While the number of them vary, the central meaning remains the same. The assumptions are:
The molecules of a certain gas are similar and move at random.
Collisions between molecules and between molecules and the container's walls are completely elastic.
As opposed to the volume of the vessel, the volume of a molecule is insignificant.
There are no intermolecular forces acting on the molecules.
The time required for a collision of two molecules is insignificant as compared to the time required for a collision between a molecule and the wall.
On the basis of these assumptions, a formula can be derived that connects the pressure, volume, the number of molecules, individual mass, and the mean velocity.
$\dfrac{{M{C^2}}}{{3V}}$ is the pressure exerted by an ideal gas molecule. The expression for the pressure of a gas molecule, which is represented as $P$ , is given by
$P = \dfrac{{M{C^2}}}{{3V}}$
Here,
The mass of the gas is $M$ ,
The root mean square velocity of the gas molecules is given by $C$ ,
The volume of a gas is given by $V$.
Thus, the pressure exerted by an ideal gas molecule is given by the expression $P = \dfrac{{M{C^2}}}{{3V}}$.

Note:
It must be noted that the kinetic theory of gases is critical for understanding the particle capture process through the diffusion mechanism. According to this theory, gas is made up of a huge number of small-sized molecules that are separated by large distances.