In deriving the ideal-gas equation from the kinetic molecular model, we ignored potential energy due to the earth’s gravity. Is this omission justified? Why or why not?

The basic ideal gas equation is -

PV=nRT

Where is pressure, V is volume, n is the number of moles, R is gas constant, and T is the absolute temperature.

The theory of treating samples of matter as a large number of small particles (atoms or molecules), all of which are in constant, random motion is known as the kinetic molecular model.

It is justified if the difference in the gravitational potential energy of an atom at the top and at the bottom of the container is much smaller than the average kinetic energy of the molecule. Let the container’s height be $h$. Then-

${\left(\frac{1}{2}m{v}^2\right)}_{avg}\gg mgh$

Here, $m$is the mass of a molecule of gas $v$is the average velocity of molecules of gas and $g$is the acceleration due to gravity.

Therefore, the derivation of the ideal-gas equation from the kinetic molecular model by ignoring potential energy is justified.