[tex]\rm v_{rms}=\sqrt{\dfrac{3k_BT}{m} }[/tex]
Kinetic Molecular Theory (KMT) states that a gas consists of molecules that move at a constant and random speed. The collisions between molecules are perfectly elastic so that no energy is wasted.
The molecules move in straight lines until they collide
Energy because this motion is expressed as Kinetic energy (KE) which can be formulated as:
[tex] \displaystyle KE = \frac {1} {2} mv ^ 2 [/tex]
The average kinetic energy value is only affected by temperature changes. The higher the temperature, the average kinetic energy of the molecule increases
This molecule is very small when compared to the distance between molecules, so the volume of gas contains mostly empty space
Gas particles move randomly (both speed and direction, as vector)
Average velocities of gases can be expressed as root-mean-square averages. (V rms)
[tex]\large {\boxed {\bold {v_ {rms} = \sqrt {\dfrac {3RT} {Mm}}}}[/tex]
R = gas constant, T = temperature, Mm = molar mass of the gas particles
From the question
R = 8,314 J / mol K
T = temperature
Mm = molar mass, kg / mol
for absolute temperature 273.15 K
, and For Boltzmann constant (k), vrms :
[tex]\rm v_{rms}=\sqrt{\dfrac{3k_BT}{m}}\\\\k=1,38.10^{-23},m=mass\:of\:a\:particle\:of\:the\:gas[/tex]
where :
[tex]\rm k=\dfrac{R}{6.022\times 10^{23}}[/tex]
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