1 pts]4) The kinetic theory describes the relationship between a distribution of molecular speeds(kinetic energy) and temperature. Consider two samples of gas with the same temperature butone with a higher molecular mass than the other. Sketch and label the distributions of molecularspeeds for the two samples.

Answered: 4) The kinetic theory describes the…

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1 pts]
4) The kinetic theory describes the relationship between a distribution of molecular speeds
(kinetic energy) and temperature. Consider two samples of gas with the same temperature but
one with a higher molecular mass than the other. Sketch and label the distributions of molecular
speeds for the two samples.

Expert Solution

Step 1

From the kinetic theory, it has been found that the molecular speeds follow the Maxwell-Boltzmann Distribution law.

According to this theory, the plot of the number of molecules with velocity is as follows:

The speed distribution function f(v) {fraction of molecules having speed between v to v+dv} with velocity v, where

$f (v) = 4 π {(\frac{M}{2 πRT})}^{3 / 2} v^{2} \exp [- \frac{{Mv}^{2}}{2 RT}]$

where M is molecular mass, v is molecular speed, R is the Universal Gas constant, and T is the temperature.

If we plot this,

The plots look the same, the only difference is the y-axis values. In the first one, it is the number of molecules and in the second it is the fraction of molecules having speed v.

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