Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.2 Kinetic gas theory 106
5.2.2 The rate of wall collisions in 3D
Earlier, we calculated the rate of wall collisions of the molecules of a gas with mass
and number density in a container of volume and the resulting gas pressure using
asimplified model by assuming that 1 r
6 of all molecules have a fixed speed = 8
in + direction (cf. Fig. 5.6). In this simple picture, we neglected the 3D molecular
velocity distribution. We obtained the correct result only due to a cancelation of two
errors (assumption of fixed 1 and 3D distribution). In the following,
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(1) we briefly review the simplified picture,
(2) we then proceed to derive the correct results by appropriate averaging over the
velocity/speed distribution.
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Figure 5.6: Simplified model for the calculation of the pressure of an ideal gas.
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Simplified model for the calculation of the pressure of an ideal gas:
• In the time , all gas molecules (mass ) inthevolume + hit the wall
area .
• Number of wall collisions in time (with number density ):
= × 1 × × (5.78)
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