So when learning about the kinetic model of gases, my teacher said that in a volume $A*v_{x}*\Delta t$, exactly half the molecules will have a velocity component of $v_x$ and the other half will have a velocity component of $-v_x$. But I think they are wrong!

Because there should be some small portion of gas molecules that will have a velocity component of: $v_x = 0$

Am I correct? So is the term for the average number of collisions with the wall during the time interval $\Delta t$, just an approximation?:

$(0.5)*A*v_{x}*\Delta t*n*N_a/V$

This is clear with an example. If there are three molecules in a container, one moving left on the x axis, one moving right on the x axis, and one moving directly up the y axis, then on average, only 1/3 of the molecules is moving towards the right wall.


You have pointed out the problem of how to handle the infinitesimal in probability theory. So yes a molecule could traveling in the $yz$ plane and have 0 $x$ velocity. However the probability of the motion being in exactly the $yz$ plane can be made as small as you like.

Let's make the problem one dimensional and choose a random angle between 0 and 359.999... degrees. So the question is what is the probability that the chosen angle will be for a vector on the x-axis?

  • To a degree if I chose 0 or 180 then the vector will be on the x-axis. Odds 2/360

  • To a tenth of a degree if I chose 0.0 or 180.0 then the vector will be on the x-axis. Odds 2/3600

  • To a hundredth of a degree if I chose 0.00 or 180.00 then the vector will be on the x-axis. Odds 2/36000

and so on...

So what probability should be assigned to a randomly chosen angle being exactly along the x-axis?

  • $\begingroup$ Are you basically arguing that the x-velocity component is best described by a continuous distribution and therefore it having an exact value of zero would be zero? $\endgroup$ – Nova Feb 14 '17 at 22:26
  • $\begingroup$ @Nova - I do like that you had your thinking cap on. You really need to look for boundary conditions on the various chemistry factoids that get thrown around. $\endgroup$ – MaxW Feb 14 '17 at 22:33

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