CH353 - Physical Chemistry I
Spring 2015, Unique 51170

Lecture Summary, 16 April  2015

Maxwell-Boltzmann Distribution: We have already seen that under a given set of conditions, a system of atoms or molecules will have a distribution of velocities described by some kind of "average."  Although knowing the average is useful, it does not tell us about outliers in the system which may be of great importance.  Therefore we need to know not just the average behavior of the system, but how it is distributed around that average.  This is worked out in the Maxwell-Boltzmann Distribution, one of the most important concepts in all of physical chemistry.  The M-D distribution says that the distribution of velocities, f(v) is proportional to v^2 and exp[-v^2].  These two dependencies on v give the M-D distribution an asymmetric shape that has a long tail to high v.  This means that at a given set of conditions, a substantial fraction of the population of the system will be moving at high velocity, and therefore might have enough kinetic energy to cause a reaction to occur when they collide with something.

Molecular Collisions:  So far everything we have done has been for a single molecule colliding with the walls of the container holding the system.  What we really need, however, is information about what happens when two separate molecules collide.  We therefore define a few new variables: 1) c(rel), relative c; 2) z(coll), collision frequency (z(coll) = (sigma(c(rel))P)/kBT); and 3) mean free path, lambda ( = kBT/(sigmaP).  NB: our result for mean free path is slightly different from the result derived in M&S.  That is because I am sticking to describing average velocity as c, rather than other options which M&S use interchangeably.