- Principles of Chemistry I: Honors
Fall 2011, Unique 51040
Lecture Summary, 15 November 2011
Model of Gasses Continued: After
working out a crms for our gas molecules, we
now care about how often molecules collide with each
other, not just with the walls of whatever container they
are in. To do this, we worked out expressions for
collision frequency (Z) and mean free path (lamba),
which is the average distance a molecule travels between
collisions. Both of these expressions contain
information about the energy with which two molecules
collide, which will be our key to understanding if they
react in some interesting way.
Real Gasses and Intermolecular Interactions: Having worked this out, we can start talking about real molecules again. Once we relax the restriction of no intermolecular interactions (necessary for working with an ideal gas), we saw that intermolecular forces could be attractive or repulsive. All of these forces respond to the distance between molecules as a function of 1/rn. I.e as the distance between the two species decreases, the magnitude of the interaction between them increases. Furthermore, larger values of n will correspond to forces that only act at very short distances.
a) Coulombic: V = 1/r
This is the longest range force we will consider. Electrostatics are important at distances greater than molecular bond lengths.
b) Dipole-dipole: V = 1/r3
These are shorter length-scale forces between two molecules with a permanent dipole-moment.
c) Induced dipole-induced dipole: V = -1/r6
These are even shorter length scale and are a always attractive.
d) Steric repulsion: V = 1/r12
These only become important at very short distance, when the two atoms begin to occupy the same space. This is a very repulsive interaction, and so at this length scale, this term will blow up and dominate all others. This interaction is always repulsive.
The last two terms are often combined into one equation, and used to describe the interactions of molecules that are not a result of chemical bonding, permanent electronic charge, and permanent dipole moment. They are therefore very important for understanding how all molecules interact with other molecules at the position of closest approach.