- Principles of Chemistry I: Honors
Fall 2015, Unique 49310
Lecture Summary, 12 November 2015
Kinetic 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.
Real Gasses: Because interesting molecules actually do have to interact, we need to incorporate what we know about intermolecular forces into a new gas law. There are many real gas state functions, but the most famous and general is the van der Waals gas law:
P = (nRT/(V-nb)) - a(n/V)2
The first part of this term modifies the ideal gas law by reducing the total volume available to any given atom or molecule. This accounts for repulsive forces, which will increase the effective pressure of the gas. The second term accounts for how often we find molecules near each other, and because it reduces the effective pressure of a gas, accounts for attractive forces. The constants a and b are properties of the individual atom or molecule.
In order to determine the relative importance of attractive vs. repulsive forces, it is often useful to compare the predictions of the ideal and van der Waals gas laws for species under certain conditions. If P(ideal) < P(vdW), then repulsive forces dominate the gas. If P(ideal) > P(vdW), then attractive forces dominate the gas. With a little bit of understanding of the structure of the particular molecule, we can also make a good guess at what intermolecular force is responsible.