- Principles of Chemistry I: Honors
Fall 2011, Unique 51040
Lecture Summary, 10 November 2011
Model of Gasses:
Now that we know how ideal gasses behave, we have to know
how often and with what energy two molecules
collide. To do this, we imagined a box filled with
molecules moving in the x direction and
colliding with the walls of the box. By calculating
the total change in momentum that occurs with each
collision, we worked out an expression for the root mean
square speed, crms, of each molecule:
crms = (3RT/(FW))1/2
This is a remarkable result because it describes the kinetic energy of a molecule (through its velocity) in terms of constants (3, R, FW), and an easily measured property, T.
We also discussed the idea that at a given temperature, the above equation will only give us the average velocity of all molecules in the system, but that individual molecules have different velocities and therefore different kinetic energy. The range of velocities is given by the Maxwell-Boltzmann distribution. Although we will not derive this explicitly, the form of the equation tells us that the distribution is asymmetric, with a long tail towards higher velocities. This means that even at low temperatures, there will always be a few molecules moving at very high velocity, and thus capable of performing high energy collisions.