- Physical Chemistry I
Spring 2013 Unique 52575
Lecture Summary, 16 January 2013
|Ideal Gases: The first system that we explore in
detail is the ideal gas. An ideal gas obeys the following
1) The particles are non-interacting point spheres.
2) The size of the particles are much smaller than the distance between them.
3) Collisions between the particles or with the walls of the vessel are rare, and when they do occur, they are perfectly elastic.
We performed a few thought experiments to arrive at the following empirical (i.e. derived through experience) conclusions:
Boyle's Law: PV = constant
Charles' Law: P = constant x T
V = constant x T
When combined, these observations lead to the ideal gas law:
PV = nRT
Our first state function.
A corollary: if we don't care about the molecular nature of the underlying system, then it doesn't matter if our ideal gas is composed of one thing or many. This leads to Dalton's Law, which says that there is no distinction between homogeneous and heterogeneous mixtures of ideal gases:
P(total) = sum(Pi)
where Pi is the partial pressure of each individual component of the ideal gas.
Intermolecular Forces: The ideal gas law assumes no interaction between species. However, intermolecular forces do occur and change the observed properties and behavior of real gases. The strength and distance scale over which intermolecular forces operate is a function of 1/r^n, where r is the distance between two species and n is an integer. The larger the value of n, the shorter the length scale at which the intermolecular force operates. In decreasing order of length scale, some important intermolecular forces are:
Electrostatic (Coulombic) Interactions: 1/r^2. These are long distance interactions that can be either attractive or repulsive, depending on the permanent charge of the species.
Dipole-Dipole Interactions: 1/r^3. These are shorter length scale interactions that can be either attractive or repulsive depending on the direction of the dipole moments.
van der Waals Interactions: -1/r^6 + 1/r^12. These are very short range interactions that include an attractive term (-1/r^6) and a repulsive term (1/r^12). All materials have van der Waals forces, regardless of chemical identity.