- Physical Chemistry I
Spring 2015, Unique 51170
Lecture Summary, 22 January 2015
Gases: A corollary to the ideal gas low: 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
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.
The idea of attractive and repulsive forces is put together in the van der Waals equation, a state function for a real gas:
P(vdW) = (nRT/(V-nb)) - a(n/V)^2
a and b are constants that depend on the identity of the gas and which determine the relative importance of attractive and repulsive interactions. Although there are many other real gas state functions, we will stick with the van der Waals equation for any non-ideal system.