- Principles of Chemistry II: Honors
Spring 2014, Unique 51880
Lecture Summary, 16 January 2014
of solutions: To figure out what is going on in the
solution, we monitor the pressure of the vapor in the head space
above the liquid. Molecules in this vapor are in equilibrium
with the liquid, and so by referencing to the vapor phase we can
figure out what is going on in the liquid phase. To do this,
our solution must obey two criteria: 1) the proportion of molecules
at the liquid-vapor interface must be identical to the bulk
solution; and 2) the probability that a molecule can escape from the
liquid to vapor phase must be identical to the pure liquid.
Solutions that obey these two criteria are called "ideal" solutions
and obey the following expression:
Pi = xiPi* (Raoult's law)
where Pi is the vapor pressure of species i above the solution, xi is the mole fraction of component i in the solution 0 <= xi <= 1, and Pi* is the vapor pressure of species i in its pure form. The criteria for ideal solutions are very restrictive, and apply only to molecules that have similar intermolecular forces (i.e. hexane and heptane). However, the general conclusions that we draw about the thermodynamics of mixing apply even to nonideal solutions, and so this is still a useful exercise.
Nonideal Solutions: The requirements that must be fulfilled for a solution to be "ideal" are quite restrictive, and there are very few completely ideal solutions. When nonideal solutions are plotted on a composition diagram, the deviations from Raoult's law behavior are instructive for determining qualitatively how the two molecules are interacting. Two examples that we discussed in class are when the system is dominated by repulsive or attractive forces. We therefore modified Raoult's law a bit:
Pi --> xiPi* as xi --> 1
In other words, Raoult's law becomes a more accurate description of a nonideal solution as the solution composition approaches 100% of species i. We then introduced a new expression:
Pi --> xiKi as xi --> 0
Where Ki, in units of pressure, is called the Henry's law constant. This constant is an experimentally determined number that depends both on the identity of species i and the identity of the molecule that i is mixed with. We are really more interested in understanding these model systems, and so we usually only care about the magnitude of Ki versus Pi*.