- Physical Chemistry I
Spring 2015, Unique 51170
Lecture Summary, 26 March 2015
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 two expressions:
Pi = xiP* (Raoult's law)
(mu)l = (mu)*l + RT ln xi
where xi is the mole fraction of component i in the solution and 0 <= xi <= 1.
It is then trivial to use these equations to derive the following:
deltaG(mix) < 0 always
deltaS(mix) > 0 always
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.
Composition Diagrams: We drew simple pressure and temperature composition diagrams for ideal binary solutions. When constructing or interpreting a composition diagram, it is critical that you first make sure you know which quantity is being expressed on each axis, and which component of the system is more or less volatile. After doing that, the phase of the solution at any pressure or temperature can be interpreted easily.