Physical Chemistry , 1st ed.

Using the fact that 0.0100 g was used to make 1.00 L of solution, we have the

relationship

0.000123 

m

L

ol

0.0100 

L

g



The liter units cancel, giving

0.000123 mol 0.0100 g

Solving for molecular weight, which has units of g/mol, we find that the mol-

ecular weight is

815,000 

m

g

ol



This is not an unusual average molecular weight for a polymer.

The osmotic pressure of a solution can be counteracted by exerting addi-
tional pressure on the side of the membrane that has the more concentrated
solution. In fact, ifpextis greater than , then the osmosis process will occur
in the opposite direction.Such “reverse osmosts” processes have some extremely
practical benefits. Perhaps the most important is the production of fresh
water from seawater in desalinization plants. In the Middle East, these plants
produce drinkable water from the very salty water of the gulfs and seas in the
area. The process is a product of technology, but is much less energy-intensive
than distillation.
The van’t Hoff equation assumes that the solute dissolves molecularly. That
is, every molecule of solid solute dissolves into a single molecule of solute in a
solvated form. For compounds that dissolve into multiple solvated species
(mainly ionic compounds), the number of species that the solute dissolves into
must be taken into account. For such compounds, the van’t Hoff equation
becomes

VNxsoluteRT (7.57)

where Nrepresents the number of individual species a compound separates
into when it dissolves.

7.9 Summary

Solutions, even binary solutions, can be complicated in their behavior. The
equations of thermodynamics help us understand this behavior. Liquid/liquid
solutions can establish equilibria with vapor phases, and the equations of
thermodynamics help us understand how the composition of the vapor phase
is related to the composition of the liquid phase. We can do the same thing
for solid/solid solutions and the liquid phase that will exist when such a so-
lution melts. Both phase changes have a special composition that acts as a
pure phase: an azeotrope or a eutectic. Both special compositions affect our
everyday life.
Phase diagrams are useful graphical representations of the phase changes
and compositions of solutions. Not only do they represent instantaneous
conditions, but they can be used to predict the behavior of a solution as
conditions change. Properly labeled and interpreted, a phase diagram indicates
the exact composition of the different phases that appear as conditions like

7.9 Summary 201