# Solid-Liquid Systems

There are two things about solid-liquid systems that we will consider important in this class: the amount of solid material that can be dissolved in a liquid solvent, and the effect of this solute on the phase characteristics of the solvent.

This section is somewhat easy to understand because we have simple every-day experiences to draw on for these two phenomena:

• You can't dissolve an arbitrary amount of sugar in your iced tea
(we will ignore for this class the length of time that the sugar might take to dissolve)
• Dropping salt on ice melts the ice!

### Solubility

##### DEFINITION:

The solubility refers to the maximum amount of solute that you can dissolve in a solvent at a given temperature. (In other words, the solubility depends on BOTH the solute-solvent pair AND the temperature.)

##### NOTE:

Solubilities are typically reported as being functions of temperature only. In fact, they are functions of T and P (verify this using Gibbs phase rule), however solid solubilities are almost always very weak functions of P.

As with vapor-liquid equilibrium, the solution (gas phase) is said to be saturated with the solute (vapor) at equilibrium.

FYI, if we somehow added more than the equilibrium amount the solution is called supersaturated (this must be done very carefully because the solid will precipitate out at the earliest chance) and if we add less it is subsaturated.

##### NOTE:

Solubilities are typically reported in (mass solute)/(mass solvent) units.

##### Outcome:

Estimate the composition of liquids in equilibrium with solids

##### Test Yourself

You want to make "sweet tea", but you are not sure how much sugar can dissolve in the water at serving temperatures (~5C). Determine how much sugar to use for the sweetest possible tea if you have 2 liters of tea. (The solubility of glucose in water at 5C is 0.1 g glucose/g water.)

### Colligative Properties

We all know that adding salt to ice makes the ice melt, but do we know WHY?

##### DEFINITION:

Colligative solution properties refer to the changes in the value of certain solvent properties when a solute is added to them (vapor pressure, boiling point, freezing point, and osmotic pressure).

It is fairly easy to see why this is true (that solvent properties change) if we consider the effect of dissolving a solute in a liquid on that liquid's vapor pressure (we won't actually talk about the ice problem, but it is very similar to this discussion).

If we ignore for a second where the "foreign material" came from, but assume that it is only a small amount of material, we can recall that Raoult's Law says that the partial pressure of the solvent will be given by

pi = (1-x) pi*

where x is the mole fraction of solute.

If we now consider the partial pressure of the solvent to be the "vapor pressure" of the solution (i.e., that we have only one condensable component since the solute will not form a vapor), we now have a lower "vapor pressure" than we would if we had a pure solvent!

We can look at how this would effect the phase diagram of the solution:

With a "hand waving" argument, we can "prove" that if the difference in "boiling point" is dependent only on the mole fraction of the solute, then the difference in freezing point is also dependent only on the mole fraction of the solute (hence the ice really works!).