Phase Equilibria

What are the three main states of matter and how do they relate to each other?

	Solid
Melting	$\downarrow \uparrow$	Freezing
	Liquid
Evaporating	$\downarrow \uparrow$	Condensing
	Gas

By what processes do solids and gases relate to each other?

	Solid
Sublimation	$\downarrow \uparrow$	Deposition
	Gas

Dry ice is the classic example of sublimation in which solid carbon dioxide becomes a gas; another is ice in your freezer - over time, the ice cubes ``disappear''. The formation of frost is an example of deposition.

What is a phase diagram?

A diagram which relates pressure and temperature with corresponding phase states for a given substance. Invariably, a point exists where all three phases coexist in a thermodynamic equilibrium:

Figure 34.7: Phase diagram: (a) the triple point where all three states coexist, and (b), the critical point: the temperature over which a gas cannot be liquefied by increasing pressure.

What are do you call the temperature transition between solids to liquids, liquids to solids and liquids to gases?

A no-brainer: melting point (solid to liquid), freezing point (liquid to solid) and boiling point (liquid to gas).

What is molality and why is it useful?

Molality (m) indicates the number of moles of a given substance per kilogram of solvent. For example, 3.0 kilograms of solvent, containing 1.0 mole of dissolved particles, constitutes a molality of 0.33 $mol/kg$ or 0.33 molal.

Molality is useful because it's a unit that is constant in regards to physical conditions like pressure and temperature.

What are colligative properties?

Properties that are determined by the concentration of solute in a liquid and not in the identity of the solute.

What are four colligative properties?

1. Vapor pressure
2. Boiling point elevation
3. Freezing point depression
4. Osmotic pressure

What is Raoult'Ős law?

Raoult's law states that the vapor pressure of a liquid is equal to the vapor pressure of the liquid times the molar fraction of the solvent:

$$P = (P_{Pure \ Liquid})(Liquid_{Mole \ fraction})$$ (35.9)

Where $P$ is equal to the vapor pressure of a mixed liquid, $P_{Pure \ Liquid}$ is equal to the vapor pressure of the pure liquid and $Liquid_{Mole \ fraction}$ equals the mole fraction of the liquid. Remember that mole fraction is equal to (moles of substance in question)/(total moles of all substances).

What does Raoult's law show?

Raoult's law shows how a solute affects the vapor pressure of a liquid. Therefore, the changes in vapor pressure are directly related to the molality of the solute in the solution.

Note: Just like Dalton's Law of Partial Pressure, this is an additive formula if there is more than one solute

What is boiling point elevation?

$$\Delta T_{b} = k_{b}m_{Solution}$$ (35.10)

By adding solute to a liquid, the vapor pressure is lowered and the boiling point is increased, i.e. more energy is needed to expel the solvent into the air. You can think of it as the solute ``infiltrating'' the surface (i.e. the liquid-gas interface) and thereby decreasing the ``concentration'' of the surface molecules which ultimately are the ones trying to escape. If there are less molecules available to escape, the vapor pressure is lower. Again, boiling point elevation is directly related to the molality of the solution (for every 1 $m$ increase, boiling point is $elevated$ by 0.51 $^{o}$C).

This is why salt is added to water when you make pasta: The presence of the salt increases the boiling temperature of the water making it hotter than unsalted water. This in turn makes the pasta cook faster (not to mention makes it taste better).

What is freezing point depression?

$$\Delta T_{f} = k_{f}m_{Solution}$$ (35.11)

By adding solute to a liquid, the ability to form a crystalline lattice is decreased and the freezing point is decreased, i.e. a colder temperature is needed to help organize the liquid into a solid. Again, freezing point depression is directly related to the molality of the solution (for every 1 $m$ increase, freezing point is $decreased$ by 1.86 $^{o}$C).

Automobile cooling systems use anti-freeze (ethylene glycol) to decrease coolant freezing temperatures to prevent freezing in the winter and increase coolant boiling temperatures to prevent boiling in the summer.

What is osmotic pressure ($\psi$)?

The pressure that a liquid exerts across a semi-permeable membrane when the number of solutes (i.e. concentration) on either side of the membrane is different. This results in a net movement of water from regions of lower solute concentrations to areas of higher solute concentration occuring when two conditions are met:

1. A solute gradient exists across a membrane
2. The solute cannot pass through the membrane

If the membrane is permeable to water, then the movement of water will compensate and rectify the disequilibrium of solute concentrations. The net flux of water will continue until the concentration of solutes is equilibrated on both sides. See figure 34.8 below.

Figure 34.8: Osmotic equilibration: Flow of water through a semipermeable membrane to balance solute concentrations: Before (left) and after (right) equilibration.

What are colloids?

Droplets of a substance that are dispersed into another, forming an apparently homogenous substance. Examples include fog at da club, milk, smoke, and blood.

What is Henry's Law?

Law 2   The mass of a gas that is dissolved into a liquid is directly proportional to the partial pressure of that gas.