Consider an ideal binary solution, one where both component 1 and component 2 follow Raoult's law. For component 1, its partial pressure can be given by P₁ = x₁P₁^o, where P₁^o is the pure liquid vapor pressure. Similarly P₂ = x₂P₂^o, and the total pressure over the solution is P = P₁+P₂. Now let's increase the temperature of the binary solution and ask ourselves the question "When will something start to boil and what will that something be"? We know that a pure liquid boils when its vapor pressure equals the ambient pressure. At 1 bar, this temperature is called the normal boiling point of the pure liquid.

However for the binary solution, the partial pressure of each component is less than its pure vapor pressure at the same temperature. Therefore, at the normal boiling point of pure component i, the partial pressure will be less than P_i^o, therefore less than the atmospheric pressure. Component i will not yet be ready to boil. Since each of the P_i^os depends upon temperature, increasing T will increase the partial pressure of each component above the solution until the partial pressure of one component will finally equal the ambient atmosphere, and boiling will begin. The more volatile component (the one with the bigger P_i^o) will boil first, but it will be at a higher boiling point than that of the pure liquid.

We can generalize this behavior to all kinds of solutions, whether or not the second component is volatile. Because we want to treat the solution as ideal, our only restriction will be that the solution is sufficiently dilute. For an ideal solution, nonvolatile solutes increase the boiling point of a liquid in direct proportion to their concentration in solution. Because the boiling point elevation depends only upon the amount and not the type of solute molecules, it is said to be a colligative property. If we keep the solution dilute in the nonvolatile solute, the expression for the boiling point elevation, ΔT, is particularly simple

ΔT = k_bm

ΔT needs to be added to the pure solvent boiling point temperature. In this equation, m is the molality of the solute in moles solute/1000 grams solvent and k_b is the boiling point elevation constant that depends only upon the solvent properties

The coefficient k_b has the very delightful name of ebullioscopic constant and to calculate it you need to know M_solvent, the molecular weight of the solvent in grams/mole, Δ_vapH^o, the enthalpy of vaporization of the solvent, and T_b, its normal boiling point. Your energy units must be the same on the enthalpy of vaporization and the ideal gas constant and your temperature must be in Kelvin. At the high school level, values of k_b are usually given to the student.

The simple equation ΔT = k_bm works well for dilute solution of nonelectrolytes, for example sucrose dissolved in water. However, electrolytes dissociate into the individual ions upon dissolution, for example NaCl into Na⁺ and Cl^-, each of which contributes to the boiling point increase. The correction for solute dissociation is called the van't Hoff factor<

ΔT = i k_bm

where i is the number of species formed by dissociation; 2 for NaCl, 3 for Na₂SO₄, etc. Here is a worked example of boiling point elevation for each nonelectrolyte and electrolyte solutions.

One everyday experience most people have with boiling point elevation results from adding salt to a pan of water for cooking purposes. However, salting the water is more a "taste thing" than an aid to more rapid cooking since the effect of adding a small pinch of salt to a quart or so of water is actually quite small. The boiling point increase of aqueous solutions is fairly small, and so if you plan to demonstrate colligative properties you need a very sensitive thermometer - one that you can read to 0.05 degrees or less - and you will need pretty concentrated solutions just to see a few degrees change in the boiling point.

Dissolving a non-volatile solute in a solvent will also lower its freezing point over that observed for the pure solvent and the corresponding equation is

where ΔT now needs to be subtracted from the pure solvent freezing point temperature and i = 1 for nonelectrolytes and the number of species from each formula unit for electrolytes. The coefficient k_f is called the cryoscopic constant and can be calculated in a manner similar to the ebullioscopic constant

Again, tables of k_f are not too difficult to find and cryoscopic constant values are generally provided to students at the introductory level.

Freezing point depressions are easier to measure than are boiling point elevations, at least for aqueous solutions, and their measurement makes a good lab for high school students. Both the salting of sidewalks in the winter to help melt ice and the addition of antifreeze to car radiators to prevent the water from freezing are everyday applications likely to be familiar to students, at least those from the colder climates. A popular lab that can be performed in a qualitative manner involves making ice cream. Depending upon what you know and what you wish to learn, you can also use freezing point depressions to determine the enthalpy of fusion for the solvent or the molecular weight of the solute.

A final colligative property we will study is that of osmosis. Osmosis depends upon the presence of a semipermeable membrane

The membrane lets the solvent (usually water) pass from one side to the other, but does not let the solvent through. If we start out with pure water inside A and an aqueous solution is side B, water inside A will flow into side B to try to equalize the concentrations. This flow does not continue indefinitely, however, because as the pure water flows from side A to side B, the pressure on the solution inside B increases in proportion to the extra amount of water. The flow stops when the pressure increases by

Π = cRT

An interesting tutorial with lots of animation can be found at the web page constructed by Drs. Patlak and Watter. Click on the osmosis choice and follow the arrows through the osmotic pressure sections. To activate the animations that don't have start buttons, point your mouse arrow over the picture and watch the molecules diffuse!

Osmosis is a very important factor in biological phenomena and controls the flow of water across cell membranes. Kidney dialysis (hemodialysis ) works on the principle of osmotic flow. Techniques which employ the measurement of osmotic pressures are also often used in biochemical laboratories, To determine molecular weights for very large biomolecules, you simply measure the osmotic pressure for a know mass of the biomolecule to determine the concentration, c, at a carefully controlled temperature and then just work backwards to obtain the molecular weight.

c = grams/molecular weight

The osmotic pressure generated by the presence of a semipermiable membrane separating a solution and a pure solvent is real. You can "push" on the solution side by increasing the pressure on the solvent, effectively "squeezing" the water out ono the pure side of the osmotic semipermeable membrane. This process is called reverse osmosis and is used in water purification applications such as desalination.

Dialysis membrane which is available from biology supply companies is a convenient semipermeable membrane for labs on osmotic pressure. For a very simple activity suitable for elementary and middle school students, check out the potato dehydration .