Colligative Properties of Solutions

(Colligative means collective.)

Properties of a solution are influenced by the number of solute particles present.
1. VP (Vapor Pressure) is lowered.
2. BP (Boiling Point) is elevated.
3. FP (Freezing Point) is lowered.
4. OP (Osmotic Pressure) is increased.

Nonvolatile Nonelectrolyte Solutions
(Volatility is the tendency of a substance to become a gas.)
(Electrolytes are a mixture of ions that when dissolved in solution conduct a current.)

When a nonvolatile nonelectrolyte substance is dissolved in solution:

1. VP is lowered.
The nonvolatile solute particles don't leave the surface of the solution, so the percentage of particles on the surface of the solution that can leave it is smaller than in the pure solvent. Particles can still enter the solution from the atmosphere at the same rate however, so the ratio of particles leaving to entering is lower than in the pure solvent.

The relationship between amount of solute and VP (known as Raoult's law) is:

VPsolvent = Xsolvent * VPpure solvent

VPsolvent = the vapor pressure of the solvent in the solution.
VPpure solvent = the vapor pressure of the pure solvent.
X= mole fraction.

If we want to know the magnitude of the change in VP we can obviously see that:

VPpure solvent - VPsolvent = ∆VP

(∆= change in)

Further:

Xsolvent + Xsolute = 1
rearranging
Xsolvent = 1 - Xsolute

thus

VPsolvent = Xsolvent * VPpure solvent = (1 - Xsolute ) * VPpure solvent

so

VPsolvent = VPpure solvent - (Xsolute * VPpure solvent)
rearranging
VPpure solvent - VPsolvent = Xsolute * VPpure solvent

so

Xsolute * VPpure solvent also = ∆VP

2. BP is elevated.
The BP of a liquid is when its VP = external pressure.
As the VP of a nonvolatile solution is lower than that of the pure solvent it needs to be heated more before the VP becomes equal to the external pressure. Thus BP is elevated.

Change in BP is directly proportional to number of solute particles.

Change in BP = Kb * m

Kb is the molal boiling point elevation constant and is specific to a given solvent, it is given in units of (degrees C/m)
m = moles of solute.

3. FP is lowered.
Similar to the reason why VP is raised. The solute particles don't solidify, therefore the ratio of particles leaving the solid unit to those entering is greater than in the pure solvent. Thus the temperature at which more particles are entering than leaving will be lower and so the FP is lower.

Change in FP = Kf * m

Kf is the molal freezing point depression constant and is specific to a given solvent, it is also given in units of (degrees C/m)

4. OP is increased.
OP is the pressure required to prevent the net movement of water from pure solvent to solution through a semipermiable membrane.

Because the solute particles cannot travel through the membrane, the amount of particles going through from the pure solvent on one side will be greater than the amount going through the other way from the solution on the other.
If the solutions on both sides are the same the OP is 0.

OP is directly proportional to the number of solute particles(n) in a given volume(V) of solution, that is, the molarity (M) of the solution.
The proportionality constant is R times the temperature (T)
So the relationship is:

OP = (nsolute/Vsolution) * RT = MRT

We can use change in VP, BP, FP and/or OP with all these relationships to find the molar mass of the solute.

Volatile Nonelectrolyte Solutions
From Raoult's law we know that:

VPsolvent = Xsolvent * VPpure solvent

If the solute is volatile the same applies to it.

VPsolute = Xsolute * VPpure solute

From the VP exerted by each gas we can find what fraction of the vapor each gas makes up.
The gas of the more volatile liquid will be a higher fraction of the vapor.

This principle is used in fractional distillation, more of the gas of the more volatile liquid is present in the vapor than the gas of the less volatile liquid. When that vapor condenses, relatively more of the more volatile liquid will be present in the solution. The more this process is repeated the more concentrated the more volatile liquid will become.

Electrolyte Solutions
Positive and negative ions in solution tend to cluster together, and this causes some of the ions to behave as if they were "tied up" (as if they were still bonded.) This reduces the effective concentration of the ions and causes the electrolyte solution to exhibit nonideal behavior.

1 mole of NaCl should dissociate into 1 mole of Na and 1 mole of Cl, but because some ions are "tied up" not all of them will affect the properties of the solution. To find how many do, we use the van't Hoff factor (i)

i = (measured value of an electrolyte solution)/(expected value of a nonelectrolyte solution)

for example:

i = (change in boiling point of a solution when 1m of NaCl is added)/(expected change in boiling point of solution if 1m of glucose was added)

in this case it's is (0.049 degrees C)/(0.026 degrees C) = 1.9

What nonelectrolyte is used doesn't matter as it is the number of dissolved particles that effect these properties and not the type.

For an electrolyte solution we would multiply the side of the equation containing the factor relating to the number of particles (m, X and M) by the number of moles of particles the electrolyte dissociates into. (NaCl into 2 for example) But since some atoms are "tied up" we multiply by i instead which gives the effective number particles affecting the solution rather than the actual number.

For example:
for NaCl instead of using

FP = 2 * (Kf * m)

we would use

FP = i * (Kf * m)
(i=1.9 in this case)

The more concentrated the solution the more ions are "tied up" and vice versa, so the more dilute the solution the closer to ideal its behavior will be.