SAT Subject Test Chemistry

PART 2

REVIEW OF MAJOR TOPICS

CHAPTER 7

Liquids, Solids, and Phase Changes

COLLIGATIVE PROPERTIES OF SOLUTIONS

Colligative properties are properties that depend primarily on the concentration of particles and not the type of particle. There is usually a direct relationship between the concentration of particles and the effect recorded.

The vapor pressure of an aqueous solution is always lowered by the addition of more solute. From the molecular standpoint, it is easy to see that there are fewer molecules of water per unit volume in the liquid, and therefore fewer molecules of water in the vapor phase are required to maintain equilibrium. The concentration in the vapor drops and so does the pressure that molecules exert. This is shown graphically below.

Notice that the effects of this change in vapor pressure are registered in the freezing point and the boiling point. The freezing point is lowered, and the boiling point is raised, in direct proportion to the number of particles of solute present. For water solutions, the concentration expression that expresses this relationship is molality (m), that is, the number of moles of solute per kilogram of solvent. For molecules that do not dissociate, it has been found that a 1 m solution freezes at −1.86°C (271.14 K) and boils at 100.51°C (373.51 K). A 2 m solution would then freeze at twice this lowering, or −3.72°C (269.28 K), and boil at twice the 1 molal increase of 0.51°C, or 101.02°C (374.02 K).

Vapor Pressure Versus Temperature for Water and a Solution

The chart below summarizes the colligative effect for aqueous solutions.

EXAMPLE 1: A 1.50-gram sample of urea is dissolved in 105.0 grams of water and produces a solution that boils at 100.12°C. From these data, what is the molecular mass of urea?

Because this property is related to the molality, then you must find the number of grams in 1000 g of water.

x = 14.28 g in 1,000 g of water

The boiling point change is 0.12°C, and since each mole of particles causes a 0.51° increase, then

Then 14.28 g = 0.235 mol

and

x = 60.8 g/mol

EXAMPLE 2. Suppose that there are two water solutions, one of glucose (molar mass = 180.), the other of sucrose (molar mass = 342). Each contains 50.0 grams of solute in 1,000. grams (1 kg) of water. Which has the higher boiling point? The lower freezing point?
The molality of each of these nonionizing substances is found by dividing the number of grams of solute by the molecular mass.


Therefore their respective molalities are 0.278 m and 0.146 m. Since the freezing point and boiling point are colligative properties, the effect depends only on the concentration. Because the glucose has a higher concentration, it will have a higher boiling point and a lower freezing point. The respective boiling points would be:

The lowering of the freezing point would be:

Using a solute that is an ionic solid and that completely ionizes in an aqueous solution introduces consideration of the number of particles present in the solution. Notice in the preceding chart that a 1 molal solution of NaCl yields a solution with 2 moles of particles because:

NaCl(aq)

 

Na+

 

Cl

1 mole of ionic

=

1 mole of

+

1 mole of

sodium chloride salt

 

Na+ ions

 

Cl ions

Thus a 1 molal solution of NaCl has 2 moles of ion particles in 1,000 grams of solvent. The colligative property of lowering the freezing point and raising the boiling point depends primarily on the concentration of particles and not the type of particles.

In a 1 molal solution of NaCl, 1 mole of sodium chloride salt would be dissolved in 1,000 grams of water so that a total of 2 moles of ions were released—1 mole of Na+ ions and 1 mole of Cl ions. Because this provides 2 moles of particles, it will cause a 2 × −1.86°C (drop caused by 1 mole) = −3.72°C drop in the freezing point. Likewise, it will cause a 2 × 0.51°C (rise caused by 1 mole) = +1.02°C rise in the boiling point or a boiling point of 101.02°C.

The chart also shows that CaCl2 releases 3 moles of particles from 1 mole of CaCl2 dissolved in 1,000 grams of water. Note that its effect is to lower the freezing point to 3 × −1.86°C or to −5.58°C. The boiling point rise is also 3 times the molal rise of 0.51°C, resulting in a boiling point of 101.53°C.

This explains the use of salt on icy roads in the winter and the increased effectiveness of calcium chloride per mole of solute. The use of glycols in antifreeze solutions in automobile radiators is also based on this same concept.