IMAT Chemistry · Solutions and Concentration

Boiling Point, Freezing Point and Osmotic Pressure

Some properties of a solution depend only on how many solute particles it contains, not on what they are: it boils higher, freezes lower and draws water across a membrane.

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Why this matters

The past papers have touched this page only once, in 2020, through a statement about the freezing point of a sugar solution. The syllabus lists colligative properties, and osmosis links straight to the cell biology questions.

Concept 1 of 3: Colligative properties and the van 't Hoff factor

Dissolved particles get in the way of the solvent: fewer solvent molecules sit at the surface to escape, and the solvent is less free to freeze. Each particle has the same effect whatever it is, so what matters is how many particles there are. A salt that splits into ions gives more particles than the same amount of sugar.

Definition

Colligative properties depend on the number of dissolved particles, not their identity: vapour pressure lowering, boiling point elevation, freezing point depression and osmotic pressure.
The van 't Hoff factor $i$ is the number of particles one formula unit gives in solution.
Non-electrolytes (glucose, sucrose, urea): $i = 1$ . Strong electrolytes: NaCl $i = 2$ , $\mathrm{CaCl_2}$ $i = 3$ , $\mathrm{Na_3PO_4}$ $i = 4$ .
Weak electrolytes have $i$ only a little above 1. In concentrated solutions real values are a little below the ideal ones; IMAT uses the ideal values.
The concentration of particles is $i$ times the concentration of solute.

Concentration of dissolved particles

c_{\text{particles}} = i \times c

$i$ van 't Hoff factor: particles per formula unit
$c$ concentration of the solute

Worked example

Rank these 0.10 mol/L solutions by their concentration of dissolved particles: glucose, sodium chloride, calcium chloride, aluminium sulfate

\mathrm{Al_2(SO_4)_3}

Practice this conceptself-check · 4 quick reps

Count particles, not formula units

At the same concentration, a sodium chloride solution has twice the effect of a glucose solution, because each NaCl gives two ions. Comparing solute concentrations without multiplying by

i

picks the wrong solution.

Concept 2 of 3: Boiling point elevation and freezing point depression

Solute particles lower the vapour pressure of the solvent, so the solution must be heated further before it boils. They also disturb the ordered solid that forms on freezing, so the solution must be cooled further before it freezes. Both changes grow in proportion to the number of particles.

Definition

A solution boils above and freezes below the pure solvent: its liquid range widens at both ends.
The changes are proportional to the molality of particles, $i \times b$ .
For water: $K_b = 0.512\ \text{K kg/mol}$ and $K_f = 1.86\ \text{K kg/mol}$ . A change of 1 K equals a change of 1 °C.
Uses: salt spread on icy roads, antifreeze (ethylene glycol) in car radiators.
The lowering of vapour pressure (Raoult's law: the solvent's vapour pressure is proportional to its mole fraction) is the cause of the higher boiling point.

Boiling and freezing point changes

\Delta T_b = i\,K_b\,b \qquad \Delta T_f = i\,K_f\,b

$\Delta T_b, \Delta T_f$ rise in boiling point, fall in freezing point, in K
$K_b, K_f$ constants of the solvent, in K kg/mol
$b$ molality of the solute, in mol/kg
$i$ van 't Hoff factor

Worked example

Find the freezing point and boiling point of a 0.50 mol/kg sodium chloride solution in water. (

K_f = 1.86

K_b = 0.512\ \text{K kg/mol}

)

Practice this conceptself-check · 4 quick reps

A solution boils higher and freezes lower

Dissolving a solute raises the boiling point and lowers the freezing point. A saturated sugar solution does not freeze at 0 °C; it freezes below it. Options with the change in the wrong direction are common.

Concept 3 of 3: Osmosis and osmotic pressure

A semipermeable membrane lets water through but not the solute. Water moves from the side where it is more concentrated (fewer solute particles) to the side where it is less concentrated (more solute particles). The pressure needed to stop this flow is the osmotic pressure, and like the other colligative properties it depends on the number of particles.

Definition

Osmosis: net movement of water through a semipermeable membrane from a solution of lower solute concentration to one of higher solute concentration.
Osmotic pressure $\pi$ : the pressure needed to stop osmosis. It rises with particle concentration and temperature.
Compared with a cell: an isotonic solution has the same particle concentration (no net flow); a hypotonic one has fewer particles (water enters, red blood cells swell and may burst, haemolysis); a hypertonic one has more (water leaves, red blood cells shrink, crenation).
0.9% NaCl (about 0.15 mol/L, so about 0.3 mol/L of particles) is isotonic with blood.

Osmotic pressure

\pi = i\,c\,R\,T

$c$ molar concentration of the solute (mol/L with R = 0.0821 L atm/(mol K), or mol/m³ with R = 8.314 J/(mol K))
$T$ absolute temperature, in K
$i$ van 't Hoff factor

Worked example

What is the osmotic pressure of a 0.10 mol/L glucose solution at 27 °C? (

R = 0.0821\ \text{L atm/(mol K)}

)

Practice this conceptself-check · 4 quick reps

Water moves towards the more concentrated solution

In osmosis it is water, not solute, that moves, and it moves towards the side with more dissolved particles. Count particles: 0.15 mol/L NaCl matches 0.30 mol/L glucose, not 0.15 mol/L glucose.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Colligative properties and the van 't Hoff factor
Concentration of dissolved particles
$c_{\text{particles}} = i \times c$
Boiling point elevation and freezing point depression
Boiling and freezing point changes
$\Delta T_b = i\,K_b\,b \qquad \Delta T_f = i\,K_f\,b$
Osmosis and osmotic pressure
Osmotic pressure
$\pi = i\,c\,R\,T$

Watch out for (3)

Count particles, not formula units
→ Colligative properties and the van 't Hoff factor
A solution boils higher and freezes lower
→ Boiling point elevation and freezing point depression
Water moves towards the more concentrated solution
→ Osmosis and osmotic pressure

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