Chemistry · Lesson

Colligative properties and osmosis

Connect dilute-solution composition with solvent vapour pressure, phase-change temperatures and osmosis. State ideality, particle-count and membrane assumptions before calculating a property.

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By the end, you can

Use molality for an ideal freezing-point depression.
Define the role of the van’t Hoff factor under a stated concentration basis.
Interpret osmotic pressure for a membrane that passes solvent and retains solute.

An ideal solvent responds to composition

For an ideal solution, the solvent’s equilibrium vapour partial pressure is p = x_solvent p*, where p* is the pure solvent’s vapour pressure at the same temperature. Adding a nonvolatile solute reduces the solvent mole fraction. The simple relation concerns the solvent component; a volatile solute can contribute its own vapour pressure.

In dilute ideal settings, boiling-point elevation and freezing-point depression are approximately proportional to solute molality: ΔT_b = K_b b and ΔT_f = K_f b for a nonelectrolyte counted as independent solute entities. These are approximate dilute relations with the solvent and relevant phase behaviour specified.

Count the entities appropriate to the model

If b counts analytical formula amounts of a solute that supplies several species, an effective van’t Hoff factor i gives ΔT_f = iK_f b. In the dilute independent-ion limit, NaCl has an ideal factor near 2. A molecular nonelectrolyte counted as molecules has i near 1.

Real factors can depart from those integers because solution interactions and association affect the response. “Colligative” identifies composition-based relationships in the appropriate limit; it does not mean chemical identity never matters in real solutions or that every concentration obeys a dilute ideal law.

A selective membrane changes what can move

Consider the same solvent at the same temperature on two sides of a membrane that passes solvent but retains the relevant solute. Starting at equal pressure, net solvent transfer can occur toward the side with lower solvent chemical potential, typically the more concentrated ideal solution. Individual solvent molecules still move in both directions.

A solution’s osmotic pressure relative to pure solvent is the pressure difference that balances the tendency for net solvent transfer under the specified membrane conditions. For a dilute ideal nonelectrolyte against pure solvent, π = cRT, using solute amount concentration c, absolute temperature T and the molar gas constant R. For two dilute ideal solutions at the same temperature, the corresponding pressure difference is Δπ = RTΔc. Membrane permeability, leaks or unequal initial pressures can change the physical situation.

Different relations need different denominators

The freezing relation uses molality b, with kilograms of solvent in the denominator. The osmotic relation uses amount concentration c, with final solution volume in the denominator. Substituting one for the other merely because both contain an amount of solute changes the calculation.

State the solvent, nonvolatility where required, ideal dilute approximation and which entities are counted. A computed depression or osmotic pressure is a model prediction under those conditions.

Choose the concentration basis for the relation

Relation	Required composition basis	Stated model input	Calculated response
ΔT_f = K_f b	Solute amount / kg solvent	Water K_f ≈ 1.86 K kg mol⁻¹; b = 0.100 mol kg⁻¹	Freezing-point depression 0.186 K
π = cRT	Solute amount / final solution volume	c = 0.0100 mol L⁻¹; T = 298.15 K; reference side is pure solvent	Osmotic pressure approximately 24.8 kPa
p = x_solvent p*	Solvent mole fraction	Same temperature; ideal solution	Solvent vapour partial pressure scales with x_solvent

Illustrative ideal dilute nonelectrolyte calculations. The solvent and conditions are explicit; the rows describe different experiments and are not one shared sample.

Worked examples

Calculate a dilute freezing depression

For an ideal dilute nonvolatile nonelectrolyte in water, use b = 0.100 mol kg⁻¹ solvent and approximate K_f = 1.86 K kg mol⁻¹. Find ΔT_f.

Use i = 1 for the stated independent molecular solute count.
Multiply ΔT_f = 1 × 1.86 × 0.100.
The mol and kg units cancel, leaving K.

ΔT_f = 0.186 K. This is the predicted depression relative to the pure solvent’s freezing temperature at the same pressure.

Calculate the balancing pressure

A dilute ideal nonelectrolyte solution has c = 0.0100 mol L⁻¹ and T = 298.15 K, with pure solvent on the reference side. The membrane passes solvent and retains solute. Estimate its osmotic pressure π relative to pure solvent.

Use π = cRT.
Choose R = 8.314462618… kPa L mol⁻¹ K⁻¹.
π = 0.0100 × 8.314462618… × 298.15 = 24.78957… kPa.

π ≈ 24.8 kPa under the stated ideal model and membrane conditions.

Try it yourself

Which denominator belongs to b in ΔT_f = K_f b?
Show the answer and reasoning
Kilograms of solvent.
This is molality, not amount per litre of final solution.
In the independent-ion dilute NaCl limit, what ideal particle factor corresponds to one analytical formula amount?
Show the answer and reasoning
2.
One Na⁺ and one Cl⁻ supply two ideal independently effective entities.
What must the model membrane pass and retain in the stated osmotic case?
Show the answer and reasoning
Pass solvent and retain the relevant solute.
If solute crosses freely, the stipulated osmotic setting changes.
In p = x_solvent p*, does p refer to solvent partial pressure or automatically to all vapour pressure?
Show the answer and reasoning
Solvent partial pressure.
A volatile second component can also contribute to the total.

What to carry forward

State ideal dilute assumptions and the entity count.
Freezing depression uses molality; osmotic pressure uses amount concentration.
A selective membrane’s permeability is part of the model.
Real solution interactions can change ideal particle factors.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.