“Count particles, not kind”
What colligative means
One mole of sugar and one mole of NaCl do not behave alike, because NaCl gives two particles. It is the number of particles in solution that matters, never their identity.
Chemistry, Class 11 and 12 · Gujarat Board, CBSE, GUJCET, JEE and NEET
Solutions and Colligative Properties formulas
Colligative properties depend on how many particles are dissolved, not on what they are. That one sentence explains every formula here, and the van't Hoff factor is what turns it from theory into a numerical.
16 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Expressing concentration
| What | Formula | Symbols and notes |
|---|---|---|
| Molarity | M = moles of solute / litres of solution | temperature dependent |
| Molality | m = moles of solute / kg of solvent | temperature independent, so used in these formulas |
| Mole fraction | x = ni/ntotal | adds to 1 over all components |
| Mass percentage | (mass of solute / mass of solution) × 100 | the everyday way of stating strength |
Vapour pressure
| What | Formula | Symbols and notes |
|---|---|---|
| Raoult's law | p = xsolvent × p° | p° is the vapour pressure of the pure solvent |
| Relative lowering | (p° − p)/p° = xsolute | equal to the mole fraction of the solute |
| Ideal solution | ΔHmix = 0, ΔVmix = 0 | obeys Raoult's law at all compositions |
| Positive deviation | weaker new interactions, higher vapour pressure | for example ethanol and acetone |
| Negative deviation | stronger new interactions, lower vapour pressure | for example chloroform and acetone |
| Henry's law | p = KHx | solubility of a gas rises with pressure |
The four colligative properties
| What | Formula | Symbols and notes |
|---|---|---|
| Boiling point elevation | ΔTb = iKbm | Kb for water is 0.52 K kg mol−1 |
| Freezing point depression | ΔTf = iKfm | Kf for water is 1.86 K kg mol−1 |
| Osmotic pressure | π = iCRT | C is molarity; the most sensitive of the four |
| Relative lowering of vapour pressure | (p° − p)/p° = ixsolute | the fourth colligative property |
| van't Hoff factor | i = observed value / calculated value | 2 for NaCl, 3 for CaCl₂, less than 1 for association |
| Molar mass from a colligative property | M = iwK/(ΔT × W) | w solute mass, W solvent mass in kg |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“i is how many it breaks into”
The van't Hoff factor
NaCl gives 2, CaCl₂ gives 3, glucose gives 1. If the solute associates instead, as benzoic acid does in benzene, i falls below 1.
“Salt on ice, sugar in the pot”
Which way each effect goes
Adding solute lowers the freezing point and raises the boiling point. Salt melts ice on a road; sugar syrup boils above 100 °C.
Where marks go
The mistakes that cost the most.
- Using molarity in the boiling point and freezing point formulas. Both need molality.
- Leaving out the van't Hoff factor for an ionic solute, which halves or thirds the right answer.
- Getting the direction wrong: boiling point goes up, freezing point goes down.
- Applying Raoult's law to a non-volatile solute's own vapour pressure. It has none.
- Using the molar mass formula with the solvent mass in grams. It must be in kilograms.
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