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Solutions and Colligative Properties JEE Notes give you every definition, law and formula you must remember for the JEE pattern numerical that appear from this chapter. Use the tables for a 10-minute recap, then solve a couple of fresh numerical to lock the ideas in.
Solutions and Colligative Properties JEE Notes: Important Concepts
NCERT coverage: Class XII Chemistry Part I, Chapter 2.
Current JEE syllabus: Definitions of solution terms, vapour pressure, Raoult’s law, ideal and non-ideal solutions, Henry’s law, colligative properties and abnormal molar mass.
- Solution: Homogeneous mixture of two or more components.
- Solvent: Component present in larger amount; determines the physical state.
- Solute: Other component(s) present in smaller amount.
- Colligative properties: Properties that depend only on the number of solute particles present, not on their nature.
- Ideal solution: Obeys Raoult’s law over the entire composition range, $$\Delta H_{mix}=0$$ and $$\Delta V_{mix}=0$$.
- Non-ideal solution: Shows positive or negative deviation from Raoult’s law; non-zero enthalpy or volume of mixing.
Concentration Terms, Ideal & Non-ideal Solutions
Concentration units you must manipulate fluently
| Symbol | Definition | Formula | Typical JEE Use |
|---|---|---|---|
| Mole fraction $$x_i$$ | Ratio of moles of component to total moles | $$x_i=\dfrac{n_i}{\sum n}$$ | Raoult’s law & vapour phase composition |
| Molarity $$M$$ | Moles of solute per litre of solution | $$M=\dfrac{n}{V_{solution}}$$ | Titration data, osmotic pressure |
| Molality $$m$$ | Moles of solute per kg of solvent | $$m=\dfrac{n}{w_{solvent}\ (\text{kg})}$$ | Boiling point elevation, freezing point depression |
| Mass % | Mass of component per 100 g of solution | $$\%\,w/w=\dfrac{w_i}{w_{solution}}\times100$$ | Nomenclature in NCERT tables |
Ideal vs non-ideal behaviour
- For an ideal binary liquid A–B, partial vapour pressures follow $$p_A = x_A p_A^{\ast}$$ and $$p_B = x_B p_B^{\ast}$$ where $$p^{\ast}$$ is the vapour pressure of pure component at the same T.
- Positive deviation: $$p_{total}\gt x_A p_A^{\ast}+x_B p_B^{\ast}$$. Endothermic mixing, weaker A–B interactions. Example: ethanol + acetone.
- Negative deviation: $$p_{total}\lt x_A p_A^{\ast}+x_B p_B^{\ast}$$. Exothermic mixing, stronger A–B interactions. Example: chloroform + acetone.
- Minimum or maximum boiling azeotropes form when the deviation is large. JEE occasionally asks to recognise these from given data.
After revising definitions, practise converting molarity to molality for temperature-dependent data inside the solved numerical set on JEE Questions.
Vapour Pressure and Raoult’s Law
Raoult’s law for volatile solutes
At a fixed temperature the partial pressure of each component equals the product of its mole fraction in the liquid phase and vapour pressure of the pure component.
$$p_i = x_i p_i^{\ast}$$
Total pressure: $$p = p_A + p_B = x_A p_A^{\ast} + x_B p_B^{\ast}$$.
Henry’s law for sparingly soluble gases
Pressure of a gas above the solution is directly proportional to its mole fraction in the solution: $$p = k_H x$$ where $$k_H$$ increases with temperature.
Worked example 1: vapour pressure of an ideal binary
A solution contains 0.4 mol benzene (vapour pressure 120 mm Hg) and 0.6 mol toluene (vapour pressure 40 mm Hg) at the same temperature. Calculate total vapour pressure and the mole fraction of benzene in the vapour.
- $$x_{benzene}=0.4/(0.4+0.6)=0.4$$
- $$x_{toluene}=0.6/(1.0)=0.6$$
- $$p=0.4\times120+0.6\times40=48+24=72\;\text{mm Hg}$$
- Partial pressures: $$p_B=48$$, $$p_T=24$$.
- Mole fraction in vapour: $$y_{benzene}=p_B/p=48/72=0.667$$.
Answer: $$p_{total}=72\;\text{mm Hg},\;y_{benzene}=0.667$$.
Colligative Properties: RLVP, BPE, FPD and Osmotic Pressure
Relative lowering of vapour pressure (RLVP)
$$\dfrac{p^{\ast}-p}{p^{\ast}}=x_B$$
Valid only for non-volatile solute in an ideal dilute solution.
Elevation of boiling point (BPE)
The rise in boiling point is proportional to molality:
$$\Delta T_b = K_b m$$
- $$K_b$$: ebullioscopic constant of the solvent.
- If the solute dissociates or associates, multiply concentration by van’t Hoff factor $$i$$.
Depression of freezing point (FPD)
$$\Delta T_f = K_f m$$
Kf is larger than Kb for most common solvents, so FPD experiments are preferred in JEE labs.
Osmotic pressure
$$\Pi = C R T = i M R T$$
For dilute aqueous solutions at 298 K: $$\Pi (\text{atm}) \approx 0.0821\;iM(298)$$.
van’t Hoff factor $$i$$ and abnormal molar mass
$$i = \dfrac{\text{observed colligative property}}{\text{calculated assuming no association/dissociation}} = \dfrac{M_{theoretical}}{M_{observed}}$$.
Worked example 2: molar mass from FPD with association
2 g of acetic acid is dissolved in 250 g benzene. The freezing point is lowered by 0.45 K. $$K_f$$ for benzene = 5.12 K kg mol-1. Acetic acid dimerises in benzene. Find the molar mass.
- Molality if no association: $$m = \dfrac{2/ M}{0.250}$$.
- $$\Delta T_f = K_f m$$ gives $$0.45 = 5.12 \dfrac{2/ M}{0.250}$$ ⇒ $$M = \dfrac{5.12 \times 2}{0.45 \times 0.250}=91.1$$ g mol-1.
- Theoretical molar mass of CH3COOH = 60. Dimerisation doubles mass but halves particles ⇒ expected observed ≈120. Our 91 implies partial association.
Answer: Observed molar mass = 91 g mol-1.
Worked example 3: osmotic pressure with ionisation
An aqueous 0.01 M solution of MgCl2 (assume complete ionisation) is taken at 27 °C. Calculate osmotic pressure.
- Number of particles per formula unit $$i = 3$$.
- $$\Pi = i M R T = 3 \times 0.01 \times 0.0821 \times 300 = 0.739\;\text{atm}$$.
Answer: $$\Pi = 0.74\;\text{atm (to two significant figures)}$$.
Prepare a one-page print-out of the four property formulae or download them from the complete chemistry JEE Formula Sheets to keep in your last-day folder.
Important Formulas and Results at a Glance
| Topic | Formula | Key Units | JEE Tip |
|---|---|---|---|
| Raoult’s law (volatile) | $$p_i = x_i p_i^{\ast}$$ | p in mm Hg or kPa | Works only in liquid phase mole fractions |
| Raoult’s law (non-volatile) | $$\dfrac{p^{\ast}-p}{p^{\ast}} = x_B$$ | Dimensionless | Straight molar mass questions |
| Henry’s law | $$p = k_H x$$ | k_H in kPa | $$k_H$$ rises with T, so solubility drops |
| Elevation of B.P. | $$\Delta T_b = i K_b m$$ | K_b: K kg mol-1 | Always small (≪10 K) |
| Depression of F.P. | $$\Delta T_f = i K_f m$$ | K_f: K kg mol-1 | Most sensitive method for M determination |
| Osmotic pressure | $$\Pi = i M R T$$ | atm when R = 0.0821 | Use for macromolecules (proteins, polymers) |
| van’t Hoff factor | $$i=\dfrac{M_{theoretical}}{M_{observed}}$$ | Dimensionless | Association: $$i<1$$, dissociation: $$i>1$$ |
JEE Important Points, Common Mistakes and Quick Revision
- Convert units first. Many errors arise because Kf is in K kg mol-1, but mass of solvent is given in grams.
- Keep the sign: $$\Delta T_f$$ is taken as positive even though the temperature decreases.
- For electrolytes, write the complete dissociation equation and count ions before taking $$i$$.
- When dealing with Raoult’s law numericals, average molar mass of the solution may be asked. Use $$\bar{M}=1/(\sum x_i/M_i)$$.
- The graph of $$p$$ versus $$x_B$$ is a straight line for ideal solutions and curved for non-ideal. Sketch it once, you will remember the direction of deviation.
- Osmotic pressure questions often hide in biology context: blood saline, IV fluids. Take R = 0.0821 L atm K-1 mol-1 and T = 310 K when the question says “body temperature”.
- Before the exam, solve at least five past-paper numericals from the colligative section inside JEE Mains Previous Papers to calibrate speed and rounding.
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