ChemistryHigh Weightage β
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Class 12
Solutions & Colligative Properties
Mole fraction, Henry's law, Raoult's law, elevation of boiling point, depression of freezing point, and osmotic pressure β 3β4 direct EAPCET numerical questions.
3β4Questions in EAPCET
~3%Paper Weightage
8Core Formulas
4Mistake Traps
Concept Core
Concentration, Raoult's law, colligative properties, and van't Hoff factor.
Concentration Units β Quick Reference
| Unit | Definition | Temperature Dependent? |
|---|
| Molarity (M) | moles of solute per litre of solution | Yes (volume changes with T) |
| Molality (m) | moles of solute per kg of solvent | No |
| Mole fraction (Ο) | moles of component / total moles | No |
| Mass % | (mass of solute / mass of solution) Γ 100 | No |
Preferred for colligative properties: Molality (m) β temperature independent.
Raoult's Law & Vapour Pressure
For an ideal solution, partial vapour pressure of a component = mole fraction Γ pure vapour pressure:
P_A = Ο_A Γ PΒ°_A P_total = P_A + P_B
Relative lowering of VP: ΞP/PΒ°_A = Ο_B (mole fraction of solute)
= n_B/(n_A + n_B) β n_B/n_A (dilute solution)
Elevation of Boiling Point
ΞT_b = K_b Γ m = K_b Γ (w_B/M_B) Γ (1000/w_A)
where K_b = molal elevation constant (ebullioscopic constant)
w_B = mass of solute (g); M_B = molar mass of solute
w_A = mass of solvent (g)
K_b for water = 0.52 KΒ·kg/mol. Boiling point increases with solute addition.
Depression of Freezing Point
ΞT_f = K_f Γ m = K_f Γ (w_B/M_B) Γ (1000/w_A)
where K_f = molal depression constant (cryoscopic constant)
K_f for water = 1.86 KΒ·kg/mol (larger than K_b). Anti-freeze in cars uses this principle.
Freezing point is DEPRESSED (decreased); Boiling point is ELEVATED (increased).
Osmotic Pressure
Ο = CRT = (n/V)RT (van't Hoff equation)
Ο = MRT (M = molarity)
For electrolytes: Ο = iCRT (i = van't Hoff factor)
Osmosis: solvent moves from dilute (low Ο) to concentrated (high Ο) across a semi-permeable membrane.
van't Hoff Factor (i)
i = observed colligative property / calculated value (for non-electrolyte)
For electrolytes: i = 1 + (nβ1)Ξ±
where n = number of ions; Ξ± = degree of dissociation
NaCl: i β 2 (fully dissociates β 2 ions)
KβSOβ: i β 3 (β 3 ions)
For association: i < 1 (fewer particles than expected).
Formula Vault
All solution and colligative property formulas.
Molality
m = (w_B/M_B) Γ (1000/w_A)
w_B in g; w_A in g; M_B in g/mol
Raoult's Law
P_A = Ο_A Γ PΒ°_A
For ideal solution; Ο_A = mole fraction
Relative VP Lowering
ΞP/PΒ° = Ο_B
Ο_B = mole fraction of solute
Boiling Point Elevation
ΞT_b = K_b Γ m
K_b(water) = 0.52 KΒ·kg/mol
Freezing Point Depression
ΞT_f = K_f Γ m
K_f(water) = 1.86 KΒ·kg/mol
Osmotic Pressure
Ο = CRT = MRT
C = molarity; T in Kelvin; R = 0.0821 LΒ·atm/mol/K
van't Hoff Factor
i = 1 + (nβ1)Ξ±
n = ions formed; Ξ± = degree of dissociation
Henry's Law
p = K_H Γ Ο (gas)
Solubility of gas β its partial pressure
Worked Examples
5 problems β molality, Raoult's law, boiling point, osmotic pressure, and van't Hoff factor.
EasyFind boiling point elevation: 10g glucose (M=180) in 100g water. K_b=0.52βΎ
10 g of glucose (M=180 g/mol) is dissolved in 100 g of water. K_b = 0.52 KΒ·kg/mol. Find ΞT_b.
1
m = (w_B/M_B) Γ (1000/w_A) = (10/180) Γ (1000/100) = 0.0556 Γ 10 = 0.556 mol/kg
2
ΞT_b = K_b Γ m = 0.52 Γ 0.556 = 0.289 K β 0.29Β°C
β ΞT_b = 0.29 K (boiling point rises from 100Β°C to 100.29Β°C)
EasyFind osmotic pressure: 0.5 M sucrose solution at 27Β°CβΎ
Calculate the osmotic pressure of 0.5 M sucrose solution at 27Β°C. R = 0.0821 LΒ·atm/mol/K.
1
T = 300 K, C = 0.5 mol/L
2
Ο = CRT = 0.5 Γ 0.0821 Γ 300 = 12.32 atm
β Ο = 12.32 atm
MediumRelative lowering of vapour pressure: 9g glucose in 90g water. M_glucose=180, M_water=18.βΎ
Find the relative lowering of vapour pressure when 9 g of glucose is dissolved in 90 g of water.
1
n_glucose = 9/180 = 0.05 mol; n_water = 90/18 = 5 mol
2
Ο_glucose = 0.05/(0.05+5) = 0.05/5.05 β 0.00990
3
ΞP/PΒ° = Ο_solute = 0.00990 β 0.01
β Relative VP lowering = 0.0099 β 1%
EAPCET LevelFind molar mass of solute: 5g in 50g water, ΞT_f = 0.372Β°C, K_f = 1.86βΎ
5 g of a non-electrolyte dissolved in 50 g of water causes ΞT_f = 0.372 K. K_f(water) = 1.86 KΒ·kg/mol. Find molar mass of solute.
1
ΞT_f = K_f Γ m β m = ΞT_f/K_f = 0.372/1.86 = 0.2 mol/kg
2
m = (w_B/M_B) Γ (1000/w_A) β 0.2 = (5/M_B) Γ (1000/50) = 100/M_B
3
M_B = 100/0.2 = 500 g/mol
β Molar mass = 500 g/mol
Trap QuestionNaCl and glucose solutions of same molality have same ΞT_f β True or False?βΎ
Equal molality NaCl and glucose solutions. A student claims both have the same ΞT_f since ΞT_f = K_f Γ m.
1
ΞT_f = i Γ K_f Γ m. The van't Hoff factor i matters for electrolytes.
2
Glucose (non-electrolyte): i = 1. ΞT_f = 1 Γ K_f Γ m = K_fΒ·m
3
NaCl (strong electrolyte): NaCl β NaβΊ + Clβ». i β 2 (assuming complete dissociation).
4
ΞT_f(NaCl) = 2 Γ K_f Γ m = 2K_fΒ·m β TWICE as large as glucose.
5
The trap: forgetting the van't Hoff factor i for electrolytes.
β False β NaCl has i β 2 (two ions), so ΞT_f is approximately double that of glucose
Mistake DNA
4 solution errors from EAPCET distractor analysis.
π§
Freezing Point Elevated (Not Depressed) on Adding Solute
Adding solute LOWERS the freezing point (ΞT_f is a depression). Students confuse with boiling point elevation.
β Wrong
Solute added to water:
freezing point = 0 + ΞT_f β
(freezing point rises!?)
β Correct
Freezing point = 0 β ΞT_f β
(depressed below 0Β°C) β
Boiling point: elevated β
(increased above 100Β°C)
Adding solute: (1) raises boiling point β harder to vaporise. (2) lowers freezing point β harder to freeze. Anti-freeze in cars uses freezing point depression to prevent water from freezing.
π’
Using Molarity Instead of Molality in Colligative Property Formulas
ΞT_b = K_b Γ m uses MOLALITY (moles per kg solvent). Students use molarity (moles per litre solution).
β Wrong
ΞT_f = K_f Γ Molarity β
(molarity depends on
temperature; wrong unit)
β Correct
ΞT_f = K_f Γ Molality β
molality = mol/(kg solvent) β
Temperature independent β
All colligative property formulas use molality (m) β moles of solute per kilogram of SOLVENT (not solution). Molality is temperature-independent, making it the correct concentration measure for thermodynamic colligative properties.
βοΈ
van't Hoff Factor i Ignored for Electrolytes
For electrolytes, all colligative properties are multiplied by the van't Hoff factor i. Forgetting i gives values that are too small by factor i.
β Wrong
NaCl ΞT_b calculation:
ΞT_b = K_b Γ m β
(forgot i=2 for NaCl)
β Correct
ΞT_b = i Γ K_b Γ m β
i(NaCl) β 2 β
ΞT_b = 2 Γ 0.52 Γ m β
Van't Hoff factor i = number of particles a formula unit produces in solution. NaCl β 2, KβSOβ β 3, glucose β 1. All colligative properties for electrolytes: multiply by i.
π«§
Raoult's Law: Partial Pressure = Ο Γ PΒ°_A of SOLVENT (Not Solute)
Raoult's law gives vapour pressure of the SOLVENT above a solution. P_A = Ο_A Γ PΒ°_A where A is the solvent.
β Wrong
Vapour pressure of solution:
P = Ο_solute Γ PΒ°_solvent β
(wrong mole fraction)
β Correct
P_solvent = Ο_solvent Γ PΒ°_solvent β
Relative lowering:
ΞP/PΒ° = Ο_solute β
Raoult's law: P_A = Ο_A Γ PΒ°_A, where A = solvent, Ο_A = mole fraction of SOLVENT. The relative lowering ΞP/PΒ° = Ο_B (mole fraction of solute) β a neat result showing the depression is proportional to solute concentration.
Chapter Intelligence
Solutions is numerically predictable β the same four formulas appear year after year in EAPCET.
EAPCET Weightage (2019β2024)
Boiling point elevation~8 Freezing point depression~7 Osmotic pressure (van't Hoff)~6 Relative VP lowering (Raoult's)~5 High-Yield PYQ Patterns
ΞT_b = K_bΒ·m calculationFind molar mass from ΞT_fOsmotic pressure Ο = CRTRelative VP lowering = Ο_soluteEffect of i for NaCl vs glucoseIsotonic solutions (equal Ο)Reverse osmosis condition
Exam Strategy
- All four colligative properties use molality, not molarity. Convert: m = (g_solute/M_solute) Γ (1000/g_solvent).
- Electrolytes have i > 1 (dissociation gives more particles). For NaCl iβ2, KβSOβ iβ3, MgSOβ iβ2. Always include i for salts.
- Finding molar mass: set up ΞT_f = K_f Γ (w_B/M_B) Γ (1000/w_A), plug in and solve for M_B. This is a guaranteed 1β2 marks per EAPCET.
- Osmotic pressure is the most sensitive colligative property (can detect small concentrations). Ο = CRT at 27Β°C (T=300K).
- Solutions connects to Equilibrium (Raoult's law derivation), Electrochemistry (electrolyte solutions), and Kinetics (concentration effects on rate).
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