CBSE Class 12 · Chemistry · NCERT Chemistry-I
Solutions: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A solution is homogeneous at the…
- Concentration can be expressed as…
- Raoult's law states that the partial…
- An ideal solution obeys Raoult's law…
- Colligative properties — relative…
- For electrolytes, the van 't Hoff…
- Osmotic pressure π = iCRT, where C…
- Formulas and facts
- Molarity (M)
- Molality (m)
- Mole fraction
- Raoult's law
- Relative lowering of vapour pressure
- Boiling-point elevation
- Freezing-point depression
- Worked examples
- Converting molality to mole fraction
- Boiling-point elevation
- Osmotic pressure of an electrolyte
- Watch out for
- Confusing molarity and molality
- Forgetting to use the van 't Hoff…
- Using ΔT in Celsius where Kelvin is…
- Applying Raoult's law to highly…
- Taking mole fraction of solute as…
What this chapter is about
This chapter introduces the quantitative study of solutions — homogeneous mixtures where one or more substances (solutes) dissolve uniformly in another substance (solvent). You learn how to express the amount of solute present using different concentration units, and why the choice of unit matters in different contexts such as laboratory work, industrial processes and medical applications.
Key ideas
- A solution is homogeneous at the molecular level; the solute cannot be separated by filtration or settling.
- Concentration can be expressed as molarity (mol/L), molality (mol/kg solvent), mole fraction, mass percentage, or parts per million (ppm).
- Raoult's law states that the partial vapour pressure of each volatile component equals its mole fraction in solution multiplied by its pure-component vapour pressure: p₁ = x₁ × p₁°.
- An ideal solution obeys Raoult's law at all compositions; mixing produces no enthalpy change and no volume change. Real solutions show positive or negative deviations.
- Colligative properties — relative lowering of vapour pressure, boiling-point elevation, freezing-point depression, osmotic pressure — depend on the number of solute particles, not their identity.
- For electrolytes, the van 't Hoff factor i accounts for dissociation or association: i = (observed colligative property) / (calculated for non-electrolyte).
- Osmotic pressure π = iCRT, where C is molarity in mol/L, R = 0.0821 L atm K⁻¹ mol⁻¹, and T is temperature in kelvin.
Formulas and facts to remember
- Quantity: Molarity (M) · Formula: M = n(solute) / V(solution in L) · Meaning: Moles of solute per litre of solution
- Quantity: Molality (m) · Formula: m = n(solute) / mass of solvent in kg · Meaning: Moles of solute per kilogram of solvent; independent of temperature
- Quantity: Mole fraction · Formula: x₁ = n₁ / (n₁ + n₂) · Meaning: Fraction of total moles that is component 1
- Quantity: Raoult's law · Formula: p₁ = x₁ × p₁° · Meaning: Partial pressure equals mole fraction times pure vapour pressure
- Quantity: Relative lowering of vapour pressure · Formula: (p° − p) / p° = x₂ · Meaning: Equals mole fraction of non-volatile solute
- Quantity: Boiling-point elevation · Formula: ΔT_b = i × K_b × m · Meaning: K_b is molal elevation constant (K kg mol⁻¹)
- Quantity: Freezing-point depression · Formula: ΔT_f = i × K_f × m · Meaning: K_f is molal depression constant
- Quantity: Osmotic pressure · Formula: π = iCRT · Meaning: C in mol/L, R = 0.0821 L atm K⁻¹ mol⁻¹, T in K
- Quantity: van 't Hoff factor · Formula: i = (observed property) / (expected for non-electrolyte) · Meaning: i > 1 for dissociation, i < 1 for association
Common mistakes
- Confusing molarity and molality → Molarity uses solution volume; molality uses solvent mass — they differ especially for concentrated solutions.
- Forgetting to use the van 't Hoff factor for salts → Strong electrolytes produce more particles than formula units; always multiply by i.
- Using ΔT in Celsius where Kelvin is needed → For the elevation and depression formulae the change is the same numerically, but osmotic-pressure calculations need absolute temperature in kelvin.
- Applying Raoult's law to highly non-ideal mixtures without noting deviations → Mixtures of ethanol–water or acetone–chloroform show significant deviations; ideal-solution equations give only approximate answers.
- Taking mole fraction of solute as moles solute divided by moles solvent alone → Mole fraction uses total moles (solute + solvent) in the denominator.
Quick revision
- Molality is temperature-independent; molarity changes with temperature because volume changes.
- Raoult's law: partial pressure = mole fraction × pure vapour pressure.
- Colligative properties depend on particle count, not particle identity.
- Boiling point rises and freezing point falls when a non-volatile solute is added.
- π = iCRT — osmotic pressure is the most sensitive colligative property for molar-mass determination.
- van 't Hoff factor i corrects for dissociation (i > 1) or association (i < 1).