Solutions — NEET notes

Types of Solutions

Solutions are homogeneous mixtures of two or more components. The component present in larger amount is the solvent; the other is the solute. Solutions can be solid, liquid, or gaseous. Concentration is expressed in molarity, molality, mole fraction, and ppm — NEET loves unit-conversion numericals.

Molality (m) = moles of solute mass of solvent (kg)

Solute, Solvent & Nine Types

Any combination of solid, liquid, or gas can form a solution. The solvent is the component present in the largest amount; the rest are solutes.

A solution is a homogeneous mixture of two or more substances. The component present in the largest amount is called the solvent, and the other component(s) are called solute(s). When you dissolve sugar in water, water is the solvent and sugar is the solute.

• Binary solution = exactly 2 components (1 solute + 1 solvent)
• When both components are liquids, the one present in larger amount is the solvent
• When a solid or gas dissolves in a liquid, the liquid is always the solvent regardless of amount
• Aqueous solution = water is the solvent; non-aqueous = any other solvent (e.g., benzene, CCl _4 )

Concentration Terms

Concentration tells you how much solute is dissolved per unit of solution or solvent. Each term — mass %, molarity, molality, mole fraction, ppm — has specific advantages. NEET loves interconversion problems.

There are multiple ways to express how concentrated a solution is. Each has its own advantage — molarity is convenient for volumetric work, molality doesn't change with temperature, and mole fraction is key for Raoult's law.

Mass % = mass of solute mass of solution 100

Molarity (M) = moles of solute volume of solution (L)

Molality (m) = moles of solute mass of solvent (kg)

Mole fraction: x_A = n_A n_A + n_B , x_A + x_B = 1

ppm = mass of solute mass of solution 10^6

• Molarity changes with temperature (because volume expands/contracts with T)
• Molality does NOT change with temperature (mass doesn't change with T) — preferred for colligative property calculations
• Mole fraction is dimensionless and always between 0 and 1
• ppm is used for very dilute solutions (e.g., pollutant levels in water, fluoride in drinking water)

Solubility

Solubility is the maximum amount of solute that dissolves in a given amount of solvent at a given temperature. For gases, solubility follows Henry's law (p = K_H × x). Temperature increases solid solubility (usually) but decreases gas solubility. NEET asks Henry's law numericals and Le Chatelier-based reasoning.

p = K_H x

Solubility of Solids in Liquids

A solid dissolves in a liquid when solute-solvent interactions are comparable to solute-solute and solvent-solvent interactions. Temperature effect depends on whether dissolution is exothermic or endothermic.

Solubility of a solid in a liquid depends on the nature of both solute and solvent. The golden rule: like dissolves like. Polar solutes dissolve in polar solvents (NaCl in water), non-polar solutes dissolve in non-polar solvents (naphthalene in benzene).

• Saturated solution: maximum solute dissolved at given T; any more solute remains undissolved
• Unsaturated solution: less solute than the maximum — more can dissolve
• Supersaturated solution: more solute than the saturation limit — unstable, crystallizes on disturbance
• For endothermic dissolution ( H > 0 ): solubility increases with T (e.g., KNO _3 , NaNO _3 )
• For exothermic dissolution ( H < 0 ): solubility decreases with T (e.g., CeSO _4 , Ca(OH) _2 )

Henry's Law

The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the solution. Higher pressure = more gas dissolved. Higher temperature = less gas dissolved.

Henry's law states that at constant temperature, the partial pressure of a gas above a solution is directly proportional to the mole fraction of the gas dissolved in the solution.

p = K_H x

Here, p = partial pressure of gas above solution, x = mole fraction of gas in solution, and K_H = Henry's law constant. Higher K_H means lower solubility (the gas needs more pressure to dissolve).

• K_H is different for different gases — O_2 has a different K_H than CO_2 in water
• K_H increases with temperature → gas solubility decreases with increasing T
• Henry's law is valid only at low pressures and for dilute solutions where gas doesn't react with solvent
• Gases like NH_3 , HCl that react with water do NOT obey Henry's law

Raoult's Law

Raoult's law states that the partial vapour pressure of each volatile component equals its mole fraction times its pure vapour pressure. Ideal solutions obey it perfectly. Real solutions show positive or negative deviations, forming azeotropes. This is the single most tested topic from Solutions in NEET.

p_A = x_A p_A^

Raoult's Law for Volatile Solutes

For a solution of two volatile liquids A and B, each component's partial vapour pressure is proportional to its mole fraction in the liquid phase. Total pressure is the sum of both partials.

Consider a solution of two volatile liquids A and B. Raoult's law says the partial vapour pressure of each component equals its mole fraction in the liquid phase multiplied by its pure-component vapour pressure.

p_A = x_A p_A^ p_B = x_B p_B^

p_ total = p_A + p_B = x_A p_A^ + x_B p_B^

Since x_A + x_B = 1 , we get x_B = 1 - x_A . Substituting: p_ total = p_B^ + (p_A^ - p_B^ ) x_A . This is a straight line when plotted against x_A — the hallmark of an ideal solution.

• p_A^ = vapour pressure of pure A (no solute) — a property of the liquid at that temperature
• Adding a non-volatile solute always lowers the vapour pressure of the solvent (fewer solvent molecules at the surface to escape)
• The composition of vapour above the solution differs from the liquid — the more volatile component is enriched in the vapour phase
• Mole fraction in vapour: y_A = p_A p_ total (Dalton's law)

Raoult's Law for Non-volatile Solutes

When the solute is non-volatile (e.g., sugar, NaCl in water), only the solvent contributes to vapour pressure. The lowering of vapour pressure is proportional to the mole fraction of the solute.

When the solute is non-volatile (its own vapour pressure ≈ 0), only the solvent evaporates. Raoult's law for the solvent becomes: p = x_ solvent p^ . Since x_ solvent < 1 , the solution's vapour pressure is always less than the pure solvent's.

p^ - p p^ = p p^ = x_ solute

This is the relative lowering of vapour pressure — it equals the mole fraction of the solute. This is a colligative property because it depends only on how many solute particles are present, not on what they are.

• p / p^ = x_2 where x_2 = mole fraction of solute — this is the first colligative property
• Works only for dilute solutions of non-volatile, non-electrolyte solutes
• For electrolytes, multiply by van't Hoff factor i : p / p^ = i x_2
• This relationship is used to determine molar mass of unknown solutes

Ideal vs Non-Ideal Solutions

Ideal solutions obey Raoult's law at all concentrations. Real solutions deviate — positive deviation means weaker A-B forces (more evaporation), negative deviation means stronger A-B forces (less evaporation). Deviations lead to azeotropes.

An ideal solution obeys Raoult's law over the entire range of concentrations. This happens when A-B interactions are roughly the same strength as A-A and B-B interactions. Mixing is neither favoured nor opposed.

• Ideal solution conditions: H_ mix = 0 , V_ mix = 0 , obeys Raoult's law for all x
• Example: benzene + toluene, n -hexane + n -heptane, chlorobenzene + bromobenzene
• Ideal solutions are formed by structurally similar molecules with similar intermolecular forces

Azeotropes are constant-boiling mixtures that distil without change in composition. Positive deviation → minimum boiling azeotrope (e.g., ethanol-water at 95.5% ethanol, 78.1°C). Negative deviation → maximum boiling azeotrope (e.g., HCl-water at 20.2% HCl, 108.6°C).

• Azeotropes cannot be separated by simple distillation — the vapour has the same composition as the liquid
• Minimum boiling azeotrope: boils below either pure component (positive deviation)
• Maximum boiling azeotrope: boils above either pure component (negative deviation)
• Ethanol-water azeotrope (95.5% ethanol) is why you can't get 100% ethanol by distillation alone

Colligative Properties Intro

Colligative properties depend only on the NUMBER of solute particles, not their chemical nature. The four colligative properties are: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. This concept is the foundation for everything that follows in colligative calculations.

Colligative property number of solute particles

What 'Colligative' Means

The word colligative comes from Latin 'colligatus' meaning 'bound together'. These properties depend collectively on the number of solute particles in solution, regardless of their nature.

Colligative literally means 'depending on the collection'. A colligative property depends ONLY on the number of solute particles present in a given amount of solvent — NOT on the size, charge, or chemical identity of those particles.

• The four colligative properties: (1) Relative lowering of vapour pressure, (2) Elevation of boiling point, (3) Depression of freezing point, (4) Osmotic pressure
• All four increase as you add more solute particles
• Non-electrolytes (sugar, urea, glucose): 1 mole gives 1 mole of particles
• Electrolytes (NaCl, CaCl_2 ): 1 mole gives MORE than 1 mole of particles due to dissociation → larger colligative effect

The Mechanism

All colligative effects trace back to one cause: solute particles lower the vapour pressure of the solvent. This single change cascades into elevation of boiling point, depression of freezing point, and generation of osmotic pressure.

Every colligative property is a consequence of vapour pressure lowering. Here's the cascade:

• Step 1: Solute particles block solvent molecules from the surface → vapour pressure drops
• Step 2: Since vapour pressure is lower, the solution needs a higher temperature to boil (vapour pressure must reach atmospheric pressure) → boiling point elevation
• Step 3: The solution's vapour pressure curve intersects the solid's curve at a lower temperature → freezing point depression
• Step 4: Across a semipermeable membrane, pure solvent (higher vapour pressure) flows into the solution (lower vapour pressure) → osmotic pressure

The next concepts cover each colligative property in detail with formulas and calculations. This concept is the 'why' — the next ones are the 'how much'.

Elevation of Boiling Point & Depression of Freezing Point

Adding a non-volatile solute raises the boiling point by ΔTb = Kb·m and lowers the freezing point by ΔTf = Kf·m. Kb and Kf are molal elevation and depression constants specific to the solvent. These are the most numerically tested colligative properties in NEET.

T_b = K_b m T_f = K_f m

Elevation of Boiling Point

A liquid boils when its vapour pressure equals atmospheric pressure. Adding solute lowers vapour pressure, so the solution must be heated MORE to reach atmospheric pressure. The extra temperature needed is ΔTb.

A pure liquid boils when its vapour pressure equals atmospheric pressure. A solution has lower vapour pressure than pure solvent (Raoult's law). So the solution needs a higher temperature to build up enough vapour pressure to boil.

T_b = T_b - T_b^ = K_b m

Here T_b = boiling point of solution, T_b^ = boiling point of pure solvent, K_b = ebullioscopic constant (molal boiling point elevation constant) of the solvent, and m = molality of the solution.

• K_b for water = 0.52 K kg mol ^ -1 (NCERT value — memorize this!)
• K_b depends ONLY on the solvent, not on the solute
• T_b is always positive — the solution always boils at a higher T than the pure solvent
• Higher molality → higher elevation → higher boiling point
• K_b = R T_b^ 2 M_1 1000 _ vap H — theoretical derivation (rarely asked in NEET, but good to know)

Depression of Freezing Point

A liquid freezes when its vapour pressure equals that of the solid phase. Solute lowers the liquid's vapour pressure, so the intersection with the solid's vapour pressure curve shifts to a LOWER temperature.

Freezing occurs when the vapour pressure of the liquid equals the vapour pressure of the solid. Adding a non-volatile solute lowers the liquid's vapour pressure, but the solid's vapour pressure is unchanged (the solute doesn't enter the crystal lattice). So the two curves now intersect at a lower temperature.

T_f = T_f^ - T_f = K_f m

Here T_f^ = freezing point of pure solvent, T_f = freezing point of solution, K_f = cryoscopic constant (molal freezing point depression constant), and m = molality.

• K_f for water = 1.86 K kg mol ^ -1 (memorize — appears in almost every NEET paper)
• K_f depends ONLY on the solvent, not on the solute
• T_f is always positive (because T_f^ > T_f ) — the solution freezes at a lower T
• Note: K_f > K_b for water (1.86 > 0.52) — freezing point is more sensitive to solute addition than boiling point

Osmotic Pressure

Osmosis is the spontaneous flow of solvent through a semipermeable membrane from a region of lower solute concentration to higher. The minimum pressure needed to stop this flow is osmotic pressure (π = CRT). Reverse osmosis, isotonic/hypertonic/hypotonic solutions are key NEET applications.

= CRT

Osmosis & Osmotic Pressure

Osmosis is the spontaneous movement of solvent molecules through a semipermeable membrane from a dilute solution (or pure solvent) to a concentrated solution. Osmotic pressure is the minimum pressure needed to stop this flow.

Place pure water on one side of a semipermeable membrane (SPM) and a sugar solution on the other. Water flows spontaneously through the membrane into the sugar solution. This is osmosis. The membrane allows solvent molecules to pass but blocks solute molecules.

= CRT = n V RT

Here = osmotic pressure (atm), C = molarity of solution (mol/L), R = 0.0821 L atm K ^ -1 mol ^ -1 , and T = temperature in Kelvin. This equation looks exactly like the ideal gas equation ( PV = nRT ) — van't Hoff showed this deliberately.

• Osmosis is a colligative property — depends on the number of solute particles
• SPM examples: cellophane, pig's bladder, copper ferrocyanide Cu_2[Fe(CN)_6] (used in lab)
• Osmotic pressure is measured by the Berkeley-Hartley method (better than the older Pfeffer's method)
• Even a tiny concentration produces measurable osmotic pressure — making it the most sensitive method for molar mass determination

Isotonic, Hypertonic & Hypotonic

Two solutions with equal osmotic pressure are isotonic. The one with higher π is hypertonic; lower π is hypotonic. Cells placed in hypertonic solutions shrink (crenation/plasmolysis); in hypotonic solutions they swell and may burst (lysis).

When two solutions have the same osmotic pressure, they are isotonic to each other. No net osmosis occurs between isotonic solutions.

• Isotonic solutions: _1 = _2 → C_1 = C_2 (at same T, for non-electrolytes)
• For electrolytes, isotonic means i_1 C_1 = i_2 C_2 (must account for dissociation)
• 0.9% NaCl (normal saline) is isotonic with human blood
• 5% glucose solution is also approximately isotonic with blood

Reverse Osmosis

If a pressure GREATER than the osmotic pressure is applied on the solution side, solvent flows in reverse — from solution to pure solvent. This is reverse osmosis (RO), used commercially for water purification.

In normal osmosis, solvent flows from pure solvent → solution. In reverse osmosis (RO), a pressure greater than is applied on the solution side, forcing solvent to flow from solution → pure solvent. The solute stays behind.

• Applied pressure must be greater than the osmotic pressure of the solution for RO to work
• The SPM allows water through but blocks dissolved salts, bacteria, and impurities
• Cellulose acetate membranes are commonly used in RO plants
• Desalination of seawater is the largest application of reverse osmosis

Determination of Molar Mass

Colligative properties provide experimental methods to determine the molar mass of unknown solutes. ΔTb, ΔTf, and π can each be used. Osmotic pressure is the most sensitive and preferred method. Abnormal molar masses arise when solutes associate or dissociate — the van't Hoff factor corrects for this.

M_2 = K_f w_2 1000 T_f w_1

Molar Mass from ΔTb, ΔTf, and π

Since colligative properties depend on the number of moles of solute, measuring any colligative property lets you calculate the molar mass of an unknown solute.

If you know the colligative property ( T_b , T_f , or ) and the amount of solute dissolved, you can calculate the molar mass of the solute. The logic: colligative property → molality → moles → molar mass.

From T_b: M_2 = K_b w_2 1000 T_b w_1

From T_f: M_2 = K_f w_2 1000 T_f w_1

From : M_2 = w_2 RT V

Here w_2 = mass of solute (g), w_1 = mass of solvent (g), M_2 = molar mass of solute, V = volume of solution (L), R = gas constant, and T = temperature (K).

• All three methods give the same molar mass for non-electrolyte, non-associating solutes
• Osmotic pressure method is preferred because: (1) is large even for dilute solutions, (2) measurement is at room temperature, (3) works well for biomolecules with high molar mass
• Cryoscopy ( T_f ) is preferred over ebullioscopy ( T_b ) because K_f > K_b → larger, more measurable T
• These methods give the molar mass, not the molecular formula — you need empirical formula separately

Abnormal Molar Mass

Sometimes the experimentally determined molar mass doesn't match the expected value. This happens when solute molecules associate (giving higher apparent M) or dissociate (giving lower apparent M) in solution.

Colligative property formulas assume solute particles remain as individual molecules. But in reality:

• Association: solute molecules join together → fewer particles than expected → smaller colligative effect → higher apparent molar mass (e.g., acetic acid dimerizes in benzene)
• Dissociation: solute molecules split into ions → more particles than expected → larger colligative effect → lower apparent molar mass (e.g., NaCl → Na ^+ + Cl ^- in water)

Van't Hoff Factor

The van't Hoff factor (i) corrects colligative property calculations for association and dissociation. i = observed colligative property / calculated colligative property = normal molar mass / abnormal molar mass. For dissociation i > 1; for association i < 1. All colligative formulas are modified by multiplying by i.

i = 1 + (n - 1)

Van't Hoff Factor (i)

The van't Hoff factor quantifies how much the actual number of particles in solution differs from the expected number. It connects the 'ideal' colligative property (assuming no association/dissociation) to the 'observed' value.

Van't Hoff introduced a factor i to account for the fact that electrolytes and associating solutes don't behave as simple molecular solutes.

i = observed colligative property calculated colligative property (assuming no association/dissociation)

i = normal (expected) molar mass abnormal (observed) molar mass

i = total moles of particles after association/dissociation moles of solute dissolved

• For non-electrolytes (glucose, urea, sucrose): i = 1 (no dissociation or association)
• For dissociation (electrolytes in water): i > 1 (more particles than formula units)
• For association (e.g., acetic acid in benzene): i < 1 (fewer particles than molecules dissolved)
• NaCl → Na ^+ + Cl ^- : i = 2 (ideal, complete dissociation)
• CaCl_2 → Ca ^ 2+ + 2Cl ^- : i = 3 (ideal)
• K_3[Fe(CN)_6] → 3K ^+ + [Fe(CN) _6 ] ^ 3- : i = 4 (ideal)

Relating i to Degree of Dissociation (α)

For a solute that dissociates into n particles per formula unit with degree of dissociation α, the van't Hoff factor is i = 1 + (n-1)α. For association into groups of n molecules with degree of association α, i = 1 + (1/n - 1)α.

Not all electrolytes dissociate completely. If the degree of dissociation is (fraction of molecules that actually dissociate) and each molecule produces n ions:

Dissociation: i = 1 + (n - 1)

Derivation: Start with 1 mole. After dissociation: (1 - ) moles undissociated + n moles of ions = 1 - + n = 1 + (n-1) total moles. So i = 1 + (n-1) .

Association: i = 1 + ( 1 n - 1 ) = 1 - (1 - 1 n )

For association: n molecules combine into 1 associated unit. Start with 1 mole. After association: (1 - ) moles free + /n moles associated = 1 - + /n total moles.

• If = 1 (100% dissociation): i = n exactly (e.g., NaCl fully dissociated → i = 2 )
• If = 0 (no dissociation): i = 1 (behaves as non-electrolyte)
• For strong electrolytes in dilute solution, 1 , so i n
• For weak electrolytes (CH _3 COOH, NH _3 ), 1 , so i is only slightly above 1

Modified Colligative Formulas

When dealing with electrolytes or associating solutes, every colligative property formula gets multiplied by the van't Hoff factor i. These modified formulas are what you actually use in NEET calculations.

The corrected colligative property formulas simply include the factor i :

p p^ = i x_2

T_b = i K_b m

T_f = i K_f m

= i CRT

• For non-electrolytes, i = 1 and these reduce to the standard formulas
• For electrolytes, always use i — forgetting it is the #1 error in colligative property problems
• The corrected molar mass formula: M_2 = i K_f w_2 1000 T_f w_1
• In ranking problems ('arrange solutions in order of T_f '), always multiply molality by i first, then compare

Quick recall

Rank in increasing order of freezing point: 0.1 m glucose, 0.1 m NaCl, 0.1 m CaCl₂, 0.1 m Al₂(SO₄)₃.

More particles → lower freezing point. Effective particles: glucose = 0.1, NaCl = 0.2, CaCl₂ = 0.3, Al₂(SO₄)₃ = 0.5. Lowest FP → Al₂(SO₄)₃ < CaCl₂ < NaCl < glucose (increasing order of FP).