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CHEMISTRY  |  Class XII

Chapter 2

SOLUTIONS

Concentration  ◆  Raoult's Law  ◆  Colligative Properties  ◆  Osmosis  ◆  Van't Hoff Factor

 

1. Introduction to Solutions

A solution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits. The word 'homogeneous' means that the mixture has a uniform composition and properties throughout — unlike a heterogeneous mixture (like sand in water) where regions with different compositions can be distinguished.

Solutions are everywhere in everyday life — the air we breathe is a gaseous solution of nitrogen, oxygen, argon, carbon dioxide, and other gases. The blood that circulates in our body is a liquid solution. Even metals like brass and stainless steel are solid solutions. The study of solutions is central to chemistry, biology, medicine, and materials science.

Solute: The component present in smaller quantity is called the solute. It is the substance that gets dissolved.

Solvent: The component present in larger quantity is called the solvent. It is the medium in which the solute dissolves. The solvent determines the physical state of the solution.

Binary Solution: A solution consisting of only two components (one solute + one solvent) is called a binary solution. This chapter primarily deals with binary solutions.

 

Figure 1: Types of Solutions — Solutions can exist in all three states of matter depending on the states of solute and solvent.

S. No.	Solute	Solvent	Example Solution	Type
1	Gas	Gas	Air (N₂ + O₂ + Ar + CO₂)	Gaseous solution
2	Gas	Liquid	Carbonated water (CO₂ in H₂O), O₂ in blood	Liquid solution
3	Gas	Solid	H₂ gas adsorbed in Palladium metal	Solid solution
4	Liquid	Gas	Mist or clouds (water droplets in air)	Gaseous solution
5	Liquid	Liquid	Ethanol in water, Benzene in toluene	Liquid solution
6	Liquid	Solid	Mercury amalgam (Hg in Ag or Zn)	Solid solution
7	Solid	Gas	Iodine vapour in air	Gaseous solution
8	Solid	Liquid	NaCl in water, Glucose in water	Liquid solution (aqueous)
9	Solid	Solid	Brass (Cu + Zn), Bronze (Cu + Sn)	Solid solution (alloy)

 

 

2. Expressing Concentration of Solutions

The concentration of a solution expresses the amount of solute dissolved per unit amount of solvent or solution. There are several ways to express concentration, each with specific advantages for different situations. Understanding all concentration terms and the interconversions between them is essential for quantitative chemistry.

Figure 2: All six concentration terms — Molarity, Molality, Mole Fraction, Normality, Mass % and ppm — with formula structure and key points.

2.1 Molarity (M)

Molarity is the most commonly used concentration term. It is defined as the number of moles of solute dissolved per litre of solution. Molarity depends on temperature because the volume of solution changes with temperature (thermal expansion/contraction).

Molarity (M)

M  =  moles of solute / volume of solution (in litres)  =  n / V(L)

 

Moles from Molarity

n  =  M × V(L)     or     w  =  M × V(L) × Molar mass

 

2.2 Molality (m)

Molality is defined as the number of moles of solute dissolved per kilogram of solvent (not solution). Molality is independent of temperature because it is defined in terms of mass (not volume), and mass does not change with temperature. This makes molality preferred for colligative property calculations.

Molality (m)

m  =  moles of solute / mass of solvent (in kg)  =  n / W_solvent(kg)

 

Molality from w/M

m  =  (w × 1000) / (M_r × W_solvent)     [w in g, W in g]

 

2.3 Mole Fraction (x)

Mole fraction of a component is defined as the ratio of the number of moles of that component to the total number of moles of all components present in the solution. Mole fraction is dimensionless (no units) and the sum of mole fractions of all components is always equal to 1.

Mole Fraction of Solute (x₂)

x₂  =  n₂ / (n₁ + n₂)     where n₁ = moles of solvent, n₂ = moles of solute

 

Important Identity

x₁  +  x₂  =  1     (for binary solution)

 

2.4 Mass Percentage (w/w %)

Mass percentage (also called weight percentage or weight/weight percent) is the mass of the solute present in 100 grams of the solution. It is independent of temperature since it is based on mass. This is commonly used for commercial products like bleaching powder, hydrochloric acid, and sodium hydroxide.

Mass % (w/w)

w/w%  =  (mass of solute / mass of solution) × 100

 

2.5 Volume Percentage (v/v %)

Volume % (v/v)

v/v%  =  (volume of solute / volume of solution) × 100

 

Used for liquid in liquid solutions. For example, '40% alcohol by volume' means 40 mL of alcohol in 100 mL of solution.

2.6 Parts Per Million (ppm)

Parts per million is used when the concentration is very small — for trace elements in water, pollutants in air, or micro-nutrients in biology. It is the number of parts of solute per million parts of solution by mass.

ppm	ppm  =  (mass of solute / mass of solution) × 10⁶

 

Similarly, ppb (parts per billion) = (mass of solute / mass of solution) × 10⁹, used for ultra-trace concentrations.

2.7 Normality (N)

Normality is the number of gram-equivalents of solute dissolved per litre of solution. A gram-equivalent depends on the type of reaction (acid-base, redox, precipitation). The relationship between normality and molarity involves the n-factor (also called the valence factor).

Normality (N)

N  =  Equivalents of solute / Volume of solution (L)

 

N–M Relationship

N  =  n-factor × M     (n-factor = no. of H+ / OH- / electrons transferred)

 

2.8 Important Interconversions

M to m (Molarity to Molality)

m  =  (1000 × M) / (1000 × d  −  M × M_solute)   [d = density in g/mL]

 

m to M (Molality to Molarity)

M  =  (1000 × m × d) / (1000  +  m × M_solute)

 

Mass% to Molarity

M  =  (10 × mass% × d) / M_solute   [d in g/mL]

 

 

3. Solubility

Solubility of a substance is the maximum amount of the substance that can be dissolved in a specified amount of solvent at a given temperature to form a stable solution. When no more solute can dissolve, the solution is said to be saturated, and the concentration at that point equals the solubility.

3.1 Solubility of Solids in Liquids

The solubility of most solid solutes in liquid solvents increases with increasing temperature (endothermic dissolution), though there are exceptions (e.g., Ce₂(SO₄)₃ shows decreased solubility with rising temperature — exothermic dissolution). The general rule is: Like dissolves like — polar solvents dissolve polar solutes; non-polar solvents dissolve non-polar solutes.

◆        Unsaturated Solution: A solution that contains less solute than the solubility limit. More solute can be dissolved.

◆        Saturated Solution: A solution that contains exactly the maximum amount of dissolved solute at that temperature. An equilibrium exists between dissolved and undissolved solute.

◆        Supersaturated Solution: An unstable solution that temporarily contains more dissolved solute than the solubility limit (achieved by careful cooling of a hot saturated solution).

 

3.2 Solubility of Gases in Liquids — Henry's Law

The solubility of gases in liquids is described by Henry's Law, formulated by William Henry in 1803. It states that at constant temperature, the solubility (or mole fraction) of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid surface.

Henry's Law

p  =  K_H × x     (K_H = Henry's Law constant; x = mole fraction of gas)

 

A higher value of K_H means lower solubility of the gas in that solvent at that temperature. K_H increases with temperature — meaning gases become less soluble as temperature increases. This is why fish find it harder to breathe (dissolved O₂ decreases) in warm water.

Applications of Henry's Law

1. Carbonated Beverages: CO₂ is dissolved in soft drinks under high pressure. When the bottle is opened, pressure drops → CO₂ escapes → fizzing. 2. Scuba Diving: At great depths, high pressure dissolves more N₂ in blood. If a diver ascends too quickly, N₂ forms bubbles in the blood — a painful and dangerous condition called 'the bends' (decompression sickness). 3. Oxygen in Blood: O₂ dissolves in blood plasma according to Henry's Law, supplementing the O₂ carried by haemoglobin. 4. Aerated Fish Tanks: High-pressure air is bubbled in to maintain adequate dissolved O₂ for the fish.

 

 

4. Vapour Pressure and Raoult's Law

The vapour pressure of a liquid is the pressure exerted by its vapour when the liquid and vapour are in dynamic equilibrium at a given temperature. When a non-volatile solute is dissolved in a solvent, the vapour pressure of the resulting solution is always lower than that of the pure solvent. This is the basis of Raoult's Law.

4.1 Raoult's Law for Volatile Solutes

For a solution of two volatile liquids (e.g., benzene and toluene), Raoult's Law states that the partial vapour pressure of each component is equal to the product of the vapour pressure of the pure component and its mole fraction in the solution.

Raoult's Law — Component 1

p₁  =  P₁*  ×  x₁     (P₁* = vapour pressure of pure component 1)

 

Raoult's Law — Component 2

p₂  =  P₂*  ×  x₂

 

Total Vapour Pressure (Dalton's Law)

P_total  =  p₁ + p₂  =  P₁*x₁  +  P₂*x₂

 

Figure 3: Raoult's Law — Partial pressures p₁ and p₂ are linear in mole fraction; total pressure P is also linear for ideal solutions (straight line between P₁* and P₂*).

4.2 Raoult's Law for Non-Volatile Solutes

When a non-volatile solute (like sugar or salt) is dissolved in a volatile solvent (like water), only the solvent contributes to the vapour pressure. The partial pressure of the solvent above the solution is:

Vapour Pressure of Solution

p₁  =  P₁*  ×  x₁  =  P₁* × (1 − x₂)

 

Relative Lowering of Vapour Pressure

ΔP / P₁*  =  (P₁* − p₁) / P₁*  =  x₂

 

This result — that the relative lowering of vapour pressure equals the mole fraction of the solute — is extremely important. It shows that the lowering of vapour pressure is a colligative property (depends only on the number of solute particles, not their nature).

4.3 Ideal and Non-Ideal Solutions

Property	Ideal Solution	Non-Ideal Solution
Raoult's Law	Obeys Raoult's Law at all compositions and temperatures	Deviations from Raoult's Law — positive or negative
ΔH_mixing	Zero (no heat evolved or absorbed on mixing)	ΔH_mixing ≠ 0 (heat absorbed or released)
ΔV_mixing	Zero (no volume change on mixing)	ΔV_mixing ≠ 0 (volume changes)
Interactions	Solute-solvent interactions ≈ solute-solute + solvent-solvent	Solute-solvent interactions are different from pure component interactions
Examples	Benzene + Toluene; n-Hexane + n-Heptane	Acetone + Chloroform (−ve deviation); Ethanol + Water (+ve)
Vapour Pressure	p_total is linear — between P₁* and P₂*	p_total is either above or below Raoult's ideal line

 

4.4 Azeotropes

Non-ideal solutions that show large positive or negative deviations from Raoult's Law can form Azeotropes — constant-boiling mixtures that cannot be separated by simple fractional distillation because the liquid and vapour at the azeotropic composition have the same composition.

◆        Maximum Boiling Azeotrope: Formed by solutions showing large negative deviation (e.g., HNO₃ + water at 68% HNO₃ by mass, b.p. = 393.5 K; H₂SO₄ + water).

◆        Minimum Boiling Azeotrope: Formed by solutions showing large positive deviation (e.g., ethanol + water at 95.5% ethanol by volume, b.p. = 351.1 K). This is why absolute alcohol (100% ethanol) cannot be obtained by simple distillation.

 

5. Colligative Properties

Colligative properties are those properties of solutions that depend only on the number of solute particles (molecules or ions) present in a definite amount of solvent or solution — regardless of the nature, size, or chemical identity of the solute particles. There are four colligative properties: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.

Figure 4: Four Colligative Properties — all depend only on the number of solute particles, not their chemical nature or identity.

5.1 Relative Lowering of Vapour Pressure (RLVP)

As established by Raoult's Law, the vapour pressure of a solution containing a non-volatile solute is always less than that of the pure solvent. The decrease in vapour pressure relative to that of the pure solvent is the Relative Lowering of Vapour Pressure (RLVP).

RLVP = Mole Fraction of Solute

(P* − P) / P*  =  x₂  =  n₂ / (n₁ + n₂)

 

For dilute solutions (n₂ << n₁)

(P* − P) / P*  ≈  n₂ / n₁  =  w₂M₁ / (M₂w₁)

 

This formula allows us to determine the molar mass (M₂) of the solute if we measure the vapour pressure lowering experimentally.

5.2 Elevation of Boiling Point (ΔT_b)

The boiling point of a liquid is the temperature at which its vapour pressure equals the atmospheric pressure. Since adding a non-volatile solute lowers the vapour pressure, the solution must be heated to a higher temperature to reach atmospheric pressure — hence the boiling point is elevated. This is why salt water boils at a slightly higher temperature than pure water.

Elevation of Boiling Point

DeltaT_b  =  T_b(solution) − T_b(solvent)  =  K_b × m

 

Molar Mass from Boiling Point

M₂  =  (K_b × w₂ × 1000) / (DeltaT_b × w₁)    [w in grams]

 

Solvent	Normal B.P. (K)	K_b (K·kg/mol)	Notes
Water (H₂O)	373.15 K (100°C)	0.52	Most commonly used in problems
Benzene (C₆H₆)	353.3 K (80.1°C)	2.53	Useful for organic solutes
Chloroform (CHCl₃)	334.4 K (61.3°C)	3.63	Organic solvent
Carbon tetrachloride (CCl₄)	349.7 K (76.6°C)	5.02	Non-polar organic solvent
Ethanol (C₂H₅OH)	351.5 K (78.4°C)	1.20	Protic organic solvent

 

5.3 Depression of Freezing Point (ΔT_f)

The freezing point of a liquid is the temperature at which the liquid and solid phases coexist in equilibrium — i.e., the vapour pressures of the solid and liquid phases are equal. Since the solution has a lower vapour pressure than the pure solvent, it must be cooled further (to a lower temperature) for the vapour pressure of the solid to match the solution's vapour pressure. Hence the freezing point is depressed.

Depression of Freezing Point

DeltaT_f  =  T_f(solvent) − T_f(solution)  =  K_f × m

 

Molar Mass from Freezing Point

M₂  =  (K_f × w₂ × 1000) / (DeltaT_f × w₁)    [w in grams]

 

Solvent	Normal F.P. (K)	K_f (K·kg/mol)	Practical Application
Water (H₂O)	273.15 K (0°C)	1.86	Antifreeze in car radiators (ethylene glycol)
Benzene (C₆H₆)	278.6 K (5.5°C)	5.12	Widely used in lab for molar mass determination
Camphor (C₁₀H₁₆O)	452 K (179°C)	40.0	Beckmann method — very large Kf for accuracy
Acetic acid	289.9 K (16.7°C)	3.90	Used for organic acids and bases
Naphthalene	353.4 K (80.3°C)	6.80	Non-polar organic solvent

 

Applications of freezing point depression: (1) Adding rock salt (NaCl) to ice to melt snow on roads in winter — salt depresses the freezing point below 0°C. (2) Antifreeze in car radiators uses ethylene glycol mixed with water to lower the freezing point to about −40°C. (3) Sea water freezes at about −1.8°C due to dissolved salts.

5.4 Osmotic Pressure (π)

Osmosis is the spontaneous flow of solvent molecules through a semi-permeable membrane (SPM) from a region of lower solute concentration (higher solvent concentration) to a region of higher solute concentration (lower solvent concentration). The semi-permeable membrane allows the passage of solvent molecules but not solute molecules. The pressure that must be applied to the solution side to just stop osmosis is called the Osmotic Pressure (π).

Figure 5: Osmosis and Osmotic Pressure — Solvent flows through the semi-permeable membrane from pure solvent to solution side. Applied pressure to stop osmosis = osmotic pressure π.

Van't Hoff Equation for Osmotic Pressure

Pi  =  CRT  =  (n/V)RT

 

Molar Mass from Osmotic Pressure

M₂  =  (w₂RT) / (Pi × V)     [V in litres, w in grams]

 

Why Osmotic Pressure is the Most Useful Colligative Property

1. Sensitivity: Osmotic pressure is thousands of times larger than other colligative properties for the same solution. Even a very dilute 1 g/L solution of a protein (M ≈ 10,000 g/mol) gives an osmotic pressure of about 250 Pa — easily measurable. The same solution would show ΔTb ≈ 0.0005 K (unmeasurable). 2. Molar Mass Determination: Best method for determining very high molar masses of biopolymers (proteins, DNA, polymers). 3. Isotonic Solutions: IV fluids given in hospitals must have the same osmotic pressure as blood plasma (~7.4 atm) to prevent cell damage. 4. Reverse Osmosis: By applying pressure greater than osmotic pressure, pure water can be extracted from sea water — desalination. 5. Biological Importance: Osmosis controls cell turgor pressure in plants, water balance in kidneys, and nutrient absorption in intestines.

 

Isotonic Solutions: Solutions with the same osmotic pressure are called isotonic solutions. Blood plasma has π ≈ 7.4 atm. Normal saline (0.9% NaCl) is isotonic with blood — used in IVs and eye drops.

Hypertonic Solution: A solution with osmotic pressure greater than the cell fluid. Cells placed in hypertonic solution lose water by osmosis (plasmolysis in plants; crenation in red blood cells).

Hypotonic Solution: A solution with osmotic pressure less than the cell fluid. Cells placed in hypotonic solution absorb water by osmosis and may swell or burst (haemolysis in red blood cells; turgidity in plants).

 

6. Abnormal Molar Mass and Van't Hoff Factor

The colligative property calculations we have done so far assume that solute particles do not associate (combine) or dissociate (break apart) when dissolved. However, many solutes behave abnormally in solution: electrolytes dissociate into ions (increasing the number of particles), and some organic molecules associate to form dimers or oligomers (decreasing the number of particles).

When a solute dissociates or associates, the experimentally observed (actual) colligative property is different from the theoretically calculated value. This discrepancy is quantified using the Van't Hoff Factor (i), introduced by Jacobus Henricus van't Hoff in 1886.

Figure 6: Van't Hoff Factor i — Dissociation (i > 1, e.g. NaCl), Normal behaviour (i = 1, e.g. glucose), Association (i < 1, e.g. acetic acid in benzene).

Van't Hoff Factor (i)

i  =  Observed colligative property / Theoretical colligative property

 

Alternative Definition

i  =  Total particles after dissociation or association / Original formula units

 

Modified Raoult's (RLVP)

(P* − P) / P*  =  i × x₂

 

Modified Boiling Point Elevation

DeltaT_b  =  i × K_b × m

 

Modified Freezing Point Depression

DeltaT_f  =  i × K_f × m

 

Modified Osmotic Pressure

Pi  =  i × CRT  =  i × (n/V) × RT

 

6.1 Degree of Dissociation (α)

For an electrolyte that dissociates into n ions (e.g., AB → A⁺ + B⁻ gives n = 2; AlCl₃ → Al³⁺ + 3Cl⁻ gives n = 4), the degree of dissociation α is the fraction of solute that has dissociated. The Van't Hoff factor is related to α by:

i from Degree of Dissociation

i  =  1 + (n − 1) × alpha     (n = number of ions per formula unit)

 

Degree of Dissociation from i

alpha  =  (i − 1) / (n − 1)

 

For strong electrolytes (e.g., NaCl, KCl, HCl) that dissociate completely, α = 1 and i = n (e.g., i = 2 for NaCl, i = 3 for CaCl₂, i = 4 for AlCl₃). For weak electrolytes (e.g., CH₃COOH, NH₄OH), α is between 0 and 1, and i is between 1 and n.

6.2 Degree of Association (α)

Some solutes associate (combine) in solution, reducing the total number of particles. For example, acetic acid (CH₃COOH) forms dimers in benzene through hydrogen bonding. If n molecules associate into one cluster, the Van't Hoff factor is:

i from Degree of Association

i  =  1 − alpha(1 − 1/n)     (n = number of molecules associating)

 

Degree of Association from i

alpha  =  (1 − i) × n / (n − 1)

 

Solute	Solvent	Behaviour	n (ions/molecules)	i value	Example
Glucose, Urea	Water	Normal (no dissociation/association)	1	1	i = 1 always
NaCl	Water	Dissociation: NaCl → Na⁺ + Cl⁻	2	~1.87 (not exactly 2 due to ion pairing)	Complete dissociation
CaCl₂	Water	Dissociation: CaCl₂ → Ca²⁺ + 2Cl⁻	3	~2.47	Trivalent → i closer to 3
AlCl₃	Water	Dissociation: AlCl₃ → Al³⁺ + 3Cl⁻	4	~3.0	Strong electrolyte
K₂SO₄	Water	Dissociation: K₂SO₄ → 2K⁺ + SO₄²⁻	3	~2.5 (dilute)	Electrolyte
CH₃COOH	Benzene	Association: 2CH₃COOH → dimer	2 per dimer	0.5 (fully associated)	Dimer formation
CH₃COOH	Water	Partial dissociation (weak acid)	2 (Ka = 1.8×10⁻⁵)	~1.004 (dilute)	Weak electrolyte

 

 

7. Master Formula Table — Chemistry: Solutions

Formula / Property	Expression	Key Notes
Molarity	M = n / V(litres)	Changes with temperature
Molality	m = n / W_solvent(kg)	Temperature-independent — use for colligative props
Mole Fraction	x₂ = n₂/(n₁+n₂); x₁+x₂=1	Dimensionless; always sums to 1
Mass % (w/w)	w% = (w_solute/w_solution)×100	Based on mass; temp-independent
ppm	ppm = (w_solute/w_solution)×10⁶	For trace concentrations
Henry's Law	p = K_H × x	KH increases with T → gas less soluble at high T
Raoult's Law	p₁ = P₁* × x₁	For ideal solutions with volatile components
RLVP	(P*−P)/P* = x₂	Mole fraction of solute
Boiling Point Elevation	ΔTb = Kb × m	Water: Kb = 0.52 K·kg/mol
Freezing Point Depression	ΔTf = Kf × m	Water: Kf = 1.86 K·kg/mol
Osmotic Pressure	π = CRT = (n/V)RT	C = molarity; R = 0.0821 L·atm/mol·K
Molar Mass from ΔTf	M₂ = (Kf×w₂×1000)/(ΔTf×w₁)	w in grams; gives molar mass of solute
Molar Mass from π	M₂ = w₂RT/(π×V)	Best for high molar mass (polymers, proteins)
Van't Hoff Factor	i = observed CP / theoretical CP	i>1 (dissociation); i<1 (association)
i — Dissociation	i = 1+(n−1)α	n=ions per formula unit; α=degree of dissociation
i — Association	i = 1−α(1−1/n)	n=molecules that associate; α=degree of association
Modified ΔTb	ΔTb = i × Kb × m	For electrolytes and associating solutes
Modified ΔTf	ΔTf = i × Kf × m	Always multiply by i for electrolytes
Modified π	π = i × CRT	For electrolyte solutions
M↔m conversion	m = 1000M / (1000d−M×M₂)	d=density g/mL, M₂=molar mass of solute

 

 

8. Quick Revision — Key Points

Concentration & Solubility — Must Know

* Molarity (M) = moles/litre of solution — changes with T. Molality (m) = moles/kg of solvent — constant with T. * Mole fraction: x₁ + x₂ = 1 always. Used in Raoult's Law. * Henry's Law: p = KH × x. Higher KH → less soluble. Gas solubility decreases with rising temperature. * 'Like dissolves like' — polar solvents dissolve polar/ionic solutes; non-polar dissolve non-polar. * Solubility of gases increases with pressure (Henry's Law) and decreases with temperature. * Supersaturated solution contains more dissolved solute than the equilibrium solubility — unstable.

 

Raoult's Law & Vapour Pressure — Must Know

* Ideal solution obeys Raoult's Law: p_total = P₁*x₁ + P₂*x₂. ΔH_mix = 0, ΔV_mix = 0. * Positive deviation: A-B interactions weaker than A-A + B-B (e.g. ethanol + water). P_total > Raoult ideal. * Negative deviation: A-B interactions stronger (e.g. acetone + chloroform). P_total < Raoult ideal. * Relative Lowering of Vapour Pressure = mole fraction of solute: ΔP/P* = x₂. * Azeotropes: cannot be separated by fractional distillation. Min-boiling (positive deviation), Max-boiling (negative deviation).

 

Colligative Properties & Van't Hoff Factor — Must Know

* All four colligative properties depend ONLY on the NUMBER of solute particles, not their nature. * ΔTb = Kb×m; ΔTf = Kf×m; π = CRT; RLVP = x₂. All are proportional to molality (or molarity). * Water constants: Kb = 0.52 K·kg/mol, Kf = 1.86 K·kg/mol. Benzene: Kb = 2.53, Kf = 5.12. * Osmotic pressure is the most sensitive colligative property — best for high molar mass determination. * Van't Hoff factor i: Electrolytes (i > 1, dissociation). Association like CH3COOH in benzene (i < 1). * Modified formulas for electrolytes: ΔTb = i×Kb×m; ΔTf = i×Kf×m; π = i×CRT. * Degree of dissociation: α = (i−1)/(n−1). Degree of association: α = (1−i)×n/(n−1). * Isotonic solutions have same osmotic pressure. Blood plasma π ≈ 7.4 atm = 0.9% NaCl (normal saline).

 

Important Numerical Values

* R = 0.0821 L·atm/(mol·K) = 8.314 J/(mol·K). Use 0.0821 when π is in atm, V in litres. * Water: Kf = 1.86 K·kg/mol, Kb = 0.52 K·kg/mol, density = 1.0 g/mL at 25°C. * Benzene: Kf = 5.12 K·kg/mol, Kb = 2.53 K·kg/mol. * Camphor: Kf = 40.0 K·kg/mol — used in Beckmann method for solid solutes (high sensitivity). * NaCl fully dissociates → i ≈ 2. CaCl₂ → i ≈ 3. AlCl₃ → i ≈ 4 (in dilute solution). * Glucose (C₆H₁₂O₆), Urea (CO(NH₂)₂), Sucrose — non-electrolytes, i = 1 always.

 

— End of Chapter 2: Solutions (Chemistry) —