1. PHYSICAL CHEMISTRY

Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of the principles, practices, and concepts of physics.

ATOMIC STRUCTURE

Planck's Quantum Theory

Energy of one photon = \( hv = \frac{hc}{\lambda} \)

Photoelectric Effect

\[ hv = hv_0 + \frac{1}{2} m_e v^2 \]

Bohr's Model for Hydrogen-like Atoms

1. \( mvr = n \frac{h}{2\pi} \) (Quantization of angular momentum)

2. \( E_n = -\frac{E_1}{n^2} z^2 = -2.178 \times 10^{-18} \frac{z^2}{n^2} \, J/atom = -13.6 \frac{z^2}{n^2} \, eV \)

3. \( r_n = \frac{n^2}{Z} \times \frac{h^2}{4\pi^2 e^2 m} = \frac{0.529 \times n^2}{Z} \, Å \)

4. \( v = \frac{2\pi ze^2}{nh} = \frac{2.18 \times 10^6 \times z}{n} \, m/s \)

De-Broglie Wavelength

\[ \lambda = \frac{h}{mc} = \frac{h}{p} \text{ (for photon)} \]

Wavelength of Emitted Photon

\[ \frac{1}{\lambda} = \overline{v} = RZ^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Heisenberg's Uncertainty Principle

\[ \Delta x \cdot \Delta p > \frac{h}{4\pi} \quad \text{or} \quad m \Delta x \cdot \Delta v \geq \frac{h}{4\pi} \]

Quantum Numbers

Principal quantum number (n) = 1, 2, 3, 4 .... to ∞
Orbital angular momentum of electron in any orbit = \( \frac{nh}{2\pi} \)
Azimuthal quantum number (ℓ) = 0, 1, .... to (n - 1)
Number of orbitals in a subshell = \( 2\ell + 1 \)
Maximum number of electrons in particular subshell = \( 2 \times (2\ell + 1) \)
Orbital angular momentum L = \( \frac{h}{2\pi} \sqrt{\ell(\ell+1)} = \hbar \sqrt{\ell(\ell+1)} \)

2. STOICHIOMETRY

Relative Atomic Mass (R.A.M)

\[ \text{R.A.M} = \frac{\text{Mass of one atom of an element}}{\frac{1}{12} \times \text{mass of one carbon atom}} \]

Density

Specific gravity = \( \frac{\text{density of the substance}}{\text{density of water at 4°C}} \)

For gases:

Absolute density (mass/volume) = \( \frac{\text{Molar mass of the gas}}{\text{Molar volume of the gas}} \)

\[ \Rightarrow \rho = \frac{\text{PM}}{\text{RT}} \]

Mole-Mole Analysis

Mass \( \div \) At. wt. / Mol. Wt. \( \rightarrow \) Mole

Concentration Terms

Molarity (M):

\[ \text{Molarity (M)} = \frac{w \times 1000}{(\text{Mol. wt of solute}) \times V_{\text{in ml}}} \]

Molality (m):

\[ \text{Molality} = \frac{\text{number of moles of solute}}{\text{mass of solvent in gram}} \times 1000 = 1000 \, w_1 / M_1 w_2 \]

Mole fraction (x):

\[ \text{Mole fraction of solution } (x_1) = \frac{n}{n + N} \] \[ \text{Mole fraction of solvent } (x_2) = \frac{N}{n + N} \] \[ x_1 + x_2 = 1 \]

Percentage Calculations

(i) % w/w = \( \frac{\text{mass of solute in gm}}{\text{mass of solution in gm}} \times 100 \)

(ii) % w/v = \( \frac{\text{mass of solute in gm}}{\text{Volume of solution in ml}} \times 100 \)

(iii) % v/v = \( \frac{\text{Volume of solute in ml}}{\text{Volume of solution}} \times 100 \)

3. GASEOUS STATE

Temperature Scale

\[ \frac{C - O}{100 - O} = \frac{K - 273}{373 - 273} = \frac{F - 32}{212 - 32} = \frac{R - R(O)}{R(100) - R(O)} \]

where R = Temp. on unknown scale.

Gas Laws

Boyle's law: At constant temperature, \( V \alpha \frac{1}{P} \)

\[ P_1 V_1 = P_2 V_2 \]

Charles law: At constant pressure, \( V \alpha T \)

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Gay-Lussac's law: At constant volume, \( P \alpha T \)

\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \rightarrow \text{temp on absolute scale} \]

Ideal Gas Equation

\[ PV = nRT \] \[ PV = \frac{w}{m} RT \text{ or } P = \frac{d}{m} RT \text{ or } Pm = dRT \]

Dalton's Law of Partial Pressure

\[ P_1 = \frac{n_1 RT}{v}, \quad P_2 = \frac{n_2 RT}{v}, \quad P_3 = \frac{n_3 RT}{v} \text{ and so on.} \]

Total pressure = \( P_1 + P_2 + P_3 + \) ......

Partial pressure = mole fraction × Total pressure.

Graham's Law

Rate of diffusion \( r \propto \frac{1}{\sqrt{d}} \); \( d = \text{density of gas} \)

\[ \frac{r_1}{r_2} = \frac{\sqrt{d_2}}{\sqrt{d_1}} = \frac{\sqrt{M_2}}{\sqrt{M_1}} = \sqrt{\frac{V \cdot D_2}{V \cdot D_1}} \]

Thermodynamics

Thermodynamic Processes

Isothermal process: T = constant, dT = 0, ΔT = 0
Isochoric process: V = constant, dV = 0, ΔV = 0
Isobaric process: P = constant, dP = 0, ΔP = 0
Adiabatic process: q = 0 (no heat exchange with surroundings)

IUPAC Sign Convention

Work done on the system = Positive
Work done by the system = Negative

First Law of Thermodynamics

ΔU = (U₂ - U₁) = q + w

Law of Equipartition of Energy

U = (f/2)nRT (only for ideal gas)
ΔE = (f/2)nR(ΔT)
where f = degrees of freedom (3 for monoatomic, 5 for diatomic/linear polyatomic, 6 for non-linear polyatomic)

Heat Capacity

Total heat capacity: C_T = Δq/ΔT = dq/dT (J/°C)
Molar heat capacity: C = Δq/(nΔT) = dq/(ndT) (J mole^-1 K^-1)
C_p = γR/(γ - 1), C_v = R/(γ - 1)
Specific heat capacity: S = Δq/(mΔT) = dq/(mdT) (J gm^-1 K^-1)

Work Done (w)

Isothermal Reversible expansion/compression: W = -nRT ln(V_f/V_i)
Reversible isobaric process: W = P(V_f - V_i)
Adiabatic reversible expansion: T₂V₂^γ-1 = T₁V₁^γ-1
Reversible Work: W = (P₂V₂ - P₁V₁)/(γ - 1) = nR(T₂ - T₁)/(γ - 1)

Application of First Law

ΔU = ΔQ + ΔW ⇒ ΔW = -PΔV ⇒ ΔU = ΔQ - PΔV
At constant volume: du = (dq)_v, du = nC_vdT, C_v = (1/n)(du/dT) = (f/2)R
Enthalpy: H = U + PV ⇒ C_p - C_v = R (only for ideal gas)

Second Law of Thermodynamics

ΔS_universe = ΔS_system + ΔS_surrounding > 0 (for spontaneous process)

Entropy (S)

ΔS_system = ∫_A^B (dq_rev/T)
For ideal gas: ΔS_system = nC_vln(T₂/T₁) + nRln(V₂/V₁)

Third Law of Thermodynamics

The entropy of perfect crystals of all pure elements & compounds is zero at absolute zero temperature.

Gibbs Free Energy (G)

G_system = H_system - TS_system
Criteria of spontaneity:
- ΔG_system < 0 ⇒ spontaneous
- ΔG_system > 0 ⇒ non-spontaneous
- ΔG_system = 0 ⇒ equilibrium

Standard Free Energy Change (ΔG°)

1. ΔG° = -2.303 RT log₁₀ K
2. At equilibrium ΔG = 0
3. -ΔG = W_net = 2.303 nRT log₁₀ (V₂/V₁)
4. ΔG_f° for elemental state = 0
5. ΔG_f° = G°_products - G°_reactants

Thermochemistry

ΔH° = H°_m,2 - H°_m,1 = heat added at constant pressure = C_pΔT
ΔH_reaction = H_products - H_reactants
ΔH°_reaction = H°_products - H°_reactants
Positive ΔH = endothermic, Negative ΔH = exothermic

Temperature Dependence of ΔH (Kirchoff's Equation)

For constant pressure: ΔH₂° = ΔH₁° + ΔC_p(T₂ - T₁)
For constant volume: ΔE₂° = ΔE₁° + ∫ΔC_vdT

Enthalpy of Reaction from Enthalpies of Formation

ΔH_f° = Σv_BΔH_f°_products - Σv_BΔH_f°_reactants
v_B = stoichiometric coefficient

Enthalpy from Bond Enthalpies

ΔH = (Enthalpy to break reactants into gaseous atoms) - (Enthalpy released to form products from gaseous atoms)

Resonance Energy

ΔH_f°_resonance = ΔH_f°_experimental - ΔH_f°_calculated

Chemical Equilibrium

At Equilibrium

Rate of forward reaction = rate of backward reaction
Concentration of reactant and product becomes constant
ΔG = 0
Q = K_eq

Equilibrium Constant (K)

K = K_f/K_b = rate constant of forward reaction / rate constant of backward reaction

Types of Equilibrium Constants

K_c = [C]^c[D]^d/[A]^a[B]^b (concentration)
K_p = (P_C)^c(P_D)^d/(P_A)^a(P_B)^b (partial pressure)
K_x = x_C^cx_D^d/x_A^ax_B^b (mole fraction)

Relations Between Equilibrium Constants

K_p = K_c·(RT)^Δn
K_p = K_x(P)^Δn
log(K₂/K₁) = (ΔH/2.303R)[(1/T₁) - (1/T₂)]
ΔG° = -2.303 RT log K

Reaction Quotient (Q)

Q = [C]^c[D]^d/[A]^a[B]^b (same form as K but at any point in reaction)

Degree of Dissociation (α)

α = moles dissociated / initial moles taken = fraction of moles dissociated out of 1 mole
% dissociation = α × 100

Observed Molecular Weight and Vapour Density

Observed molecular weight = molecular weight of equilibrium mixture / total no. of moles
α = (D - d)/[(n-1) × d] = (M_T - M_o)/[(n-1)M_o]

Le Chatelier's Principle

If a system at equilibrium is disturbed, the system will react to minimize the effect of the disturbance.

Effect of Concentration

Increased reactant concentration shifts equilibrium forward
Increased product concentration shifts equilibrium backward

Effect of Volume

Increased volume (decreased pressure) shifts equilibrium toward more moles of gas
Decreased volume (increased pressure) shifts equilibrium toward fewer moles of gas
No effect if Δn = 0

Effect of Pressure

Increased pressure shifts equilibrium toward fewer moles of gas.

Effect of Inert Gas Addition

Constant pressure: Inert gas increases volume, shifting equilibrium toward more moles of gas
Constant volume: No effect

Effect of Temperature

Endothermic (ΔH > 0): K increases with temperature, shifts forward
Exothermic (ΔH < 0): K decreases with temperature, shifts backward

Vapour Pressure of Liquid

Relative Humidity = (Partial pressure of H₂O vapours) / (Vapour pressure of H₂O at that temp.)

Thermodynamics of Equilibrium

ΔG = ΔG° + 2.303 RT log₁₀Q
Van't Hoff equation: log(K₁/K₂) = (ΔH°/2.303R)((1/T₂) - (1/T₁))

Ionic Equilibrium

Ostwald Dilution Law

For weak acid: K_a = [H⁺][A^-]/[HA] = Cα²/(1-α) ≈ Cα² (if α << 1)
α = √(K_a/C) = √(K_a × V)
For weak base: α = √(K_b/C)

Acidity and pH Scale

pH = -log a_H⁺ ≈ -log[H⁺]
pOH = -log[OH^-]
pK_a = -log K_a
pK_b = -log K_b
K_w = [H⁺][OH^-] = 10^-14 at 25°C
pH + pOH = 14 at 25°C

Properties of Water

In pure water [H⁺] = [OH^-] ⇒ neutral
Molarity of water = 55.56 M
K_w = [H⁺][OH^-] = 10^-14 at 25°C
Degree of dissociation of water: α = 10^-7/55.55 ≈ 1.8 × 10^-7%
Absolute dissociation constant: K_a = K_b = 1.8 × 10^-16, pK_a = pK_b = 15.74

pH Calculations

(a) Strong Acid Solution

Concentration > 10^-6 M: Neglect H⁺ from water
Concentration < 10^-6 M: Must consider H⁺ from water

(b) Strong Base Solution

Calculate [OH^- first, then [H⁺] = K_w/[OH^-]

(c) Mixture of Two Strong Acids

[H⁺] = (N₁V₁ + N₂V₂)/(V₁ + V₂)

(d) Mixture of Two Strong Bases

[OH^-] = (N₁V₁ + N₂V₂)/(V₁ + V₂)

(e) Mixture of Strong Acid and Strong Base

If N₁V₁ > N₂V₂: [H⁺] = (N₁V₁ - N₂V₂)/(V₁ + V₂)
If N₂V₂ > N₁V₁: [OH^-] = (N₂V₂ - N₁V₁)/(V₁ + V₂)

(f) Weak Acid (Monoprotic) Solution

K_a = Cα²/(1-α) ≈ Cα² (if α < 0.1 or 10%)
α = √(K_a/C)

Relative Strength of Two Acids

[H⁺]_acid1/[H⁺]_acid2 = √(K_a1C₁/K_a2C₂)

Salt Hydrolysis

Salt Type	Hydrolysis Type	K_h	h	pH
Weak acid & strong base	Anionic	K_w/K_a	√(K_w/K_aC)	7 + ½ pK_a + ½ log C
Strong acid & weak base	Cationic	K_w/K_b	√(K_w/K_bC)	7 - ½ pK_b - ½ log C
Weak acid & weak base	Both	K_w/K_aK_b	√(K_w/K_aK_b)	7 + ½ pK_a - ½ pK_b
Strong acid & strong base	No hydrolysis	-	-	7

Buffer Solutions

Acidic Buffer (e.g., CH₃COOH + CH₃COONa):
pH = pK_a + log([Salt]/[Acid]) (Henderson's equation)

Basic Buffer (e.g., NH₄OH + NH₄Cl):
pOH = pK_b + log([Salt]/[Base])

Solubility Product

For A_xB_y: K_sp = (xs)^x(ys)^y = x^x·y^y·s^x+y
Precipitation occurs if ionic product > K_sp
Saturated solution if ionic product = K_sp

Electrochemistry

Electrode Potential

Oxidation potential = -Reduction potential
E_cell = R.P. of cathode - R.P. of anode
E_cell = R.P. of cathode + O.P. of anode
E°_cell = SRP of cathode - SRP of anode

Gibbs Free Energy Change

ΔG = -nFE_cell
ΔG° = -nFE°_cell

Nernst Equation

ΔG = ΔG° + RT lnQ
ΔG° = -RT lnK_eq
E_cell = E°_cell - (RT/nF) lnQ
E_cell = E°_cell - (0.0591/n) logQ (at 298K)
At equilibrium: ΔG = 0, E_cell = 0
logK_eq = nE°_cell/0.0591

Concentration Cell

A cell with both electrodes made of same material ⇒ E°_cell = 0

(a) Electrolyte Concentration Cell

e.g., Zn(s) | Zn²⁺(c₁) || Zn²⁺(c₂) | Zn(s)
E = (0.0591/2) log(C₂/C₁)

(b) Electrode Concentration Cell

e.g., Pt, H₂(P₁ atm) | H⁺(1M) | H₂(P₂ atm), Pt
E = (0.0591/2) log(P₁/P₂)

Different Types of Electrodes

Metal-Metal ion Electrode M(s)|Mⁿ⁺:
Mⁿ⁺ + ne^- → M(s)
E = E° + (0.0591/n) log[Mⁿ⁺]
Gas-ion Electrode:
H⁺(aq) + e^- → ½ H₂ (P atm)
E = E° - 0.0591 log(P_H2^½/[H⁺])
Oxidation-reduction Electrode:
Fe³⁺ + e^- → Fe²⁺
E = E° - 0.0591 log([Fe²⁺]/[Fe³⁺])
Metal-Metal insoluble salt Electrode:
AgCl(s) + e^- → Ag(s) + Cl^-
E = E° - 0.0591 log[Cl^-]

Electrolysis

Order of Deposition at Cathode:

K⁺, Ca²⁺, Na⁺, Mg²⁺, Al³⁺, Zn²⁺, Fe²⁺, H⁺, Cu²⁺, Ag⁺, Au³⁺

Order of Liberation at Anode:

SO₄^2-, NO₃^-, OH^-, Cl^-, Br^-, I^-

Faraday's Laws of Electrolysis

First Law:

w = zq = zit (z = electrochemical equivalent)

Second Law:

w/E = constant ⇒ w₁/E₁ = w₂/E₂ = ...
w/E = (i × t × current efficiency factor)/96500

Condition for Simultaneous Deposition

E°_Cu2+/Cu - (0.0591/2) log(1/[Cu²⁺]) = E°_Fe2+/Fe - (0.0591/2) log(1/[Fe²⁺])

Conductance

Conductance = 1/Resistance
Specific conductance (K) = 1/ρ (ρ = specific resistance)
Equivalent conductance: λ_E = (K × 1000)/Normality (ohm^-1 cm² eq^-1)
Molar conductance: λ_m = (K × 1000)/Molarity (ohm^-1 cm² mole^-1)

Kohlrausch's Law

For strong electrolyte: λ_M^c = λ_M^∞ - b√c
For weak electrolytes: λ_∞ = n₊λ₊^∞ + n_-λ_-^∞

Applications of Kohlrausch's Law

Calculation of λ_M⁰ of weak electrolytes
Calculate degree of dissociation: α = λ_m^c/λ_m⁰
Calculate solubility (S) of sparingly soluble salt & their K_sp:
λ_M^c = λ_M^∞ = K × 1000/solubility
K_sp = S²

Transport Number

t_c = μ_c/(μ_c + μ_a) (cation)
t_a = μ_a/(μ_a + μ_c) (anion)

Solution & Colligative Properties

Osmotic Pressure (π)

π = ρgh (ρ = density of solution, h = equilibrium height)
Van't Hoff Formula: π = CRT = (n/V)RT (similar to ideal gas equation)
C = total concentration of all particles = C₁ + C₂ + C₃ + ...
For mixed solutions: π = [(C₁V₁ + C₂V₂)/(V₁ + V₂)]RT

Types of Solutions

Isotonic: Two solutions with same osmotic pressure (π₁ = π₂)
Hypertonic: π₁ > π₂ (solution 1 is hypertonic relative to solution 2)
Hypotonic: π₂ < π₁ (solution 2 is hypotonic relative to solution 1)

Abnormal Colligative Properties

Van't Hoff factor (i) = observed value / theoretical value
i = observed no. of particles / theoretical no. of particles
i = theoretical molar mass / observed molar mass
For dissociation: i > 1
For association: i < 1
π = iCRT

Relation Between i and Degree of Dissociation/Association

For dissociation: i = 1 + (n - 1)α (n = x + y)
For association: i = 1 + (1/n - 1)β

Relative Lowering of Vapour Pressure (RLVP)

Lowering in VP = P - Pₛ = ΔP
RLVP = ΔP/P = mole fraction of solute = n/(n + N)
(P - Pₛ)/Pₛ = (molality) × (M/1000)
For abnormal cases: (P - Pₛ)/Pₛ = i × (molality) × (M/1000)

Raoult's Law

For non-volatile solutes:
p₁ = p₁°X₁ (X₁ = mole fraction of solvent)
(p₁° - p₁)/p₁° = X₂

Elevation in Boiling Point

ΔTₐ = i × Kₐ × m
Kₐ = RTₐ²/(1000 × Lᵥₐₚ) or Kₐ = RTₐ²M/(1000 × ΔHᵥₐₚ)

Depression in Freezing Point

ΔTₐ = i × Kₐ × m
Kₐ = RTₐ²/(1000 × Lᶠᵤₛᵢₒₙ) or Kₐ = RTₐ²M/(1000 × ΔHᶠᵤₛᵢₒₙ)

Raoult's Law for Binary Mixture of Volatile Liquids

Pₐ = XₐPₐ°; Pₐ = XₐPₐ°
If Pₐ° > Pₐ°, A is more volatile than B (B.P. of A < B.P. of B)
Total pressure: Pₜ = Pₐ + Pₐ = XₐPₐ° + XₐPₐ°
Pₐ = XₐPₐ° = Xₐ'Pₜ (Xₐ' = mole fraction in vapor phase)
1/Pₜ = Xₐ'/Pₐ° + Xₐ'/Pₐ°

Ideal Solutions

Follow Raoult's law at all temperatures:

ΔHₘᵢₓ = 0
ΔVₘᵢₓ = 0
ΔSₘᵢₓ = +ve
ΔGₘᵢₓ = -ve

Examples: Benzene + Toluene, Hexane + Heptane, C₂H₅Br + C₂H₅I

Non-Ideal Solutions

Positive Deviation:

Pₜ,ₑₓₚ > (XₐPₐ° + XₐPₐ°)
A---A and B---B interactions > A---B interactions
ΔHₘᵢₓ = +ve (energy absorbed)
ΔVₘᵢₓ = +ve
Examples: H₂O + CH₃OH, H₂O + C₂H₅OH, C₂H₅OH + hexane

Negative Deviation:

Pₜ,ₑₓₚ < XₐPₐ° + XₐPₐ°
A---A and B---B interactions < A---B interactions
ΔHₘᵢₓ = -ve
ΔVₘᵢₓ = -ve
Examples: H₂O + HCOOH, H₂O + CH₃COOH, CHCl₃ + CH₃OCH₃

Immiscible Liquids

Pₜₒₜₐₗ = Pₐ° + Pₐ°
Pₐ°/Pₐ° = nₐ/nₐ = (WₐMₐ)/(MₐWₐ)
B.P. of solution is less than individual B.P.'s of both liquids

Henry's Law

Mass of gas dissolved per unit volume ∝ pressure of gas
m = kp (m = weight of gas/volume of liquid)

Solid State

Crystal Systems

Crystal System	Unit Cell Dimensions	Bravais Lattices	Example
Cubic	a = b = c; α = β = γ = 90°	SC, BCC, FCC	NaCl
Orthorhombic	a ≠ b ≠ c; α = β = γ = 90°	SC, BCC, end centred & FCC	Sr
Tetragonal	a = b ≠ c; α = β = γ = 90°	SC, BCC	Sn, ZnO₂
Monoclinic	a ≠ b ≠ c; α = γ = 90° ≠ β	SC, end centred	S
Rhombohedral	a = b = c; α = β = γ ≠ 90°	SC	Quartz
Triclinic	a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90°	SC	H₃BO₃
Hexagonal	a = b ≠ c; α = β = 90°; γ = 120°	SC	Graphite

Analysis of Cubic System

Property	SC	BCC	FCC
Atomic radius (r)	a/2	(√3/4)a	a/(2√2)
Atoms per unit cell (Z)	1	2	4
Coordination number	6	8	12
Packing efficiency	52%	68%	74%
Number of voids	-	-	4 octahedral, 8 tetrahedral

Neighborhood of Particles

(I) Simple Cubic (SC) Structure:

Type of neighbor	Distance	No. of neighbors
Nearest	a	6
Next¹	a/√2	12
Next²	a/√3	8

(II) Body Centered Cubic (BCC) Structure:

Type of neighbor	Distance	No. of neighbors
Nearest	a√3/2	8
Next¹	a	6
Next²	a√2	12

(III) Face Centered Cubic (FCC) Structure:

Type of neighbor	Distance	No. of neighbors
Nearest	a/√2	12
Next¹	a	6
Next²	a√(3/2)	24

Density of Lattice Matter

d = (Z × M)/(Nₐ × a³)
Nₐ = Avogadro's number, M = atomic/molecular mass

Ionic Crystals

C.N.	Limiting radius ratio (r₊/r₋)	Geometry
3	0.155 - 0.225	Triangular
4	0.225 - 0.414	Tetrahedral
6	0.414 - 0.732	Octahedral
8	0.732 - 0.999	Cubic

Examples of Ionic Crystals

Rock Salt (NaCl): C.N. (6:6)
CsCl: C.N. (8:8), Edge length aₛₐ = (2/√3)(r₊ + r₋)
Zinc Blende (ZnS): C.N. (4:4), aₜₐₐ = (4/√3)(r₂ₙ²⁺ + rₛ²⁻)
Fluorite (CaF₂): C.N. (8:4), aₜₐₐ = (4/√3)(rₐₐ²⁺ + rₐ⁻)

Crystal Defects (Imperfections)

Stoichiometric	Non-Stoichiometric
Schottky (ion pairs missing) Frenkel (dislocation of ions)	Metal excess Electron in place of anion Extra cation in interstitial Non-metal excess Vacant site in place of cation

Chemical Kinetics & Radioactivity

Rate of Chemical Reaction

Rate = Δc/Δt = mol lit⁻¹ time⁻¹ = mol dm⁻³ time⁻¹
Average rate = (C₁ - C₂)/(t₂ - t₁)
Instantaneous rate = -d[R]/dt = d[P]/dt

Rate Law

Rate = K[conc.]^order
For m₁A + m₂B → products: R ∝ [A]^p[B]^q
p = order wrt A, q = order wrt B, (p + q) = overall order
K = rate constant (units: (conc)^1-order time⁻¹)

Integrated Rate Laws

(a) Zero Order Reactions:

Rate = k[conc.]⁰ = constant
Cₜ = C₀ - kt
t₁/₂ = C₀/(2k) (depends on initial concentration)

(b) First Order Reactions:

t = (2.303/k) log(a/(a - x)) or k = (2.303/t) log(C₀/Cₜ)
t₁/₂ = 0.693/k (independent of initial concentration)
tₐᵥ₉ = 1/k = 1.44 t₁/₂

(c) Second Order Reactions:

For A + A → products: 1/(a - x) - 1/a = kt

Methods to Determine Reaction Order

Initial rate method: Compare rates at different initial concentrations
Integrated rate law: Trial and error with different order equations
Half-life method: For nᵗʰ order: t₁/₂ ∝ 1/[R₀]ⁿ⁻¹
Ostwald Isolation Method: Isolate one reactant at a time

Monitoring Reaction Progress

Gaseous reactions: Measure total pressure or volume changes
Titration method: k = (2.303/t) log(V₀/Vₜ)
Optical rotation: k = (2.303/t) log[(θ₀ - θ∞)/(θₜ - θ∞)]

Effect of Temperature on Reaction Rate

Temperature coefficient = Kₜ₊₁₀/Kₜ ≈ 2 to 3 (for most reactions)

Arrhenius Theory

k = Ae⁻ᴱᵃ/ᴿᵀ
ln k = ln A - Eₐ/(RT)
log(k₂/k₁) = (Eₐ/2.303R)[(1/T₁) - (1/T₂)]
Eₐ = activation energy, A = frequency factor

Energy Profile

Eₚ > Eᵣ ⇒ endothermic
Eₚ < Eᵣ ⇒ exothermic
ΔH = (Eₚ - Eᵣ) = Eₐₐ - Eₐₐ
Eₜₕᵣₑₛₕₒₗₚ = Eₐₐ + Eᵣ = Eₐ + Eₚ

INORGANIC CHEMISTRY

Inorganic chemistry is the study of the synthesis, reactions, structures and properties of compounds of the elements. This field covers all chemical compounds except the myriad organic compounds (carbon-based compounds, usually containing C-H bonds).

PERIODIC TABLE & PERIODICITY

Development of Modern Periodic Table

(a) Dobereiner's Triads: He arranged similar elements in groups of three elements called triads.

(b) Newland's Law of Octave: He was the first to correlate chemical properties of elements with their atomic masses.

(c) Lother Meyer's Classification: He plotted atomic masses against atomic volumes and found periodic patterns.

Mendeleev's Periodic Table

Mendeleev's Periodic Law: The physical and chemical properties of elements are periodic functions of their atomic masses.

Periods	Number of Elements	Called as
1st (n=1)	2	Very short period
2nd (n=2)	8	Short period
3rd (n=3)	8	Short period
4th (n=4)	18	Long period
5th (n=5)	18	Long period
6th (n=6)	32	Very long period
7th (n=7)	19	Incomplete period

Modern Periodic Table (Moseley's Periodic Table)

Modern Periodic Law: If elements are arranged in order of increasing atomic number, after regular intervals, elements with similar properties are repeated.

Periodicity: The repetition of properties of elements after regular intervals when arranged by increasing atomic number.

Classification of Elements

(a) s-Block Elements: Group 1 & 2, general configuration [inert gas] ns^1-2

(b) p-Block Elements: Group 13-18, general configuration [inert gas] ns² np^1-6

(c) d-Block Elements: Group 3-12, general configuration [inert gas] (n-1)d^1-10 ns^1-2

(d) f-Block Elements: General configuration (n-2)f^1-14 (n-1)d^0-1 ns²

CHEMICAL BONDING

Types of Chemical Bonds

Ionic Bond: Formed by complete transfer of electrons from one atom to another.

Covalent Bond: Formed by sharing of electron pairs between atoms.

Coordinate Bond: Special type of covalent bond where both electrons come from one atom.

Valence Bond Theory

Explains bond formation through overlapping of atomic orbitals.

Types of Overlapping:

Sigma (σ) bond: End-to-end overlapping
Pi (π) bond: Side-by-side overlapping

VSEPR Theory

Valence Shell Electron Pair Repulsion theory predicts molecular geometry based on electron pair repulsion.

Hybridization

Steric Number	Hybridization	Geometry
2	sp	Linear
3	sp²	Trigonal planar
4	sp³	Tetrahedral
5	sp³d	Trigonal bipyramidal
6	sp³d²	Octahedral

COORDINATION COMPOUNDS

Basic Concepts

Central Atom/Ion: Metal atom/ion to which ligands are attached.

Ligands: Ions or molecules bound to the central atom.

Coordination Number: Number of ligand donor atoms attached to the metal.

Nomenclature

Rules for naming coordination compounds:

Cation named before anion
Ligands named alphabetically
Oxidation state of metal indicated by Roman numeral
Anionic ligands end with -o, neutral ligands use their names

Isomerism in Coordination Compounds

Structural Isomerism: Different bonding patterns (ionization, hydrate, linkage, coordination).

Stereoisomerism: Same bonds, different spatial arrangements (geometrical, optical).

METALLURGY

Basic Concepts

Ore: Mineral from which metal can be economically extracted.

Gangue: Unwanted material in ore.

Processes in Metallurgy

Crushing and Grinding: Ore is reduced to powder.
Concentration: Removal of gangue (gravity separation, froth floatation, etc.)
Extraction:
- Calcination (heating in absence of air)
- Roasting (heating in presence of air)
- Reduction (using carbon, CO, or other metals)
Refining: Purification of crude metal (electrolytic refining, zone refining, etc.)

Extraction of Important Metals

Aluminium: Purification by Bayer's process, electrolytic reduction by Hall-Heroult process.

Iron: Blast furnace process using haematite ore.

Copper: From copper pyrite through roasting and self-reduction.

s-BLOCK ELEMENTS & THEIR COMPOUNDS

Group 1: Alkali Metals

Includes: Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Rb), Cesium (Cs), Francium (Fr)

Physical Properties

Silvery white, soft and light metals
Low melting and boiling points
Impart characteristic colors to flame

Flame Test Colors

Li
Crimson red

Na
Golden yellow

K
Violet/Lilac

Rb
Red violet

Cs
Blue

Chemical Properties

Highly reactive due to large size and low ionization enthalpy
React vigorously with oxygen forming oxides (Li forms monoxide, Na forms peroxide, others form superoxides)
Strong reducing agents (Li most powerful, Na least powerful)

Group 2: Alkaline Earth Metals

Includes: Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), Radium (Ra)

Physical Properties

Silvery white, lustrous, relatively soft but harder than alkali metals
Higher melting and boiling points than alkali metals
Some impart characteristic colors to flame

Flame Test Colors

Ca
Brick red

Sr
Crimson

Ba
Apple Green

p-BLOCK ELEMENTS & THEIR COMPOUNDS

Group 13: Boron Family

Includes: Boron (B), Aluminum (Al), Gallium (Ga), Indium (In), Thallium (Tl)

Oxidation state: +3 (general), +1 (Tl more stable in +1 due to inert pair effect)

Boron Compounds

Borax (Na₂B₄O₇·10H₂O): Used in borax bead test
Boric Acid (H₃BO₃): Weak monobasic acid
Diborane (B₂H₆): Electron deficient compound

Group 14: Carbon Family

Includes: Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), Lead (Pb)

Oxidation states: +4 (common), +2 (increases down the group)

Allotropes of Carbon

Diamond: sp³ hybridized, 3D network
Graphite: sp² hybridized, layered structure
Fullerenes: C₆₀ (Buckminsterfullerene) with soccer ball shape

Group 15: Nitrogen Family

Includes: Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), Bismuth (Bi)

Oxidation states: -3, +3, +5 (+5 stability decreases down the group)

Nitrogen Compounds

Ammonia (NH₃): Sp³ hybridized, pyramidal
Nitric Acid (HNO₃): Strong oxidizing agent
Oxides of Nitrogen: N₂O, NO, N₂O₃, NO₂, N₂O₄, N₂O₅

Group 16: Oxygen Family

Includes: Oxygen (O), Sulfur (S), Selenium (Se), Tellurium (Te), Polonium (Po)

Oxidation states: -2, +2, +4, +6

Sulfur Compounds

Sulfuric Acid (H₂SO₄): King of chemicals
Oxoacids of Sulfur: Sulfurous (H₂SO₃), sulfuric (H₂SO₄), peroxo acids

Group 17: Halogens

Includes: Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), Astatine (At)

Oxidation states: -1 (common), +1, +3, +5, +7 (except F)

Important Compounds

Bleaching Powder (CaOCl₂): Used as disinfectant and bleaching agent
Interhalogen Compounds: ClF, BrF₃, IF₇ etc.

Group 18: Noble Gases

Includes: Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), Radon (Rn)

Compounds: Mostly inert but form compounds with F and O (XeF₂, XeF₄, XeF₆, XeO₃)

d-BLOCK ELEMENTS & THEIR COMPOUNDS

General Characteristics

Electronic configuration: (n-1)d^1-10ns^0-2
High melting and boiling points (except Zn, Cd, Hg)
Variable oxidation states
Formation of colored ions
Paramagnetic behavior (due to unpaired electrons)
Catalytic properties
Formation of interstitial compounds
Formation of complexes

Important Compounds

Potassium Permanganate (KMnO₄)

Strong oxidizing agent
Purple colored
Used in titrations (oxidizes Fe²⁺, oxalates, etc.)

Potassium Dichromate (K₂Cr₂O₇)

Orange colored
Oxidizing agent in acidic medium
Used in chrome tanning and dyeing

QUALITATIVE ANALYSIS

Preliminary Tests

Flame Test

Colour of Flame	Inference
Crimson Red / Carmine Red	Lithium
Golden yellow	Sodium
Violet/Lilac	Potassium
Brick red	Calcium
Apple Green/Yellowish Green	Barium
Green with a Blue centre	Copper

Borax Bead Test

Metal	Colour in Oxidizing Flame	Colour in Reducing Flame
Copper	Green (hot), Blue (cold)	Colorless (hot), Brown red (cold)
Iron	Brown yellow (hot), Pale yellow (cold)	Bottle green
Cobalt	Blue	Blue
Nickel	Violet	Grey

Anion Analysis

Carbonate (CO₃^2-)

Dilute H₂SO₄ test: Effervescence of CO₂
Lime water test: Turns milky

Sulfide (S^2-)

Dilute H₂SO₄ test: H₂S gas (rotten egg smell)
Lead acetate test: Black precipitate (PbS)

Cation Analysis

Group I (Pb²⁺, Hg₂²⁺, Ag⁺)

Precipitated as chlorides by dilute HCl
PbCl₂: Soluble in hot water
AgCl: Soluble in NH₄OH
Hg₂Cl₂: Turns black with NH₄OH

Group II (Cu²⁺, Cd²⁺, Bi³⁺, Hg²⁺, As³⁺, Sb³⁺, Sn^2+/4+)

Precipitated as sulfides by H₂S in acidic medium
CuS: Black
CdS: Yellow

Inorganic Chemistry: Elements & Qualitative Analysis

s-Block Elements & Their Compounds

Group 1: Alkali Metals

Li, Na, K, Rb, Cs, Fr

Physical Properties

Soft, silvery-white metals
Low melting points
Highly reactive
Good conductors of heat/electricity

Chemical Properties

React vigorously with water
Form strong bases (MOH)
Form ionic compounds
Strong reducing agents

Important Compounds

NaOH (caustic soda)
Na₂CO₃ (washing soda)
NaHCO₃ (baking soda)
KNO₃ (saltpeter)

Flame Test Colors

Li
Crimson red

Na
Golden yellow

K
Violet/Lilac

Rb
Red violet

Cs
Blue

Group 2: Alkaline Earth Metals

Be, Mg, Ca, Sr, Ba, Ra

Physical Properties

Harder than alkali metals
Higher melting points
Less reactive than Group 1
Form divalent cations

Chemical Properties

React with water (except Be)
Form oxides and hydroxides
Form ionic compounds
Good reducing agents

Important Compounds

CaO (quicklime)
Ca(OH)₂ (slaked lime)
CaCO₃ (limestone)
MgSO₄·7H₂O (Epsom salt)

Flame Test Colors

Ca
Brick red

Sr
Crimson

Ba
Apple Green

p-Block Elements & Their Compounds

Group 13: Boron Family

B, Al, Ga, In, Tl

Boron is metalloid, others are metals
+3 oxidation state common
Important compounds:
- B₂H₆ (diborane)
- Al₂O₃ (alumina)
- AlCl₃ (Lewis acid)

Group 14: Carbon Family

C, Si, Ge, Sn, Pb

Carbon shows catenation
+4 and +2 oxidation states
Important compounds:
- CO₂, CO (oxides of carbon)
- SiO₂ (silica)
- SnCl₂ (stannous chloride)

Group 15: Nitrogen Family

N, P, As, Sb, Bi

Nitrogen forms strong triple bond
-3 to +5 oxidation states
Important compounds:
- NH₃ (ammonia)
- HNO₃ (nitric acid)
- PCl₅ (phosphorus pentachloride)

Group 16: Oxygen Family

O, S, Se, Te, Po

Oxygen is diatomic (O₂)
-2 to +6 oxidation states
Important compounds:
- H₂SO₄ (sulfuric acid)
- SO₂ (sulfur dioxide)
- H₂O₂ (hydrogen peroxide)

Group 17: Halogens

F, Cl, Br, I, At

Highly reactive nonmetals
-1 oxidation state common
Important compounds:
- HCl (hydrochloric acid)
- NaClO (bleach)
- AgBr (photography)

Group 18: Noble Gases

He, Ne, Ar, Kr, Xe, Rn

Monoatomic gases
Very low reactivity
Important compounds:
- XeF₂, XeF₄, XeF₆
- XeO₃
- KrF₂

d-Block Elements & Their Compounds

General Characteristics

Electronic Configuration

(n-1)d^1-10ns^0-2

Physical Properties

High melting/boiling points
High density
Good conductors
Malleable and ductile

Chemical Properties

Variable oxidation states
Form colored compounds
Paramagnetic behavior
Catalytic activity

Important Compounds

Potassium Permanganate (KMnO₄)

Strong oxidizing agent
Purple crystals
Used in titrations

Potassium Dichromate (K₂Cr₂O₇)

Orange-red crystals
Oxidizing agent
Used in leather tanning

Ferrous Compounds

FeSO₄·7H₂O (green vitriol)
FeCl₃ (ferric chloride)
K₄[Fe(CN)₆] (potassium ferrocyanide)

Qualitative Analysis

Preliminary Tests

Flame Test

Color	Element
Crimson red	Lithium (Li)
Golden yellow	Sodium (Na)
Violet/lilac	Potassium (K)
Brick red	Calcium (Ca)
Apple green	Barium (Ba)

Borax Bead Test

Metal	Oxidizing Flame	Reducing Flame
Copper	Green (hot), Blue (cold)	Colorless (hot), Red (cold)
Iron	Yellow-brown	Green
Nickel	Violet	Grey

Anion Analysis

Carbonate (CO₃^2-)

Test: Add dilute acid → effervescence (CO₂)
Confirmation: Turns lime water milky

Sulfate (SO₄^2-)

Test: Add BaCl₂ → white ppt (BaSO₄)
Confirmation: Insoluble in acids

Halides (Cl^-, Br^-, I^-)

Test: Add AgNO₃ → ppt (AgCl white, AgBr pale yellow, AgI yellow)
Confirmation: Different solubility in NH₃

Cation Analysis

Group I (Pb²⁺, Ag⁺, Hg₂²⁺)

Precipitant: Dilute HCl
Precipitate: Chlorides (PbCl₂, AgCl, Hg₂Cl₂)

Group II (Cu²⁺, Cd²⁺, Bi³⁺, Hg²⁺)

Precipitant: H₂S in acidic medium
Precipitate: Sulfides (CuS black, CdS yellow)

Group III (Fe³⁺, Al³⁺, Cr³⁺)

Precipitant: NH₄OH + NH₄Cl
Precipitate: Hydroxides

ORGANIC CHEMISTRY

About Organic Chemistry

Organic chemistry is the study of carbon-containing compounds and their properties, structure, composition, reactions, and preparation. It encompasses a vast array of molecules including those essential to life (like proteins, DNA, and carbohydrates) as well as synthetic materials (like plastics and pharmaceuticals). The unique ability of carbon to form stable bonds with itself and other elements allows for the tremendous diversity of organic compounds.

Points to remember in Nomenclature

Examples of compounds containing different functional groups with common/trivial names:

No. of carbon atoms	Prefix	–CHO (Aldehyde)	–COOH(–ic acid)	–COCl.(–yl chloride)	–CONH₂ (Amide)
1	Form	HCHO Formaldehyde	HCOOH Formic acid	HCOCl Formyl chloride	HCONH₂ Formamide
2	Acet	CH₃CHO Acetaldehyde	CH₃COOH Acetic acid	CH₃COCl Acetyl chloride	CH₃CONH₂ Acetamide
3	Propion	CH₃CH₂CHO Propion aldehyde	CH₃CH₂COOH Propionic acid	CH₃CH₂COCl Propionyl chloride	CH₃CH₂CONH₂ Propionamide
4	Butyr	CH₃CH₂CH₂CHO n-Butyraldehyde	CH₃CH₂CH₂COOH n-Butyric acid	CH₃CH₂CH₂COCl n-Butyryl chloride	CH₃CH₂CH₂CONH₂ n-Butyramide
5	Valer	CH₃CH₂CH₂CH₂CHO n-Valeraldehyde	CH₃CH₂CH₂CH₂COOH n-Valeric acid	CH₃CH₂CH₂CH₂COCl n-Valeryl chloride	CH₃CH₂CH₂CH₂CONH₂ n-Valeramide
3C+1 Double bond	Acryl	CH₂=CH-CHO Acrylaidehyde	CH₂=CH–COOH Acrylic acid	CH₂=CH–COCl Acryl chloride	CH₂=CH–CONH₂ Acrylamide
4C + 1 Double bond (at 2^nd Carbon atom)	Croton	CH₃–CH=CH–CHO Crotonaldehyde	CH₃CH₂=CH–COOH Crotonic acid	CH₃CH₂=CH–COCl Crotonyl chloride	CH₃CH₂=CH–CONH₂ Crotonamide

Secondary suffix of some common functional groups (IUPAC)

A secondary suffix is added to the primary suffix to indicate the nature of the functional group present in the organic compounds. Secondary suffix of important functional groups are given below in their decreasing order of seniority.

Class	Name	Suffix	Prefix
R–COOH	Alkanoic Acid	–oic acid (carboxylic acid)	carboxy
R–SO₃H	Alkane sulfonic Acid	–sulphonic acid	sulpho
R–C–O–C–R ║ ║ O O	Alkanonic Anhydride	–oic anhydride (carboxylic anhydride)	---
R–COOR	Alkyl alkanoate	–oate (carboxylate)	alkoxy carbonyl or alkanoyl oxy halo carbonyl
R–C–X ║ O	Alkanoyl halide	–oyl halide (carbonyl halide)	---
R–C–NH₂ ║ O	Alkanamide	–amide (carboxamide)	carbamoyl
R–C≡N	Alkanenitrile	–nitrile (carbonitrile)	cyano
R–C–H ║ O	Alkanal	–al (carbaldehyde)	formyl / oxo
R–C–R ║ O	Alkanone	–one	oxo
R–OH	Alkanol	–ol	hydroxy
R–SH	Alkanethiol	–thiol	mercapto
R–NH₂	Alkanamine	–amine	amino

IUPAC system of nomenclature

The IUPAC name of any organic compound consists of maximum five parts in the following sequence:

Secondary prefix + Primary prefix + Word root + Primary suffix + Secondary suffix

The following examples illustrate the use of word root, primary suffix and secondary suffix in naming of organic compounds.

Organic compounds	Word root	Primary suffix	Secondary suffix	IUPAC name
CH₃CH₂OH	Eth	an(e)	ol	Ethanol
CH₃CH₂CH₂NH₂	Prop	an(e)	amine	Propanamine
CH₃CH₂CH₂COOH	But	an(e)	oic acid	Butanoic acid
CH₃CH₂CN	Prop	an(e)	nitrile	Propanenitrile
CH₂=CHCHO	Prop	en(e)	al	Propenal
HC≡CCOOH	Prop	yn(e)	oic acid	Propynoic acid

Points to remember in Structure Isomerism

Isomers	Characteristics	Conditions
(1) Chain Isomers	They have different size of main chain or side chain	They have same nature of locants
(2) Positional Isomers	They have different position of locants	They should have same size of main chain and side chain and same nature of locant
(3) Functional Isomers	Different nature of locant	Chain and positional isomerism is not considered
(4) Metamerism	Different nature of alkyl group along a polyvalent functional group	They should have same nature of functional groups chain & positional isomer is ignored
(5) Tautomerism	Different position of hydrogen atoms	The two functional isomers remains in dynamic equilibrium to each other

Points to remember in General Organic Chemistry

1. Inductive effect

The normal C–C bond has no polarity as two atoms of same electronegativity (EN) value are connected to each other. Hence the bond is nonpolar. Consider a carbon chain in 1-Chloro butane, here due to more EN of Cl atom C–Cl bond pair is slightly displaced towards Cl atom hence creating partial negative (δ-) charge over Cl atom and partial positive (δ+) charge over C₁ atom. Now since C₁ is slightly positive, it will also cause shifting of C₁-C₂ bond pair electrons towards itself causing C₂ to acquire small positive charge. Similarly C₃ acquires slightly positive charge creating an induction of charge in carbon chain. Such an effect is called inductive effect.

Diagram showing I effect:

δ+ ← δδ+ ← δδδ+ ← Cl

C₄ ← C₃ ← C₂ ← C₁

The arrow shows electron withdrawing nature of –Cl group. Thus inductive effect may be defined as a permanent displacement of σ bond pair electrons due to a dipole. (Polar bond)

Some important points are:

It can also be defined as polarisation of one bond caused by polarisation of adjacent bond.
It is also called transmission effect.
It causes permanent polarisation in molecule, hence it is a permanent effect.
The displacement of electrons takes place due to difference in electronegativity of the two atoms involved in the covalent bond.
The electrons never leave their original atomic orbital.
Its magnitude decreases with distance and it is almost negligible after 3rd carbon atom.
The inductive effect is always operative through σ bond, does not involve π bond electron.

Types of inductive effects:

(a) –I Effect: The group which withdraws electron cloud is known as –I group and its effect is called –I effect. Various groups are listed in their decreasing –I strength as follows:

–NR₃ > –SR₂ > –NH₃ > –NO₂ > –SO₂R > –CN > –CHO > –COOH > –F > –Cl > –Br > –I > –OR > –OH > –C≡CH > –NH₂ > –C₆H₅ > –CH=CH₂ > –H.

(b) +I effect: The group which release electron cloud is known as +I group and effect is +I effect.

–O⁻ > –COO⁻ > –C(CH₃)₃ > –CH(CH₃)₂ > –CH₂–CH₃ > –CH₃ > –D > –H

The hydrogen atom is reference for +I and –I series. The inductive effect of hydrogen is assumed to be zero.

2. Resonance

Resonance is the phenomenon in which two or more structures involving in identical position of atom, can be written for a particular species, all those possible structures are known as resonating structures or canonical structures. Resonating structures are only hypothetical but they all contribute to a real structure which is called resonance hybrid. The resonance hybrid is more stable than any resonating structure.

Example:

CH₂=CH–CH=CH₂ ↔ CH₂–CH=CH–CH₂ ↔ CH₂–CH–CH=CH₂

Resonance hybrid: CH₂–CH=CH–CH₂ (with partial bonds)

The most stable resonating structure contribute maximum to the resonance hybrid and less stable resonating structure contribute minimum to resonance hybrid.

Conjugation:

A given atom or group is said to be in conjugation with an unsaturated system if:

It is directly linked to one of the atoms of the multiple bond through a single bond.
It has π bond, positive charge, negative charge, odd electron or lone pair electron.

3. Mesomeric effect (or Resonance effect)

Mesomeric effect is defined as permanent effect of π electron shifting from multiple bond to atom or from multiple bond to single bond or from lone pair to single bond. This effect mainly operates in conjugated system of double bond. So that this effect is also known as conjugate effect.

Types of Mesomeric effects:

(a) Positive Mesomeric effect (+M effect): When the group donates electron to the conjugated system it shows +M effect.

Relative order of +M groups (usually followed):

–O⁻ > –NH₂ > –NHR > –NR₂ > –OH > –OR > –NHCOR > –OCOR > –Ph > –F > –Cl > –Br > –I > –NO

(b) Negative Mesomeric effect (–M effect): When the group withdraws electron from the conjugated system, it shows –M effect.

Relative order of –M groups (usually followed):

–NO₂ > –CHO > C=O > –C–O–C–R > –C–O–R > –COOH > –CONH₂ > –C–O⁻

4. Hyperconjugation

It is delocalisation of sigma electron with p-orbital. Also known as σ-π conjugation or no bond resonance. It may takes place in alkene, alkynes, carbocation, free radical, benzene nucleus.

Necessary Condition: Presence of at least one hydrogen at saturated carbon which is α with respect to alkene, alkynes, carbocation, free radical, benzene nucleus.

5. Aromatic character [The Huckel 4n + 2 rule]

The following rules are useful in predicting whether a particular compound is aromatic or non–aromatic. Aromatic compounds are cyclic and planar. Each atom in an aromatic ring is sp² hybridised. The cyclic π molecular orbital (formed by overlap of p-orbitals) must contain (4n + 2) π electrons, i.e., 2, 6, 10, 14 …….. π electrons. Where n = an integer 0, 1, 2, 3,……………….

Aromatic compounds have characteristic smell, have extra stability and burn with sooty flame.

Characteristics	Aromatic compounds (A)	Anti Aromatic compounds (B)	Non-Aromatic compounds (C)
1. Structure	Cyclic, planar all atoms of ring sp² hybridised	Cyclic, planar all atoms of ring sp² hybridised	Cyclic or acyclic planar or non planar sp or sp² or sp³
2. No. of π e⁻s in the ring	(4n+2)πe⁻ (Huckle's rule)	(4n)πe⁻	Any no. of πe⁻s
3. MOT	Unpaired e⁻s in B.M.O.	Some πe⁻s in non-bonding M.O.	B.M.O. / Non-bonding M.O.
4. Overlapping	Favourable over lapping of p orbital	Unfavourable over lapping of p orbital	Simple overlapping like alkenes
5. Resonance energy (R.E.)	Very high R.E. > 20-25 kcal/mol	Zero	4-8 kcal/mol like alkenes
6. Stability	Have extra stability due to close conjugation of π e⁻s	Unstable not-exist at room temperature	Normal stability like a conjugated system
7. Reaction	Electrophilic substitution Reaction	Dimerisation reaction to attain stability	Electrophilic addition reaction like alkenes

Stability of compounds: Aromatic > Non-Aromatic > Anti-Aromatic

Points to remember in Alkane

Wurtz reaction (Reagent: Na, ether)

1º & 2º alkyl halides give this reaction.

R–X + 2Na + ether → R–R + 2NaX

R–X + R'–X + 2Na + ether → R–R' + R–R + R'–R' + 2NaX

Note: This reaction is useful for preparing symmetrical alkanes from alkyl halides.

Organic Chemistry - Reaction Mechanisms

Points to remember in Alkene & Alkyne

Characteristic reaction of Alkene & Alkyne is Electrophilic addition reaction

Mechanism

Step 1: Attack of the electrophile on π bond forms a carbocation.

C=C + E⁺ → C–C⁺ | E

(+ on the more substituted carbon)

Step 2: Attack by a nucleophile gives the product of addition.

C–C⁺ + Nu: → C–C | | E Nu

Examples:

(a) Addition of water

C=C + H₂O → C–C | | OH H

(b) Addition of hydrogen halides (where HX = HCl, HBr, HI)

R–C≡C–R' + HX → R–C=C–R' (Markovnikov addition) | | H X

R–C=C–R' + HX → R–C–C–R' | | | H X H

Note: When electrophiles are: Cl⁺, Br⁺, I⁺, NO₂⁺ or Hg²⁺ then stereochemistry is important and major product is formed by anti addition.

Points to remember in Alkyl Halide

Nucleophilic substitution Reaction (S_N1, S_N2)

S_N1 reaction:

R–X + H₂O + AgNO₃ → R⁺ + AgX↓ → ROH (R may rearrange)

Alkyl halides are hydrolysed to alcohol very slowly by water, but rapidly by silver oxide suspended in boiling water.

S_N2 reaction:

Mechanism:

HO⁻ + R–X → [HO···R···X]⁻ → HO–R + X⁻

Example with stereochemistry:

HO⁻ + C–X → [HO···C···X]⁻ → HO–C + X⁻ | | | a a a b b b d d d

(Inversion of configuration occurs)

Points to remember in Alcohol

S_N1 reaction:

R–OH + H⁺ → R–OH₂⁺ → R⁺ + H₂O → R–X (R may rearrange)

Reactivity of HX: HI > HBr > HCl

Reactivity of ROH: allyl, benzyl > 3° > 2° > 1° (Carbocation stability)

Example:

CH₃CHCH₃ + conc. HBr or NaBr/H₂SO₄ → CH₃CHCH₃ | reflux | OH Br

Isopropyl alcohol → Isopropyl bromide

S_N2 reaction:

ROH + PCl₅ → RCl + POCl₃

ROH + PCl₃ → RCl + H₃PO₃

ROH + SOCl₂ + Pyridine → RCl + SO₂ + HCl

Williamson's synthesis:

It is the reaction in which sodium or potassium alkoxide is heated with an alkyl halide (S_N2).

R¹O⁻ + R²–X → [R¹O···R²···X]⁻ → R¹–O–R² + X⁻

This method is particularly useful for preparing mixed ethers.

Nucleophilic Aromatic Substitution of aryl halides (S_NAr):

An electron withdrawing group at ortho or para positions with respect to a good leaving groups are necessary conditions for S_NAr.
Intermediate ion is stabilized by resonance and are stable salts called Meisenheimer salts.
A group that withdraws electrons tends to neutralize the negative charge of the ring and this dispersal of the charge stabilizes the carbanion.

Element effect: Reactivity order towards S_N2Ar with different halogens:

Ar-F > Ar-Cl > Ar-Br > Ar-I

Points to remember in Grignard Reagents

Grignard's Reagent: RMgX (alkyl magnesium halide)

Reactions with active H-containing compounds:

RMgX + H–A → R–H + MgXA (where A = OH, OR, NH₂, etc.)

Reactions with carbonyl compounds:

RMgX + HCHO → RCH₂OH (1° alcohol)

RMgX + R'CHO → RR'CHOH (2° alcohol)

RMgX + R'COR" → RR'R"COH (3° alcohol)

RMgX + CO₂ → RCOOH (after acid workup)

Reactions with esters:

2RMgX + R'COOR" → R'R₂COH + R"OH (3° alcohol)

Reactions with acid chlorides:

2RMgX + R'COCl → R'R₂COH + MgXCl (3° alcohol)

Reactions with nitriles:

RMgX + R'CN → R'RC=NH → R'RCO (after hydrolysis)

Points to remember in Reduction

(1) LiAlH₄ (Lithium aluminium hydride)

R–CHO → RCH₂OH (Aldehyde to 1° alcohol)

R–CO–R' → R–CH(OH)–R' (Ketone to 2° alcohol)

RCOOH → RCH₂OH (Acid to 1° alcohol)

R–CO–O–CO–R → 2RCH₂OH (Anhydride to alcohols)

R–COOR' → RCH₂OH + R'OH (Ester to alcohols)

R–CONH₂ → RCH₂NH₂ (Amide to 1° amine)

R–COCl → RCH₂OH (Acid chloride to 1° alcohol)

R–CN → RCH₂NH₂ (Nitrile to 1° amine)

Note: LiAlH₄ does not reduce C=C or C≡C bonds (Exception: Ph-CH=CH-COOH → Ph-CH₂-CH₂-CH₂OH)

(2) NaBH₄, EtOH (Sodium borohydride)

Aldehyde → 1° Alcohol

Ketone → 2° Alcohol

Acid halide → 1° Alcohol

(3) Na/EtOH (Bouveait Blanc reduction)

Aldehyde → 1° Alcohol

Ketone → 2° Alcohol

Acid halide → 1° Alcohol

Ester → Alcohol + Alcohol

RCN → RCH₂NH₂

(4) Na–Hg/HCl or Al[OCHMe₂]₃ (MPV Reduction)

Aldehyde → 1° Alcohol

Ketone → 2° Alcohol

(5) Rossenmund's Reduction

R–COCl + H₂/Pd/BaSO₄ → R–CHO

(6) Birch reduction (Li/Na/K + Liquid NH₃)

R–C≡C–R → R–CH=CH–R (trans alkene)

Note: Terminal alkynes not reduced

(7) Stephen's Reduction

R–C≡N + (1) SnCl₂/HCl, (2) H₂O → R–CHO

Note: DiBAL-H is also used for same conversion.

(8) Clemmensen Reduction

C=O (Keto) + Zn-Hg/HCl/Δ → CH₂ (alkane)

Note: Avoid if acid sensitive groups are present in molecule (e.g., C=C, C≡C, OH, OR)

(9) Wolff-Kishner Reduction

C=O (Keto) + NH₂-NH₂/KOH/Δ → CH₂

Note: Avoid if base sensitive groups are present in molecule (e.g., COOR, COX, CONH₂, -CO-O-CO-, R-X)

(10) Lindlar Catalyst

R–C≡C–R + H₂/Pd/CaCO₃/Quinoline → R–CH=CH–R (Syn addition, Cis alkene)

Note: H₂, Pd, BaSO₄ is also used for same conversion.

(11) Red Phosphorus and HI

Almost all functional groups containing compounds converts into corresponding alkane by red P + HI.

R–CH₂OH → R–CH₃

R–CHO → R–CH₃

R₂CO → R₂CH₂ (Alkane)

(12) DIABAL-H reduction

R–COOR' + DiBAL-H → RCHO + R'OH

R–CN + DiBAL-H → R–CHO

Note: At ordinary temperature esters reduced to alcohols but at low temperature esters reduced to aldehyde.

Points to remember in Oxidation Reaction

(1) KMnO₄ (in both medium) or K₂Cr₂O₇ (in acidic medium)

1° Alcohol → Acid

2° Alcohol → Ketone

3° Alcohol → No reaction

Alkene oxidation:

R₂C=CR'₂ → R₂C=O + R'₂C=O

Alkyne oxidation:

R-C≡C-R' → RCOOH + R'COOH

Oxidation of aromatic side chain:

(CH₂)n-CH₃ → COOH

(2) PCC (Pyridinium chloro chromate)

1° ROH → Aldehyde

2° ROH → Ketone

3° ROH → No reaction

(3) Cu/573 K

1° Alcohol → Aldehyde

2° Alcohol → Ketone

3° Alcohol → Alkene

(4) HIO₄ (Periodic Acid)

Condition: Vicinal diol, α-Hydroxy ketone & α-diketone can oxidise by HIO₄

-C(OH)-C(OH)- → 2 -C=O

-C(OH)-CO- → -COOH + -C=O

-CO-CO- → 2 -COOH

(5) Baeyer's reagent and OsO₄ + NaHSO₃

-C=C- → -C(OH)-C(OH)- (syn dihydroxylation)

(6) Baeyer-Villiger oxidation (m-CPBA or CH₃CO₃H)

R-CO-R' → R-CO-OR'

Priority of shift (O accepting aptitude): R' = Ph > Ethyl > Methyl

(7) Prilezhaev reaction

-C=C- + MCPBA → Epoxide

Epoxide + H₃O⁺ → Anti hydroxylation

(8) oxidation by HNO₃

Aldehyde → Acid

1° Alcohol → Acid

2° Alcohol → No reaction

3° Alcohol → No reaction

(9) oxidation by MnO₂

1° Alcohol → Aldehyde

2° Alcohol → Ketone

3° Alcohol → No reaction

Note: Only allylic and benzylic alcohols are oxidised by MnO₂.

Points to remember in Aldehyde & Ketones

Aldol condensation:

Carbonyl compounds having acidic sp³ α-H shows this reaction in presence of dil. NaOH or dil. acid.

2CH₃-CHO → CH₃-CH(OH)-CH₂-CHO → CH₃CH=CHCHO (after dehydration)

Crossed aldol condensation:

CH₃CHO + HCHO → HOCH₂-CH₂-CHO → CH₂=CH-CHO

CH₃COCH₃ + HCHO → CH₃CO-CH₂CH₂OH → CH₃CO-CH=CH₂

Cannizzaro reaction:

Carbonyl compounds not having sp³α-H shows following disproportion reaction

2HCHO + NaOH → CH₃OH + HCOONa (50% each)

2C₆H₅CHO + NaOH → C₆H₅CH₂OH + C₆H₅COONa (50% each)

Crossed Cannizzaro reaction:

CH₃O-CHO + HCHO + NaOH → CH₃O-CH₂OH + HCOONa

Formation of hydrazones and azines

C=O + NH₂NH₂ → C=NNH₂ → C=N-N=C (azine)

Perkin reaction:

When benzaldehyde (or any other aromatic aldehyde) is heated with the anhydride of an aliphatic acid (containing two α-hydrogen atoms) in the presence of its sodium salt, condensation takes place to form a β-arylacrylic acid.

C₆H₅CHO + (CH₃CO)₂O + CH₃CO₂Na → C₆H₅CH=CHCO₂H (cinnamic acid)

Haloform reaction:

Acetaldehyde and methylalkyl ketones react rapidly with halogen (Cl₂, Br₂ or I₂) in the presence of alkali to give haloform and acid salt.

R-CO-CH₃ + Br₂/NaOH → R-COONa + CHBr₃ (Bromoform)

Mechanism:

(a) Halogenation:

R-CO-CH₃ + Br₂ → R-CO-CBr₃

(b) Alkaline hydrolysis:

R-CO-CBr₃ + NaOH → CHBr₃ + R-COONa

Note: This reaction is used to distinguish the presence of CH₃-CO- group.

Other important reactions:

CH₂O + NH₃ → (CH₂)₆N₄ (Hexamethylene tetramine/urotropine)

CH₃CHO + NH₃ → CH₃-CH(OH)-NH₂ (Acetaldehyde ammonia)

C₆H₅CHO + NH₃ → Hydrobenzamide

C₆H₅CHO + C₆H₅NH₂ → Schiff's base (anils)

C₆H₅COCH₃ + Cl₂ → C₆H₅COCH₂Cl (Phenacyl chloride)

Points to remember in Carboxylic acid & Derivatives

Summary of reactions of carboxylic acids:

Reagent	Product
Na Metal	R–CH₂–COONa + ½ H₂
NaOH	R–CH₂–COONa + H₂O
NaHCO₃	R–CH₂–COONa + CO₂↑ + H₂O
CH₃MgBr	R–CH₂–COOMgBr + CH₄↑
NaOH (CaO) Δ	R–CH₃ + Na₂CO₃
SOCl₂	RCH₂COCl + SO₂↑
PCl₅	R–CH₂–COCl
NH₃, Δ	R–CH₂–CONH₂
P₂O₅, Δ	R–CH₂–CO–O–CO–CH₂–R (anhydride)
R'OH / H₂SO₄	R–CH₂–COOR' (ester)

Summary of reactions of acid halides:

RCOCl + H₂O → RCOOH + HCl (Hydrolysis)

RCOCl + R'OH → RCOOR' + HCl (Alcoholysis)

RCOCl + 2NH₃ → RCONH₂ + NH₄Cl (Ammonolysis)

RCOCl + R'NH₂ → RCONHR' + R'NH₃⁺Cl⁻

2RCOCl + R'COONa → (RCO)₂O + NaCl

RCOCl + C₆H₆/AlCl₃ → C₆H₅COR + HCl (Friedel-Crafts)

RCOCl + H₂/Pd-BaSO₄ → RCHO + HCl (Rosemund's reduction)

2RCOCl + R'₂Cd → 2RCOR' + CdCl₂

RCOCl + LiAlH₄ → RCH₂OH

RCOCl + KCN → R-CO-CN → R-CO-COOH + NH₃

Summary of reaction of amides:

RCONH₂ + H₂O/H⁺ → RCOOH + NH₄⁺

RCONH₂ + NaOH → RCOONa + NH₃

RCONH₂ + HCl → RCONH₂·HCl

RCONH₂ + Na → RCONHNa + ½H₂

RCONH₂ + P₂O₅ → 3RC≡N + 2H₃PO₄

RCONH₂ + SOCl₂ → RC≡N + SO₂ + HCl

RCONH₂ + HONO → RCOOH + N₂ + H₂O

RCONH₂ + Br₂ + 4KOH → RNH₂ + CO₂ + 2KBr + H₂O (Hoffmann bromide reaction)

RCONH₂ + LiAlH₄ → RCH₂NH₂ (1° Amine)

Summary of reaction of esters:

RCOOR' + H₂O/H⁺ → RCOOH + R'OH (Hydrolysis)

RCOOR' + NaOH → RCOONa + R'OH (Saponification)

RCOOR' + NH₃ → RCONH₂ + R'OH (Amonolysis)

RCOOR' + R"NH₂ → RCONHR" + R'OH

RCOOR' + R"OH/H⁺ → RCOOR" + R'OH (Trans-esterification)

RCOOR' + H₂/CuCrO₄ → RCH₂OH + R'OH

RCOOR' + Na/alcohol → RCH₂OH + R'OH (Bouveault-Blanc reduction)

RCOOR' + 2R"MgX → R-C(OH)R"₂ (3° alcohol)

Points to remember in Aromatic Compounds

Electrophilic aromatic substitution:

(a) Bromination of Benzene:

Bromination follows the general mechanism for electrophilic aromatic substitution. Bromine itself is not sufficiently electrophilic to react with benzene, but a strong Lewis acid such as FeBr₃ catalyzes the reaction.

Step 1: Formation of a stronger electrophile.

Br-Br + FeBr₃ → Br⁺ + FeBr₄⁻

Step 2: Electrophilic attack and formation of the sigma complex.

C₆H₆ + Br⁺ → C₆H₆Br⁺ (sigma complex)

Step 3: Loss of a proton gives the products.

C₆H₆Br⁺ + FeBr₄⁻ → C₆H₅Br + HBr + FeBr₃

(b) Nitration:

HNO₃ + H₂SO₄ → NO₂⁺ + H₃O⁺ + HSO₄⁻

C₆H₆ + NO₂⁺ → C₆H₅NO₂ + H⁺

(c) Sulphonation:

2H₂SO₄ → SO₃ + H₃O⁺ + HSO₄⁻

C₆H₆ + SO₃ → C₆H₅SO₃H

(d) Friedel Craft reaction:

Alkylation mechanism:

RCl + AlCl₃ → R⁺ + AlCl₄⁻

C₆H₆ + R⁺ → C₆H₅R + H⁺

Acylation mechanism:

RCOCl + AlCl₃ → RCO⁺ + AlCl₄⁻

C₆H₆ + RCO⁺ → C₆H₅COR + H⁺

Example:

C₆H₆ + CH₃COCl/AlCl₃ → C₆H₅COCH₃ (Acetophenone)

Note: Friedal-Crafts acylations are generally free from rearrangements and multiple substitution. They do not go on strongly deactivated rings.

Chemical Reactions of Benzene:

C₆H₆ + HNO₃/H₂SO₄ → C₆H₅NO₂ + H₂O (Nitration)

C₆H₆ + H₂SO₄/SO₃ → C₆H₅SO₃H (Sulfonation)

C₆H₆ + Cl₂/FeCl₃ → C₆H₅Cl + HCl (Chlorination)

C₆H₆ + RCl/AlCl₃ → C₆H₅R + HCl (Friedel-Crafts alkylation)

C₆H₆ + RCOCl/AlCl₃ → C₆H₅COR + HCl (Friedel-Crafts acylation)

C₆H₆ + D⁺/D₂O → C₆H₅D + H⁺ (Deuteration)

C₆H₆ + ArN₂⁺X⁻ → C₆H₅N=N-Ar (Diazonium coupling)

Points to remember in Polymers

Biodegradable Polymers:

A large number of polymers are quite resistant to the environmental degradation processes and are thus responsible for the accumulation of polymeric solid waste materials. These solid wastes cause acute environmental problems and remain undegraded for quite a long time. In view of the general awareness and concern for the problems created by the polymeric solid wastes, certain new biodegradable synthetic polymers have been designed and developed.

(a) Poly β-hydroxybutyrate – co–β-hydroxy valerate (PHBV):

It is obtained by the copolymerisation of 3-hydroxybutanoic acid and 3-hydroxypentanoic acid.

CH₃-CH(OH)-CH₂-COOH + CH₃-CH₂-CH(OH)-CH₂-COOH →
[-O-CH(CH₃)-CH₂-CO-O-CH(CH₂CH₃)-CH₂-CO-]n

PHBV is used in speciality packaging, orthopaedic devices and in controlled release of drugs. PHBV undergoes bacterial degradation in the environment.

(b) Nylon–2–nylon–6:

It is an alternating polyamide copolymer of glycine (H₂N–CH₂–COOH) and amino caproic acid (H₂N(CH₂)₅COOH) and it is also biodegradable polymer.

nH₂N-CH₂-COOH + nH₂N-(CH₂)₅-COOH →
[-NH-CH₂-CO-NH-(CH₂)₅-CO-]n

Some common addition polymers/chain growth polymer

S.No.	Name(s)	Formula	Monomer	Uses
1.	Polyethylene (low density LDPE)	-(CH₂-CH₂)n-	CH₂=CH₂ (ethylene)	Film wrap, Plastic Bags
2.	Polyethylene (high density HDPE)	-(CH₂-CH₂)n-	CH₂=CH₂ (ethylene)	Electrical insulation bottles, toys
3.	Polypropylene (PP)	-[CH(CH₃)-CH₂]n-	CH₂=CHCH₃ (propylene)	Ropes, toys, pipes, fibres
4.	Poly vinyl chloride (PVC)	-[CH(Cl)-CH₂]n-	CH₂=CHCl (vinyl chloride)	Rain coats, hand bags, water pipes
5.	Polystyrene (Styron)	-[CH(C₆H₅)-CH₂]n-	CH₂=CHC₆H₅ (styrene)	Insulator, wrapping material, toys
6.	Polyacrylonitrile (PAN, Orion)	-[CH(CN)-CH₂]n-	CH₂=CHCN (acrylonitrile)	Rugs, Blankets clothing
7.	Polytetrafluoroethylene (PTFE, Teflon)	-(CF₂-CF₂)n-	CF₂=CF₂ (tetrafluoroethylene)	Non-stick surfaces, electrical insulation

Some condensation polymers/step growth polymers

S.No.	Name(s)	Formula	Monomer	Uses
1.	Polyester/Dacron/Terylene	-[CO-C₆H₄-CO-O-CH₂-CH₂-O]n-	Terephthalic acid + Ethylene glycol	Fabric, Tyrecord
2.	Nylon 6,6	-[CO(CH₂)₄CO-NH(CH₂)₆NH]n-	Adipic acid + Hexamethylene diamine	Parachutes & Clothing
3.	Bakelite	Crosslinked phenol-formaldehyde resin	PhOH + HCHO (excess)	Electrical Switch, combs
4.	Urea-formaldehyde resin	(-NH-CO-NH-CH₂-)n	H₂N-CO-NH₂ + HCHO	Unbreakable cups
5.	Polycarbonate Lexan	-[O-C₆H₄-C(CH₃)₂-C₆H₄-O-CO-]n	Bisphenol A + Phosgene	Bike helmet, bullet proof glass