NCERT Chemistry Class XII Part I: Comprehensive Study Notes

General Characteristics of the Solid State and Classification

Matter exists in three states: solid, liquid, and gas. Under specific conditions of temperature and pressure, the most stable state depends on the net effect of two opposing factors: intermolecular forces, which tend to keep constituent particles (atoms, ions, or molecules) closer together, and thermal energy, which tends to keep them apart by increasing their movement. In solids, at sufficiently low temperatures, thermal energy is low enough that intermolecular forces bring particles so close that they occupy fixed positions and can only oscillate about their mean positions. This explains the characteristic rigidity of solids. The general properties of solids include having definite mass, volume, and shape; short intermolecular distances ($0.1$ to $1.0$ nm range mentioned in various contexts); and strong intermolecular forces. Their constituent particles have fixed positions and solids are generally incompressible and rigid.

Solids are classified into crystalline and amorphous forms based on the nature of order present in the arrangement of their constituent particles. A crystalline solid consists of a large number of small crystals, each having a definite characteristic geometrical shape. In a crystal, the arrangement of constituent particles is ordered and possesses long-range order, meaning there is a regular pattern of arrangement that repeats itself periodically over the entire crystal. Sodium chloride and quartz are typical examples. Conversely, an amorphous solid (Greek: amorphos = no form) consists of particles of irregular shape where the arrangement has only short-range order. In such an arrangement, a regular and periodically repeating pattern is observed over short distances only. Portions are scattered, and in between, the arrangement is disordered. The structure of amorphous solids is similar to that of liquids. Glass, rubber, and plastics are typical examples. Due to these differences, crystalline solids have sharp melting points, while amorphous solids soften over a range of temperature and can be molded. Crystalline solids are anisotropic in nature, meaning physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystal. Amorphous solids are isotropic, meaning their physical properties are the same in all directions due to the irregular arrangement.

Crystal Lattices and Unit Cells

The main characteristic of crystalline solids is a regular and repeating pattern of constituent particles. If the three-dimensional arrangement of these particles is represented diagrammatically, with each particle depicted as a point, the arrangement is called a crystal lattice. Thus, a regular three-dimensional arrangement of points in space is called a crystal lattice. There are only $14$ possible three-dimensional lattices, known as Bravais Lattices, named after the French mathematician who first described them. The characteristics of a crystal lattice include: each point is called a lattice point or lattice site; each lattice point represents one constituent particle (atom, molecule, or ion); and lattice points are joined by straight lines to bring out the geometry of the lattice.

A unit cell is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice. A unit cell is characterized by its dimensions along the three edges ($a$, $b$, and $c$) and the angles between these edges ($\alpha$ between $b$ and $c$, $\beta$ between $a$ and $c$, and $\gamma$ between $a$ and $b$). Thus, six parameters characterize a unit cell. Unit cells are divided into two categories: Primitive and Centered. In primitive unit cells, constituent particles are present only on the corner positions. Centered unit cells contain one or more constituent particles at positions other than corners in addition to those at corners. Centered unit cells are further divided into Body-centered (particle at the center of the body), Face-centered (particles at the center of each face), and End-centered (particles at the center of any two opposite faces).

Calculations and Close-Packed Structures

To calculate the number of atoms in a unit cell, we must consider the contribution of each atom. In a simple cubic unit cell, which has $8$ corners, each corner atom is shared between $8$ adjacent unit cells; thus, only $1/8$th of an atom belongs to a particular unit cell. The total number of atoms is $8 \times (1/8) = 1$ atom. In a body-centered cubic (BCC) unit cell, there are $8$ corners and $1$ atom at the body center. The total is $8 \times (1/8) + 1 = 2$ atoms. In a face-centered cubic (FCC) unit cell, there are $8$ corners and $6$ faces. Each face atom is shared between $2$ unit cells, contributing $1/2$. The total is $8 \times (1/8) + 6 \times (1/2) = 4$ atoms.

Close packing in solids aims at the maximum efficiency of space. Coordination number is the number of nearest neighbors of a particle. In one-dimensional close packing, the coordination number is $2$. In two-dimensional packing, there are square close packing (coordination number $4$) and hexagonal close packing (coordination number $6$). Hexagonal packing is more efficient. In three-dimensional close packing, stacking layers creates two types of voids: tetrahedral and octahedral. If the number of close-packed spheres is $N$, the number of octahedral voids is $N$ and the number of tetrahedral voids is $2N$. Hexagonal close-packed (HCP, ABAB… pattern) and Cubic close-packed (CCP or FCC, ABCABC… pattern) are highly efficient, each filling $74\%$ of the space. In these, each sphere is in contact with $12$ others, giving a coordination number of $12$. The density ($d$) of a unit cell is calculated as $d = \frac{z \cdot M}{a^3 \cdot N_A}$, where $z$ is the number of atoms per unit cell, $M$ is molar mass, $a$ is edge length, and $N_A$ is Avogadro's constant ($6.022 \times 10^{23} \, mol^{-1}$).

Point Defects, Electrical and Magnetic Properties

Imperfections or defects in solids are irregularities in the arrangement of constituent particles. Point defects are irregularities around a point or atom, while line defects are irregularities in entire rows. Point defects include Stoichiometric defects, Impurity defects, and Non-stoichiometric defects. Stoichiometric defects (Intrinsic or Thermodynamic) do not disturb the stoichiometry. Examples include Vacancy defects (decrease density) and Interstitial defects (increase density). Non-ionic solids show these, while ionic solids show Frenkel and Schottky defects. Frenkel defect (dislocation defect) occurs when a smaller ion (usually cation) is displaced from its normal site to an interstitial site. It does not change density. Examples: $ZnS$, $AgCl$, $AgBr$. Schottky defect is basically a vacancy defect where an equal number of cations and anions are missing to maintain neutrality. It decreases density. Examples: $NaCl$, $KCl$, $CsCl$, and $AgBr$ (note $AgBr$ shows both). Non-stoichiometric defects include metal excess (anionic vacancies called F-centres or presence of extra cations) and metal deficiency (missing cations like in $FeO$ with composition $Fe_{0.95}O$).

Solids exhibit electrical conductivities ranging over $27$ orders of magnitude from $10^{-20}$ to $10^7 \, ohm^{-1} m^{-1}$. Conductors have conductivities between $10^4$ to $10^7 \, ohm^{-1} m^{-1}$. Metals have high conductivity ($10^7$) while insulators have extremely low conductivity ($10^{-20}$ to $10^{-10}$). Semiconductors fall in between ($10^{-6}$ to $10^4$). Magnetic properties arise from electrons acting as tiny magnets due to orbital and spin motion. Substances are classified as: Paramagnetic (weakly attracted by magnetic field, e.g., $O_2$, $Cu^{2+}$), Diamagnetic (weakly repelled, e.g., $H_2O$, $NaCl$), Ferromagnetic (strongly attracted, can be permanently magnetized, e.g., $Fe$, $Co$, $Ni$, $CrO_2$), Antiferromagnetic (domains cancel out, e.g., $MnO$), and Ferrimagnetic (domains aligned unequally, e.g., $Fe_3O_4$).

Solutions and Their Concentrations

Solutions are homogeneous mixtures of two or more substances. Binary solutions consist of two components: the solvent and the solute. Common methods to express concentration include: Mass Percentage ($w/w$), Volume Percentage ($v/v$), Parts per million (ppm), and Mole Fraction ($x$). Mole fraction of a component $i$ is $x_i = n_i / ∑ n$. Molarity ($M$) is the number of moles of solute per litre (or $dm^3$) of solution. Molality ($m$) is the number of moles of solute per kilogram ($kg$) of solvent. Molarity and mass percent change with temperature as they involve volume, whereas mole fraction and molality are independent of temperature.

Solubility is the maximum amount of solute that can be dissolved in a specified amount of solvent at a given temperature. Henry's Law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid or solution: $p = K_H imes x$, where $K_H$ is the Henry's law constant. For liquid-liquid solutions, Raoult's Law states that for a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction: $p_1 = x_1 imes p_1^0$. Ideal solutions follow Raoult's law at all concentrations ($\Delta H_{mix} = 0, ∆ V_{mix} = 0$). Non-ideal solutions show positive or negative deviations due to differences in intermolecular interactions ($A-A$ and $B-B$ vs $A-B$). Minimum boiling azeotropes show large positive deviations (e.g., ethanol-water), while maximum boiling azeotropes show large negative deviations (e.g., nitric acid-water).

Colligative Properties and Abnormal Molar Mass

Colligative properties depend only on the number of solute particles and not their identity. They include: Relative lowering of vapour pressure ($(p_1^0 - p_1) / p_1^0 = x_2$), Elevation of boiling point ($∆ T_b = K_b imes m$), Depression of freezing point ($∆ T_f = K_f imes m$), and Osmotic pressure (̱ = CRT). Osmosis is the flow of solvent molecules through a semi-permeable membrane from pure solvent to solution. Reverse osmosis occurs if pressure higher than osmotic pressure is applied to the solution side, used in water desalination. Abnormal molar masses occur when solutes undergo association or dissociation in solution. The van't Hoff factor ($i$) accounts for this: $i = ext{Normal molar mass} / ext{Abnormal molar mass}$. For dissociation, i > 1; for association, i < 1. The modified colligative property equations include $i$: e.g., ̱ = iCRT.

Electrochemistry: Cells and Conductance

Electrochemistry studies the conversion of chemical energy into electrical energy and vice-versa. Galvanic (Voltaic) cells use spontaneous redox reactions to produce electricity. The Daniell cell is a classic example: $Zn(s) + Cu^{2+}(aq) ightarrow Zn^{2+}(aq) + Cu(s)$, with a cell potential of $1.10 \, V$ at standard conditions. The Nernst Equation calculates electrode potential at non-standard conditions: $E = E^0 - (RT/nF) imes ext{ln} Q$. Standard Gibbs energy of reaction is related by: $∆<em>r G^0 = -nFE^0</em>{ ext{cell}}$.

Conductance ($G$) is the reciprocal of resistance ($R$). Conductivity (̱) is the reciprocal of resistivity ($ho$). Molar conductivity (̴m) is defined as ̴_m = ̱ / c. According to Kohlrausch's law of independent migration of ions, limiting molar conductivity of an electrolyte is the sum of limiting molar conductivities of its constituent ions: ̴_m^0 = u+ λ+^0 + u- λ_-^0. Electrolysis is the process of using electrical energy to drive non-spontaneous reactions. Faraday's first law: mass of substance deposited ($w$) is proportional to charge ($Q$). Faraday's second law: for the same charge, masses are proportional to chemical equivalents. 1 Faraday ($F$) is the charge of $1 \, mole$ of electrons, approximately $96487 \, C \, mol^{-1}$.

Batteries, Fuel Cells, and Corrosion

Batteries are galvanic cells in series. Primary batteries are non-rechargeable (e.g., Dry cell/Leclanche cell with $Zn$ anode and carbon cathode, $1.5 \, V$; Mercury cell for low current, $1.35 \, V$). Secondary batteries are rechargeable (e.g., Lead storage battery with $38\%$ sulfuric acid electrolyte; Nickel-cadmium cell). Fuel cells produce electricity from high-efficiency combustion of fuels like hydrogen and oxygen ($2H_2 + O_2 ightarrow 2H_2O$). They are non-polluting and provide $70\%$ efficiency.

Corrosion is an electrochemical process. In rusting of iron, an anodic spot is formed where oxidation occurs ($Fe ightarrow Fe^{2+} + 2e^-$). Electrons move to a cathodic spot where oxygen is reduced in the presence of $H^+$ ($O_2 + 4H^+ + 4e^- ightarrow 2H_2O$). The overall reaction forms hydrated ferric oxide ($Fe_2O_3 imes x H_2O$). Prevention includes painting, alloying, or cathodic protection (using sacrificial anodes like $Mg$ or $Zn$).

Chemical Kinetics

Chemical kinetics deals with reaction rates and mechanisms. Rate of reaction is the change in concentration per unit time. Instantaneous rate is measured by the slope of the tangent to the concentration-time curve. Factors affecting rate include concentration, temperature, and catalysts. Rate Law: $ext{rate} = k[A]^x[B]^y$. The sum of powers ($x+y$) is the order of reaction. Molecularity is the number of reacting species colliding simultaneously in an elementary reaction.

Integrated Rate Equations: For zero-order reactions, $k = ([R]<em>0 - [R]) / t$. For first-order reactions, $k = (2.303 / t) imes ext{log} ([R]_0 / [R])$. Half-life ($t</em>{1/2}$) for zero-order is $[R]_0 / 2k$, and for first-order is $0.693 / k$. The temperature dependence is shown by the Arrhenius equation: $k = A e^{-E_a/RT}$. Collision theory proposes that for a reaction, molecules must collide with sufficient kinetic energy (activation energy, $E_a$) and proper orientation.

Surface Chemistry and Catalysis

Surface chemistry deals with phenomena at interfaces. Adsorption is the accumulation of molecular species at the surface. Adsorbent is the material on which adsorption occurs; Adsorbate is the substance adsorbed. Physisorption involves weak Van der Waals forces, is reversible, and has low enthalpy ($20$ to $40 \, kJ \, mol^{-1}$). Chemisorption involves chemical bonds, is irreversible, specific, and has high enthalpy ($80$ to $240 \, kJ \, mol^{-1}$). Catalysis involves substances that alter reaction rates. Homogeneous catalysis has reactants and catalyst in the same phase; heterogeneous catalysis uses a solid catalyst for gas/liquid reactants. Zeolites are shape-selective catalysts. Enzymes are highly specific biochemical catalysts.

Colloids and Emulsions

Colloids are heterogeneous systems with particles sized $1$ to $1000 \, nm$. They consist of a dispersed phase and dispersion medium. Classification is based on physical state, interaction (Lyophilic vs Lyophobic), or particle type (Multimolecular, Macromolecular, Associated/Micelles). Micelles form above the Kraft temperature ($T_k$) and critical micelle concentration (CMC). Soaps form micelles around grease/oil to remove it. Properties of colloids include the Tyndall effect (scattering of light), Brownian motion (zig-zag movement), Electrophoresis (movement in electric field), and Coagulation (precipitation by electrolytes). Emulsions are liquid-liquid systems, either oil-in-water ($O/W$) or water-in-oil ($W/O$), stabilized by emulsifying agents.

General Principles of Isolation of Metals

Metallurgy involves extracting metals from ores. Steps: 1. Concentration: Froth floatation (for sulfides), Magnetic separation, Leaching (using chemicals like $NaOH$ for bauxite). 2. Extraction: Calcinations (heating in limited air) or Roasting (heating in excess air) to get oxides, then reduction using carbon ($C$) or carbon monoxide ($CO$). Ellingham diagrams use thermodynamics ($G$ vs $T$) to select reducing agents. 3. Refining: Distillation (for $Zn$, $Hg$), Liquation (for $Sn$), Electrolysis (for $Cu$, $Zn$), Zone refining (for semiconductors like $Si$, $Ge$), Vapour phase refining (Mond process for $Ni$, van Arkel for $Zr$, $Ti$). Aluminum is extracted via the Hall-Heroult process ($Al_2O_3$ in molten cryolite).

The p-Block, d-Block, and f-Block Elements

p-Block (Groups 15 to 18): Group 15 (Nitrogen family) trends include increasing metallic character down the group. Nitrogen shows anomalous behavior (small size, high electronegativity). Ammonia ($NH_3$) is produced by Haber's process ($200 \, atm$, $700 \, K$, $Fe$ catalyst). Nitric acid ($HNO_3$) is a strong oxidizer. Phosphorous allotropes: White ($P_4$, reactive), Red (polymeric), Black. Group 16 (Oxygen/Chalcogens): Oxygen ($O_2$), Ozone ($O_3$), Sulfur allotropes (Rhombic, Monoclinic). Sulfuric acid ($H_2SO_4$) is produced by the Contact process. Group 17 (Halogens): Most electronegative elements. Fluorine is the strongest oxidizing agent. Group 18 (Noble Gases): Chemically inert, full valence shells. Xenon compounds ($XeF_2$, $XeF_4$, $XeF_6$) are known.

d-Block (Transition) and f-Block (Inner Transition) Elements: d-block elements have partially filled d-orbitals. Characteristics: high melting points, variable oxidation states, colorful ions, catalytic activity, interstitial compounds, and alloy formation. Magnetic moment $μ = √[n(n+2)]$ Bohr Magnetons ($BM$). f-block elements include Lanthanoids ($4f$, Lanthanoid contraction causes similar radii for $Zr$ and $Hf$) and Actinoids ($5f$, mostly radioactive).