G.C.E. (Advanced Level) Chemistry Comprehensive Study Notes

Atomic Structure

• Matter is defined as anything that has mass and occupies space. The physical universe consists of approximately 100 natural chemically distinct types of atoms (118 elements discovered to date, with heavier elements being short-lived and synthetic).

• Early philosophical concepts of matter:

  • Empedocles (~440 BC) proposed four fundamental elements: earth, fire, air, and water.
  • Democritus (460–370 BC) coined the term atomos (meaning indivisible or uncuttable) to describe the tiny, discrete particles forming all matter.
  • Plato and Aristotle rejected indivisible particles, causing the atomic theory to remain dormant during the era of Aristotelian dominance.

• Dalton's Atomic Theory (John Dalton, 1808) - "Golf Ball Model":

  • Elements are composed of extremely small, indivisible particles called atoms.
  • All atoms of a given element are identical in mass and size, but differ from atoms of other elements.
  • Atoms of one element cannot be transformed into atoms of another element by chemical reactions; atoms are neither created nor destroyed.
  • Compounds form when atoms of different elements combine in simple whole-number ratios.

• Cathode Rays and the Electron:

  • Johnstone G. Stoney (1891) named the fundamental unit of electricity the "electron" without experimental proof.
  • Sir William Crookes invented the Crookes tube (cathode ray tube). Applying high voltage across electrodes at low gas pressure causes the cathode (negatively charged plate) to emit invisible radiation causing residual gases to glow or fluoresce.
  • Cathode rays are deflected by electric and magnetic fields, carrying a negative charge.
  • J. J. Thomson (1897) demonstrated cathode rays are streams of negatively charged particles identical for all cathode materials and residual gases. Using a hole-centered anode tube, Thomson calculated the electron's charge-to-mass ratio ($e/m$): $\text{e/m ratio} = 1.76 \times 10^8\,\text{C\,g}^{-1}$
  • Experimental properties of cathode rays:
  • Travel in straight lines (cast sharp shadows of opaque metal crosses placed in their path).
  • Possess mass and kinetic energy (cause light paddle wheels in their path to rotate due to momentum).
  • Deflect toward positively charged electric plates and show perpendicular deflection in magnetic fields.
  • The $e/m$ ratio is constant ($1.76 \times 10^8\,\text{C\,g}^{-1}$) regardless of cathode material or gas type.
  • Thomson's "Plum-Pudding" Model (1899): Postulated the atom as a positively charged sphere with embedded electrons.
  • Robert Millikan (1909) Oil Drop Experiment: Measured the fundamental electronic charge: $e = 1.602 \times 10^{-19}\,\text{C}$
  • Electron Mass Calculation: $\text{Electron mass} = \frac{1.602 \times 10^{-19}\,\text{C}}{1.76 \times 10^8\,\text{C\,g}^{-1}} = 9.10 \times 10^{-28}\,\text{g}$
  • The mass of an electron is approximately $\frac{1}{1837}$ of the mass of a hydrogen atom. Relative charge is $-1$.

• Positive Rays and the Proton:

  • Eugen Goldstein discovered positive charges using a perforated cathode tube under high voltage ($\approx 10{,}000\,\text{V}$) and low gas pressure. Accelerated gas ions collide with gas atoms knocking off electrons, forming positive ions attracted to the cathode. Ions passing through cathode perforations form faint red glows behind the cathode ("canal rays" or anode/positive rays).
  • Properties of positive rays:
  • Travel in straight lines and cast sharp shadows.
  • Rotate light paddle wheels.
  • Deflect toward the negative electric plate.
  • Properties and $e/m$ ratios depend on the residual gas present in the tube.
  • Proton Discovery (1907): Magnetic field studies showed positive particles vary in mass. Hydrogen gas yields the lightest positive particle, approximately 1840 times heavier than an electron. Named the proton.
  • Proton properties:
  • Absolute mass = $1.6 \times 10^{-24}\,\text{g} = 1.007276\,\text{u}$ (or Da).
  • Absolute charge = $+1.6 \times 10^{-19}\,\text{C}$.
  • Relative charge = $+1$; relative mass = $1$.

• Radioactivity and Nuclear Model:

  • Henri Becquerel (1896) discovered radioactivity; Ernest Rutherford showed three radiation types:
  • Alpha ($\alpha$) rays: Positively charged particles deflected away from positive electric plates.
  • Beta ($\beta$) rays: High-energy electrons deflected away from negative electric plates.
  • Gamma ($\gamma$) rays: High-energy electromagnetic radiation with no charge, unaffected by electric or magnetic fields.
  • Rutherford's Gold Foil Experiment (1908–1909, with Geiger and Marsden):
  • Thin gold foil target bombarded with $\alpha$ particles from a radioactive source.
  • Observations: Most $\alpha$ particles passed straight through undeflected or slightly deflected; a small fraction scattered at large angles; very few bounced back ($180^\circ$).
  • Rutherford Model (1911): Atoms are mostly empty space. All positive charge and virtually all mass are concentrated in a dense central core called the nucleus.
  • Discovery of the Neutron (Sir James Chadwick, 1932):
  • Mass of neutron = $1.6749 \times 10^{-24}\,\text{g} = 1.008665\,\text{u}$.
  • Electric charge = $0$
  • Rutherford-Bohr Model (1913):
  • Electrons orbit the nucleus in defined paths. Electrostatic attraction equals centrifugal force.
  • Nucleons: Protons and neutrons forming the nucleus. A nuclide is a specific nuclear species defined by exact numbers of protons and neutrons.

• Atomic Parameters:

  • Atomic Number ($Z$): Number of protons in the nucleus = Number of electrons in a neutral atom.
  • Mass Number ($A$): Total number of nucleons (protons + neutrons). $A = Z + \text{Number of neutrons}$
  • Isotopes: Atoms of the same element ($Z$) with different mass numbers ($A$) due to differing neutron counts (e.g., $^{12}\text{C}, ^{13}\text{C}, ^{14}\text{C}$). Stable isotopes vs. radioisotopes.
  • Unified Atomic Mass Unit ($\text{u}$ or $\text{Da}$): $\text{Defined as } \frac{1}{12} \text{ the mass of an unbound } ^{12}\text{C} \text{ atom}$$1\,\text{u} = 1.66054 \times 10^{-24}\,\text{g}$$1\,\text{g} = 6.02214 \times 10^{23}\,\text{u}$
  • Average Atomic Mass: $\text{Average Atomic Mass} = \sum [(\text{Isotope Mass}) \times (\text{Fractional Isotope Abundance})]$
  • Relative Atomic Mass ($A_r$): Dimensionless ratio of the average mass per atom of an element to $\frac{1}{12}$ the mass of a $^{12}\text{C}$ atom.

• Electromagnetic Radiation (EMR):

  • Synchronized perpendicular oscillations of electric and magnetic fields propagating through a vacuum at light speed ($c = 2.998 \times 10^8\,\text{m\,s}^{-1}$).
  • Wave parameters: Wavelength ($\lambda$), Frequency ($\nu$, in $\text{Hz}$ or $\text{s}^{-1}$). $c = \nu \lambda$
  • Quantization of Energy (Max Planck, 1900): Energy is absorbed or emitted in discrete packets called quanta. $E = h \nu$$\text{Planck constant } h = 6.626 \times 10^{-34}\,\text{J\,s}$
  • Photons and Dual Nature (Albert Einstein, 1905; Louis de Broglie): $E_{\text{photon}} = h\nu = \frac{hc}{\lambda}$
  • de Broglie Wavelength of Matter: $\lambda = \frac{h}{p} = \frac{h}{mv}$

• Atomic Line Spectra & Atomic Energy Levels:

  • Successive Ionization Energies ($I_1 < I_2 < I_3 \dots$): Sharp jumps in IE provide direct evidence for discrete electron shell structure.
  • Line Spectrum of Hydrogen:
  • Lyman Series: Transition to $n_f = 1$ (Ultraviolet region).
  • Balmer Series: Transition to $n_f = 2$ (Visible region: $656\,\text{nm}$ red, $486\,\text{nm}$ blue-green, $434\,\text{nm}$ blue, $410\,\text{nm}$ violet).
  • Paschen Series: Transition to $n_f = 3$ (Infrared region).
  • Brackett Series: Transition to $n_f = 4$ (Infrared region).
  • Pfund Series: Transition to $n_f = 5$ (Infrared region).
  • Energy difference equation: $E_{\text{photon}} = h\nu = \frac{hc}{\lambda} = -\Delta E = -(E_f - E_i)$

• Quantum Mechanical Model of Orbitals:

  • Principal Quantum Number ($n = 1, 2, 3, \dots$): Defines main energy level/shell size.
  • Angular Momentum Quantum Number ($l = 0, 1, \dots, n-1$): Defines orbital shape ($l=0 \rightarrow s$, $l=1 \rightarrow p$, $l=2 \rightarrow d$, $l=3 \rightarrow f$).
  • Magnetic Quantum Number ($m_l = -l, \dots, 0, \dots, +l$): Defines spatial orientation. Number of orbitals per subshell = $2l + 1$.
  • Spin Quantum Number ($m_s = +\frac{1}{2}, -\frac{1}{2}$): Defines electron spin orientation.
  • Structural Relations:
  • Number of subshells in shell $n = n$
  • Total orbitals in shell $n = n^2$
  • Maximum electron capacity in shell $n = 2n^2$
  • Shapes of Orbitals:
  • $s$ orbital: Spherically symmetric around the nucleus.
  • $p$ orbital: Dumbbell-shaped with two lobes separated by a nodal plane at the nucleus ($p_x, p_y, p_z$).

• Principles Governing Electron Configurations:

  • Aufbau Principle: Electrons fill subshells in order of increasing potential energy ($1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d \dots$).
  • Pauli Exclusion Principle: No two electrons in an atom can have identical sets of four quantum numbers ($n, l, m_l, m_s$). Each orbital accommodates a maximum of 2 electrons with opposite spins.
  • Hund's Rule: Degenerate orbitals are occupied singly with parallel spins before double occupancy occurs.
  • Anomalous Configurations: Extra stability of half-filled ($d^5$) and fully-filled ($d^{10}$) subshells: $\text{Chromium (Cr, } Z=24): [\text{Ar}]3d^5 4s^1$$\text{Copper (Cu, } Z=29): [\text{Ar}]3d^{10} 4s^1$

• Periodic Trends (s and p Blocks):

  • Shielding/Screening Effect: Inner core electrons shield outer valence electrons from full nuclear attraction, yielding Effective Nuclear Charge ($Z_{\text{eff}} < Z$).
  • $Z_{\text{eff}}$ increases from left to right across a period.
  • Atomic Radii Definitions:
  • van der Waals radius: Half the distance between nuclei of non-bonded adjacent identical atoms in stable contact.
  • Covalent radius: Half the internuclear distance between two bonded identical atoms.
  • Metallic radius: Half the distance between nuclei of adjacent metal cations in a metallic lattice.
  • Periodic Trends in Radii:
  • Decreases left to right across a period ($Z_{\text{eff}}$ increases).
  • Increases top to bottom down a group ($n$ increases).
  • Cations are smaller than parent atoms; anions are larger than parent atoms.
  • Isoelectronic Series (e.g., $\text{O}^{2-}, \text{F}^-, \text{Ne}, \text{Na}^+, \text{Mg}^{2+}$): Radius decreases as atomic number ($Z$) increases.
  • Ionization Energy ($I_1$):
  • Increases across a period, decreases down a group.
  • Irregularities across Period 2:
    • $I_1(\text{Be}) > I_1(\text{B})$ due to filled $2s^2$ subshell.
    • $I_1(\text{N}) > I_1(\text{O})$ due to half-filled $2p^3$ subshell.
  • Electron Gain Energy ($\Delta E_{\text{EG}}$):
  • Energy change when an electron is added to a gaseous atom ($\Delta E_{\text{EG}} = -\text{Electron Affinity}$).
  • Be ($+231\,\text{kJ\,mol}^{-1}$) and N ($+134\,\text{kJ\,mol}^{-1}$) have positive $\Delta E_{\text{EG}}$ due to subshell stability.
  • Electronegativity: Ability of an atom in a molecule to attract shared electrons to itself (Pauling Scale). Increases across a period, decreases down a group.

Structure and Bonding

• Primary Chemical Bonding Types:

  • Covalent Bond: Sharing of electron pair(s) between atoms where each atom contributes one electron per shared pair.
  • Dative Covalent Bond: Sharing of an electron pair where both electrons are supplied by a single donor atom.
  • Ionic Bond: Electrostatic attraction forces between positively charged cations and negatively charged anions.
  • Metallic Bond: Lattice of positive metal cations stabilized by a delocalized sea/cloud of valence electrons.

• Octet Rule & Exceptions:

  • Atoms gain, lose, or share electrons to achieve a valence electron count of 8 ($ns^2 np^6$).
  • Incomplete Octets: Electron-deficient molecules ($\text{BeCl}_2, \text{BH}_3, \text{BCl}_3, \text{AlCl}_3$).
  • Expanded Octets: Elements in Period 3 and beyond utilize empty $d$ orbitals ($\text{SO}_2, \text{SO}_3$ valence shell exceeds 8 electrons).
  • Odd-Electron Molecules: Species containing unpaired electrons ($\text{NO}, \text{NO}_2, \text{ClO}_2$).

• Formal Charge ($FC$) Calculation: $FC = \text{Valence electrons of free atom} - [\text{Number of bonds} + \text{Unshared valence electrons}]$

• Rules for Formal Charge Evaluation:

  • Neutral molecules have a total formal charge sum of 0; polyatomic ions equal the ionic charge.
  • Most stable structures minimize formal charges close to zero.
  • Negative formal charges must reside on more electronegative atoms.
  • Adjacent atoms carrying formal charges of identical sign generate instability.

• VSEPR Theory (Valence Shell Electron Pair Repulsion):

  • Electron pair repulsive units (single, double, triple bonds, or lone pairs each count as 1 VSEPR unit) arrange around a central atom to maximize spatial separation.
  • Repulsion magnitude order: $\text{Lone pair - Lone pair} > \text{Lone pair - Bonding pair} > \text{Bonding pair - Bonding pair}$
  • VSEPR Electron Pair Geometries & Shapes:
  • 2 VSEPR Units ($180^\circ$ angle): Linear geometry/shape ($\text{CO}_2, \text{HCN}, \text{NO}_2^+$).
  • 3 VSEPR Units ($120^\circ$ angle): Trigonal planar geometry.
    • 3 bonding pairs, 0 lone pairs: Trigonal planar shape ($\text{BF}_3, \text{SO}_3, \text{HCHO}$).
    • 2 bonding pairs, 1 lone pair: Angular/V-shaped ($\text{SO}_2$).
  • 4 VSEPR Units ($109.5^\circ$ angle): Tetrahedral geometry.
    • 4 bonding pairs, 0 lone pairs: Tetrahedral shape ($\text{CH}_4, \text{CCl}_4, \text{SO}_4^{2-}$).
    • 3 bonding pairs, 1 lone pair: Trigonal pyramidal shape ($\text{NH}_3, \text{PCl}_3, \text{H}_3\text{O}^+$).
    • 2 bonding pairs, 2 lone pairs: Angular/V-shaped ($\text{H}_2\text{O}, \text{NH}_2^-$).
  • 5 VSEPR Units ($90^\circ, 120^\circ$ angles): Trigonal bipyramidal geometry.
    • 5 bonding pairs, 0 lone pairs: Trigonal bipyramidal shape ($\text{PCl}_5$).
    • 4 bonding pairs, 1 lone pair: Distorted see-saw shape ($\text{SCl}_4$).
    • 3 bonding pairs, 2 lone pairs: Distorted T-shape ($\text{ICl}_3$).
    • 2 bonding pairs, 3 lone pairs: Linear shape ($\text{XeF}_2$).
  • 6 VSEPR Units ($90^\circ$ angle): Octahedral geometry.
    • 6 bonding pairs, 0 lone pairs: Octahedral shape ($\text{SF}_6$).
    • 5 bonding pairs, 1 lone pair: Distorted square pyramidal shape ($\text{XeOF}_4$).
    • 4 bonding pairs, 2 lone pairs: Square planar shape ($\text{XeF}_4$).

• Hybridization Model:

  • Mixing of atomic orbitals of different energies/shapes to yield equivalent hybrid orbitals.
  • $sp^3$ Hybridization: 1 $s$ + 3 $p$ orbitals $\rightarrow$ 4 $sp^3$ orbitals ($109^\circ 28'$ tetrahedral orientation; 25% $s$, 75% $p$ character).
  • $sp^2$ Hybridization: 1 $s$ + 2 $p$ orbitals $\rightarrow$ 3 $sp^2$ orbitals ($120^\circ$ trigonal planar orientation; 33.3% $s$, 66.7% $p$ character; 1 unhybridized $p$ orbital perpendicular to plane).
  • $sp$ Hybridization: 1 $s$ + 1 $p$ orbital $\rightarrow$ 2 $sp$ orbitals ($180^\circ$ linear orientation; 50% $s$, 50% $p$ character; 2 unhybridized $p$ orbitals perpendicular to each other).
  • Covalent Overlap Types:
  • $\sigma$ (sigma) bond: Formed by head-on/linear overlap of hybrid or atomic orbitals along the internuclear axis.
  • $\pi$ (pi) bond: Formed by lateral/sideways overlap of unhybridized parallel $p$ orbitals.
  • Double bond: Contains 1 $\sigma$ bond and 1 $\pi$ bond (e.g., $\text{C}_2\text{H}_4$).
  • Triple bond: Contains 1 $\sigma$ bond and 2 $\pi$ bonds (e.g., $\text{C}_2\text{H}_2$).

• Resonance & Resonance Hybrids:

  • Molecules represented by multiple valid Lewis structures with identical nuclear positioning but varying $\pi$ electron/lone pair positions.
  • Resonance hybrids represent the real, lowest-energy species with delocalized $\pi$ clouds (e.g., $\text{NO}_2^-, \text{NO}_3^-, \text{CO}_3^{2-}, \text{O}_3, \text{N}_2\text{O}$).

• Dipole Moment & Factors Affecting Electronegativity:

  • Dipole Moment ($\mu$): Vector quantity measuring molecular polarity. $\mu = \delta \times r$$\text{Units: } C\,m \text{ or Debye (D), where } 1\,\text{D} = 3.34 \times 10^{-30}\,\text{C\,m}$
  • Hierarchy of Factors Influencing Electronegativity:
  1. Hybridization: Higher $s$-character increases electronegativity ($sp > sp^2 > sp^3$).
  2. Charge: Positive charge increases electronegativity ($\text{N}^+ > \text{N} > \text{N}^-$).
  3. Oxidation Number: Higher positive oxidation state increases electronegativity ($\text{S(+6)} > \text{S(+4)} > \text{S(-2)}$).
  4. Environment/Attached Atoms: Electronegative attached atoms increase central atom electronegativity ($\text{C in CF}_4 > \text{C in CCl}_4$).

• Ionic Interactions & Polarization (Fajan's Principles):

  • Cation Polarizing Power: Ability of a small, highly charged cation to distort the electron cloud of an anion.
  • Anion Polarizability: Ease with which a large, highly charged anion's electron cloud is distorted.
  • Increased polarization increases covalent character and decreases ionic character.

• Metallic Bonding Model (Drude & Lorentz):

  • Cations in a delocalized sea of valence electrons. Strength depends on:
  • Number of valence electrons donated per atom.
  • Ionic radius of metal cation (smaller radius $\rightarrow$ higher electron cloud density $\rightarrow$ stronger bond).
  • Extent of valence electron release.

• Secondary (van der Waals) Intermolecular Interactions:

  • Ion - Dipole Interactions: Attraction between an ion and a polar molecule (e.g., hydrated $\text{Na}^+$ and $\text{Cl}^-$ in water).
  • Dipole - Dipole Interactions: Attractions between permanent dipoles ($0.5 - 15\,\text{kJ\,mol}^{-1}$, e.g., formaldehyde $\text{HCHO}$).
  • Hydrogen Bonding: Exceptionally strong dipole-dipole force ($4 - 40\,\text{kJ\,mol}^{-1}$) occurring when H is bonded to highly electronegative small atoms (N, O, F).
  • Ice Density Anomaly: Water forms 4 tetrahedral hydrogen bonds per molecule at $0^\circ\text{C}$, creating an open lattice structure that is $\approx 9\%$ less dense than liquid water.
  • Intermolecular (e.g., p-nitrophenol) vs. Intramolecular (e.g., o-nitrophenol).
  • Ion - Induced Dipole Interactions: An ion induces a dipole in a nonpolar molecule (e.g., $\text{I}^-$ induces dipole in $\text{I}_2$ forming $\text{I}_3^-$).
  • Dipole - Induced Dipole Interactions: Permanent dipole induces temporary dipole in nonpolar atom/molecule (proportional to $\frac{1}{r^6}$, e.g., $\text{HCl}$ and $\text{Ar}$).
  • London Dispersion Interactions: Instantaneous induced dipole-induced dipole forces present in all atoms/molecules. Surface area increases interaction magnitude (e.g., n-pentane BP $36^\circ\text{C}$ vs. spherical neo-pentane BP $9^\circ\text{C}$).

Chemical Calculations

• Rules for Assigning Oxidation Numbers:

  • Free elemental state atoms = 0.
  • Monoatomic ions = charge of the ion.
  • Fluorine = -1 in all compounds.
  • Oxygen = -2 (except in $\text{OF}_2$ where it is +2; peroxides $\text{O}_2^{2-}$ where it is -1; superoxides $\text{O}_2^-$ where it is -1/2).
  • Hydrogen = +1 (except in active metal hydrides like $\text{NaH}$ where it is -1).
  • Neutral molecule oxidation numbers sum to 0; polyatomic ions sum to ion charge.
  • Structural assignment: Heteronuclear covalent bonds assign $-1$ to the more electronegative atom and $+1$ to the less electronegative atom; homonuclear bonds assign 0.

• Redox Concepts:

  • Oxidation: Loss of electrons; increase in oxidation number.
  • Reduction: Gain of electrons; decrease in oxidation number.
  • Oxidizing Agent: Electron acceptor; undergoes reduction.
  • Reducing Agent: Electron donor; undergoes oxidation.

• Inorganic Nomenclature Rules (IUPAC):

  • Monoatomic Cations: Unmodified element name.
  • Monoatomic Anions: Element stem name + suffix -ide.
  • Variable Valence Cations: Stock system uses Roman numerals in parentheses indicating oxidation state (e.g., iron(II) $\text{Fe}^{2+}$, iron(III) $\text{Fe}^{3+}$).
  • Binary Covalent Compounds: Less electronegative element first; prefixes (mono-, di-, tri-, tetra-, penta-, hexa-, hepta-, octa-) define atom counts. Prefix mono- is omitted for the first element.
  • Oxoacids & Oxoanions:
  • Anion suffix -ate $\rightarrow$ Acid suffix -ic acid.
  • Anion suffix -ite $\rightarrow$ Acid suffix -ous acid.
  • Halo-oxoacids series: Hypochlorous acid ($\text{HClO}$, +1) $\rightarrow$ Chlorous acid ($\text{HClO}_2$, +3) $\rightarrow$ Chloric acid ($\text{HClO}_3$, +5) $\rightarrow$ Perchloric acid ($\text{HClO}_4$, +7).

• Mole Concept & Stoichiometric Quantities:

  • Avogadro Constant ($N_A$): $6.022 \times 10^{23}\,\text{mol}^{-1}$, defined as the number of entities in exactly $12\,\text{g}$ of $^{12}\text{C}$.
  • Molar Mass ($M$): Mass per mole of substance ($\text{g\,mol}^{-1}$).
  • Empirical Formula: Simplest whole-number ratio of atoms present in a compound.
  • Molecular Formula: Actual integral number of atoms in a molecule. $\text{Molecular Formula} = (\text{Empirical Formula})_n$$n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$

• Concentration Units & Mixture Expressions:

  • Mass Fraction ($w/w$), Volume Fraction ($v/v$), Mole Fraction ($x_A$): $x_A = \frac{n_A}{n_A + n_B + n_C + \dots}$
  • Mass Percent ($w/w$): $\text{Mass \%} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 100\%$
  • Parts per thousand (ppt): $\times 10^3$ ($\text{g\,kg}^{-1}$, $\text{mg\,g}^{-1}$).
  • Parts per million (ppm): $\times 10^6$ ($\text{mg\,kg}^{-1}$, $\mu\text{g\,g}^{-1}$, $\text{mg\,dm}^{-3}$).
  • Parts per billion (ppb): $\times 10^9$ ($\mu\text{g\,kg}^{-1}$, $\mu\text{g\,dm}^{-3}$).
  • Molality ($m$): $m = \frac{\text{Moles of Solute}}{\text{Mass of Solvent in kg}} \quad (\text{mol\,kg}^{-1})$
  • Molarity ($M$ or $c$): $M = \frac{\text{Moles of Solute}}{\text{Volume of Solution in dm}^3} \quad (\text{mol\,dm}^{-3})$

• Metric Prefixes:

  • Tera ($\text{T}$, $10^{12}$), Giga ($\text{G}$, $10^9$), Mega ($\text{M}$, $10^6$), Kilo ($\text{k}$, $10^3$), Hecto ($\text{h}$, $10^2$), Deca ($\text{da}$, $10^1$).
  • Deci ($\text{d}$, $10^{-1}$), Centi ($\text{c}$, $10^{-2}$), Milli ($\text{m}$, $10^{-3}$), Micro ($\mu$, $10^{-6}$), Nano ($\text{n}$, $10^{-9}$), Pico ($\text{p}$, $10^{-12}$).

• Balancing Chemical & Nuclear Equations:

  • Inspection Method: Balance atoms appearing in fewest species first.
  • Redox Balancing - Half-Reaction Method:
  1. Split into oxidation and reduction half-reactions.
  2. Balance non-O and non-H atoms.
  3. Add electrons ($e^-$) to balance oxidation numbers.
  4. Balance ionic charges using $\text{H}^+$ (acidic medium) or $\text{OH}^-$ (basic medium).
  5. Balance H and O using $\text{H}_2\text{O}$.
  6. Multiply half-reactions by integers to equalize electron loss/gain and combine.
  • Nuclear Reactions:
  • Sum of Mass Numbers ($A$) on reactant side = Sum of Mass Numbers ($A$) on product side.
  • Sum of Atomic Numbers ($Z$) on reactant side = Sum of Atomic Numbers ($Z$) on product side.
  • Particles: Alpha ($^4_2\alpha$ or $^4_2\text{He}$), Beta ($^0_{-1}\beta$ or $^0_{-1}\text{e}$), Gamma ($^0_0\gamma$), Proton ($^1_1\text{p}$), Neutron ($^1_0\text{n}$).

Chemistry of s, p and d Block Elements

• Group 1 Elements (Alkali Metals: Li, Na, K, Rb, Cs, Fr):
  • Valence configuration $ns^1$; oxidation state +1. Soft, low density, metallic lustre.
  • Reactivity increases down group as $I_1$ decreases.
  • Reactions:
  • Oxygen: $4\text{M} + \text{O}_2 \rightarrow 2\text{M}_2\text{O}$. Excess $\text{O}_2$ yields peroxides with Na ($\text{Na}_2\text{O}_2$) and superoxides with K, Rb, Cs ($\text{MO}_2$).
  • Nitrogen: Only Lithium forms stable nitride ($6\text{Li} + \text{N}_2 \rightarrow 2\text{Li}_3\text{N}$). $\text{Li}_3\text{N} + 3\text{H}_2\text{O} \rightarrow 3\text{LiOH} + \text{NH}_3$.
  • Water: Reactivity increases down group (Li slow, Na/K vigorous/ignition, Rb/Cs explosive). Yields \text{MOH} + \text{H}_2$.\n - Hydrogen: Forms ionic hydrides (2\text{M} + \text{H}_2 \rightarrow 2\text{MH}).\n - Thermal Stability:\n - Nitrates: 4\text{LiNO}_3 \rightarrow 2\text{Li}_2\text{O} + 4\text{NO}_2 + \text{O}_2$. Other nitrates yield nitrites:$2\text{MNO}_3 \rightarrow 2\text{MNO}_2 + \text{O}_2$.
  • Carbonates: Only $\text{Li}_2\text{CO}_3$ decomposes ($\text{Li}_2\text{CO}_3 \rightarrow \text{Li}_2\text{O} + \text{CO}_2$); others melt without decomposing.
  • Hydrogen Carbonates: 2\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$.\n - Flame Colors: Li (Red), Na (Yellow), K (Lilac), Rb (Red-violet), Cs (Blue-violet).\n\n- Group 2 Elements (Alkaline Earth Metals: Be, Mg, Ca, Sr, Ba, Ra):\n - Valence configuration ns^2; oxidation state +2. Higher density and melting point than Group 1.\n - Reactions:\n - Water: Be (no reaction with water; reacts with steam), Mg (negligible cold; slow hot; steam yields \text{MgO} + \text{H}2$), Ca, Sr, Ba react readily with cold water ($\text{M(OH)}_2 + \text{H}_2).\n - Oxygen: Forms MO$($Ba$forms peroxide$\text{BaO}_2$with excess$\text{O}_2).\n - Nitrogen: All burn in \text{N}_2$to form nitrides ($3\text{M} + \text{N}_2 \rightarrow \text{M}_3\text{N}_2).\n - Thermal Stability:\n - Nitrates: All yield oxide, \text{NO}_2$, and$\text{O}_2$($2\text{M(NO}_3)_2 \rightarrow 2\text{MO} + 4\text{NO}_2 + \text{O}_2).\n - Carbonates: Stability increases down group (\text{MgCO}_3$decomp$540^\circ\text{C}$;$\text{BaCO}_3$decomp$1360^\circ\text{C}) due to decreasing cation polarizing power.\n - Solubilities:\n - Hydroxides: Solubility increases down group (\text{Mg(OH)}_2$sparingly soluble;$\text{Ba(OH)}_2 soluble).\n - Sulfates, Carbonates, Chromates, Oxalates: Solubility decreases down group (\text{MgSO}_4$soluble;$\text{BaSO}_4 insoluble).\n - Flame Colors: Ca (Orange-red), Sr (Crimson red), Ba (Yellowish-green).\n\n- Group 13 Elements (B, Al, Ga, In, Tl):\n - Valence configuration ns^2 np^1; oxidation state +3.\n - Aluminum: Amphoteric metal. Protected by impermeable \text{Al}_2\text{O}_3 oxide surface layer.\n - Acid/Base Reactions:\n2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2\n2\text{Al} + 2\text{OH}^- + 6\text{H}_2\text{O} \rightarrow 2[\text{Al(OH)}_4]^- + 3\text{H}_2\n - Hydrolysis of \text{Al}^{3+} aquo complex:\n[\text{Al(H}_2\text{O)}_6]^{3+} + \text{H}_2\text{O} \rightleftharpoons [\text{Al(H}_2\text{O)}_5(\text{OH})]^{2+} + \text{H}_3\text{O}^+\n - Electron deficiency: Gaseous aluminum chloride forms dimers (\text{Al}_2\text{Cl}_6) with dative bonds.\n\n- Group 14 Elements (C, Si, Ge, Sn, Pb):\n - Allotropes of Carbon: Diamond (sp^3$, 3D tetrahedral network), Graphite ($sp^2$, planar layers held by dispersion forces, electrical conductor), Fullerenes ($\text{C}{60} bucky-balls).\n - Carbon Monoxide (CO): Neutral, poisonous gas; ligand with strong triple bond character (\text{C}\equiv\text{O}); powerful reducing agent in metallurgy.\n - Carbon Dioxide (\text{CO}2$): Acidic oxide; sublimes (dry ice); forms weak diprotic carbonic acid ($\text{H}_2\text{CO}_3) in water.\n\n- Group 15 Elements (N, P, As, Sb, Bi):\n - Nitrogen (\text{N}_2$): Unreactive due to strong$\text{N}\equiv\text{N}$triple bond ($942\,\text{kJ\,mol}^{-1}).\n - Nitrogen Oxides & Oxoacids:\n - Nitrous acid (\text{HNO}_2$): Weak, unstable acid; disproportionates ($3\text{HNO}_2 \rightarrow \text{HNO}_3 + 2\text{NO} + \text{H}_2\text{O}).\n - Nitric acid (\text{HNO}_3$): Strong acid and powerful oxidizing agent. Light-induced decomposition produces brown$\text{NO}_2$. Concentrated$\text{HNO}_3$reacts with metals (e.g., Cu yields$\text{NO}_2$; dil$8\text{HNO}_3$yields$\text{NO}$) and nonmetals (C yields$\text{CO}_2$; S yields$\text{H}_2\text{SO}_4).\n - Ammonia (\text{NH}_3) & Ammonium Salts:\n - Reaction with \text{Cl}_2$: Excess$\text{NH}_3$yields$\text{N}_2 + \text{NH}_4\text{Cl}$; excess$\text{Cl}_2$yields$\text{NCl}_3 + \text{HCl}.\n - Brown Ring Test for \text{NO}_3^-$: Forms brown complex$[\text{Fe(NO)}]^{2+}.\n\n- Group 16 Elements (O, S, Se, Te, Po):\n - Allotropes of Sulfur: Rhombic (\alpha$-$\text{S}_8$, stable below$95^\circ\text{C}$) and Monoclinic ($\beta$-$\text{S}_8$). Both consist of crown-shaped$\text{S}_8 rings.\n - Hydrogen Peroxide (\text{H}_2\text{O}_2$): Nonplanar open-book structure (dihedral angle$111.5^\circ). Acts as oxidizing agent, reducing agent, and undergoes disproportionation:\n2\text{H}_2\text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{O}_2\n - Oxoacids of Sulfur: \text{H}_2\text{SO}_4$(strong diprotic, dehydrating agent, hot conc. is oxidizing agent),$\text{H}_2\text{SO}_3$(weak),$\text{H}_2\text{S}_2\text{O}_3$(thiosulfuric acid;$\text{S}_2\text{O}_3^{2-}$reduces$\text{I}_2$to$\text{I}^-$forming tetrathionate$\text{S}_4\text{O}_6^{2-}).\n\n- Group 17 Elements (Halogens: F, Cl, Br, I, At):\n - Reactivity and oxidizing power decrease down group (\text{F}_2 > \text{Cl}_2 > \text{Br}_2 > \text{I}_2).\n - Hydrogen Halides: Acidic strength increases down group (\text{HF} < \text{HCl} < \text{HBr} < \text{HI}$). HF is a weak acid due to high bond dissociation energy ($570\,\text{kJ\,mol}^{-1}) and hydrogen bonding.\n - Silver Halides: \text{AgCl}$(white ppt, soluble in dil$\text{NH}_3$),$\text{AgBr}$(pale yellow ppt, soluble in conc$\text{NH}_3$),$\text{AgI}$(yellow ppt, insoluble in$\text{NH}_3).\n - Disproportionation of Chlorine:\n - In water: \text{Cl}_2 + \text{H}_2\text{O} \rightleftharpoons \text{HOCl} + \text{HCl}\n - In cold dil. \text{NaOH}$:$\text{Cl}_2 + 2\text{OH}^- \rightarrow \text{Cl}^- + \text{ClO}^- + \text{H}_2\text{O}\n - In hot conc. \text{NaOH}$:$3\text{Cl}_2 + 6\text{OH}^- \rightarrow 5\text{Cl}^- + \text{ClO}_3^- + 3\text{H}_2\text{O}\n\n- Group 18 Elements (Noble Gases: He, Ne, Ar, Kr, Xe, Rn):\n - Monatomic, unreactive gases with positive electron gain enthalpies. Xenon forms compounds in positive oxidation states (+2, +4, +6, +8) with fluorine and oxygen (\text{XeF}_2, \text{XeF}_4, \text{XeF}_6, \text{XeO}_3, \text{XeO}_4).\n\n- Periodic Trends Across Period 3 (\text{Na} \rightarrow \text{Ar}):\n - Oxides: \text{Na}_2\text{O}, \text{MgO} (basic, ionic) $\rightarrow\text{Al}_2\text{O}_3 (amphoteric, ionic/covalent) $\rightarrow\text{SiO}_2 (weakly acidic, network covalent) $\rightarrow\text{P}_4\text{O}{10}, \text{SO}_3, \text{Cl}_2\text{O}_7 (strongly acidic, covalent).\n - Hydroxides: \text{NaOH} (strongly basic) $\rightarrow\text{Mg(OH)}_2 (weakly basic) $\rightarrow\text{Al(OH)}_3 (amphoteric) $\rightarrow\text{H}_2\text{SiO}_3, \text{H}_3\text{PO}_4, \text{H}_2\text{SO}_4, \text{HClO}_4 (increasingly strong acids).\n - Halide Hydrolysis: \text{NaCl}, \text{MgCl}_2$dissolve without significant hydrolysis;$\text{AlCl}_3, \text{SiCl}_4, \text{PCl}_5, \text{SCl}_2 hydrolyze vigorously yielding acidic solutions.\n\n- Transition Elements (d-Block):\n - Definition: Elements possessing partially filled d$subshells in their elemental state or in at least one stable oxidation state. Scandium (Sc) is a transition metal; Zinc (Zn) is a non-transition element because its atom ($[\text{Ar}]3d^{10}4s^2$) and ion ($\text{Zn}^{2+}, [\text{Ar}]3d^{10}$) have completely filled$d subshells.\n - General Characteristics: Variable oxidation states (+2 common due to loss of 4s$electrons; max state =$4s + 3d$valence electrons), high melting/boiling points, catalytic activity, formation of paramagnetic species, and formation of colored complex ions via$d-d transitions or charge transfer.\n - Oxide Acid-Base Character:\n - Low oxidation states: Basic (e.g., \text{CrO}$,$\text{MnO}).\n - Intermediate oxidation states: Amphoteric (e.g., \text{Cr}_2\text{O}_3$,$\text{MnO}_2).\n - High oxidation states: Acidic (e.g., \text{CrO}_3$,$\text{Mn}_2\text{O}_7).\n - Chromate-Dichromate Equilibrium:\n2\text{CrO}_4^{2-} \text{ (yellow)} + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} \text{ (orange)} + \text{H}_2\text{O}\n - Redox Properties of \text{KMnO}_4:\n - Acidic medium: \text{MnO}_4^-$(purple) reduces to$\text{Mn}^{2+} (pale pink/colourless).\n - Neutral/alkaline medium: \text{MnO}_4^-$reduces to$\text{MnO}_2 (dark brown/black ppt).\n\n- Coordination Compounds & Complexes:\n - Complex Ion: Central metal cation surrounded by electron-donating molecules/ions called ligands via dative bonds.\n - Nomenclature Rules:\n - Ligand names: Anionic ligands end in **-o** (e.g., \text{Cl}^-$chlorido,$\text{CN}^-$cyanido,$\text{OH}^-$hydroxido); neutral ligands use molecular names ($\text{NH}_3$ammine,$\text{H}_2\text{O}$aqua,$\text{CO} carbonyl).\n - Anionic complexes end in **-ate** attached to metal root (e.g., cuprate, ferrate, cobaltate, chromate).\n - Oxidation state indicated by Roman numerals in parentheses.\n - Complex Colors and Reactions:\n - [\text{Fe(H}_2\text{O)}_6]^{3+}$: Yellow-brown solution; forms reddish-brown ppt$\text{Fe(OH)}_3$with$\text{OH}^-$or$\text{NH}_3.\n - [\text{Cu(H}_2\text{O)}_6]^{2+}$: Pale blue solution; forms blue ppt$\text{Cu(OH)}_2$with limited$\text{OH}^-$/$\text{NH}_3$; dissolves in excess$\text{NH}_3$to form deep blue$[\text{Cu(NH}_3)_4]^{2+}$; forms yellow$[\text{CuCl}_4]^{2-}$with conc.$\text{HCl}.\n - [\text{Co(H}_2\text{O)}_6]^{2+}$: Pink solution; forms blue$[\text{CoCl}_4]^{2-}$with conc.$\text{HCl}.\n - [\text{Ni(H}_2\text{O)}_6]^{2+}$: Green solution; forms blue$[\text{Ni(NH}_3)_6]^{2+}$with excess$\text{NH}_3.\n - Specific Cation Identification Tests:\n - \text{Fe}^{2+}$: Dark blue precipitate$\text{KFe[Fe(CN)}_6]$with$\text{K}_3[\text{Fe(CN)}_6].\n - \text{Fe}^{3+}$: Prussian blue precipitate$\text{Fe}_4[\text{Fe(CN)}_6]_3$with$\text{K}_4[\text{Fe(CN)}_6]$; deep red complex$[\text{Fe(SCN)(H}_2\text{O)}_5]^{2+}$with$\text{NH}_4\text{SCN}.\n - \text{Cr}^{3+}$: Reaction with excess$\text{NaOH}$and$\text{H}_2\text{O}_2$produces a yellow$\text{CrO}_4^{2-}$$ solution.