Plus One Chemistry

 

Unit 1: Some Basic Concepts of Chemistry

• Chemistry Definition: The science of molecules and their transformations. It studies the preparation, properties, structure, and reactions of material substances. It is also referred to as the science of atoms and molecules.
• Matter: Anything that possesses mass and occupies space.
  • States of Matter:
    • Solid: Possess definite volume and definite shape.
    • Liquid: Possess definite volume but not definite shape; they take the shape of their container.
    • Gas: Possess neither definite volume nor definite shape; they completely occupy the space of their container.
    • These three states are interconvertible by altering temperature and pressure.
  • Classification of Matter:
    • Pure Substances: Consist of particles that are the same in chemical nature.
      • Elements: Particles consist of only one type of atoms (e.g., sodium, hydrogen, oxygen).
      • Compounds: Formed when two or more atoms of different elements combine in a fixed and definite ratio. The properties of a compound are different from those of its constituent elements, and its constituents cannot be separated by physical methods.
    • Mixtures: Contain particles of two or more pure substances present in any ratio, thus having variable composition.
      • Homogeneous Mixtures: Components completely mix with each other, having a uniform composition throughout (e.g., sugar solution, air).
      • Heterogeneous Mixtures: Components do not completely mix with each other, leading to a non-uniform composition (e.g., sand and water).
• Properties of Matter:
  • Physical Properties: Can be measured or observed without changing the identity or composition of the substance (e.g., colour, odour, melting point, density).
  • Chemical Properties: Require a chemical change to occur for measurement or observation (e.g., combustibility, reactivity with acids and bases).
• Mass vs. Weight: Mass is the amount of matter present and is constant. Weight is the force exerted by gravity on an object and may vary due to changes in gravity.
• Volume: The amount of space occupied by a substance, with SI units of m³.
• Density: The mass per unit volume of a substance. Its SI unit is kg m⁻³.
• Temperature Scales: Celsius (°C), Fahrenheit (°F), and Kelvin (K), which is the SI unit. The relationship between Kelvin and Celsius is K = °C + 273.15.
• Scientific Notation: A method to represent very large or very small numbers in the form N × 10ⁿ, where N is a number between 1.000... and 9.999...
• Significant Figures: The meaningful digits in a measurement which are known with certainty plus one which is estimated or uncertain.
• Precision vs. Accuracy:
  • Precision: Refers to the closeness of various measurements for the same quantity.
  • Accuracy: Is the agreement of a particular value to the true value of the result.
• Dimensional Analysis: A method used to convert units from one system to another.
• Laws of Chemical Combination:
  • Law of Conservation of Mass: States that mass can neither be created nor destroyed in a chemical reaction.
  • Law of Definite Proportions: States that a given compound always contains exactly the same proportion of elements by weight.
  • Law of Multiple Proportions: States that if two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
  • Avogadro's Law: States that equal volumes of all gases at the same temperature and pressure should contain equal number of molecules.
• Dalton's Atomic Theory (1808): Proposed that matter consists of indivisible atoms; atoms of a given element have identical properties; compounds are formed when atoms of different elements combine in fixed ratios; chemical reactions involve the reorganisation of atoms.
• Atomic Mass Unit (amu or u): Defined as one-twelfth of the mass of one carbon-12 atom.
• Molecular Mass: The sum of atomic masses of the elements present in a molecule.
• Formula Mass: Used for ionic compounds (e.g., NaCl) where discrete molecules do not exist; it is the sum of atomic masses in the formula unit.
• Mole: The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. This number is known as the Avogadro constant (N_A), approximately 6.022 × 10²³.
• Molar Mass: The mass of one mole of a particular substance.
• Percentage Composition: Provides information regarding the percentage of a particular element present in a compound.
• Empirical Formula: Represents the simplest whole number ratio of various atoms present in a compound.
• Molecular Formula: Shows the exact number of different types of atoms present in a molecule of a compound.
• Stoichiometry: Deals with the calculation of masses (and sometimes volumes) of reactants and products involved in a chemical reaction.
• Limiting Reagent: The reactant which gets consumed first in a chemical reaction, thereby limiting the amount of product formed.
• Concentration of a Solution: Can be expressed in various ways when substances are present in solution:
  • Mass per cent (w/w %): (Mass of solute / Mass of solution) × 100.
  • Mole Fraction: Ratio of the number of moles of a particular component to the total number of moles of the solution.
  • Molarity (M): The number of moles of the solute in 1 litre of the solution. (Note: depends on temperature due to volume dependence).
  • Molality (m): The number of moles of solute present in 1 kg of solvent. (Note: does not change with temperature as mass is unaffected).

Exam-Oriented Questions & Answers (Unit 1)

• Q1: Distinguish between a homogeneous mixture and a heterogeneous mixture. Provide an example for each.
  • A1:
    • In a homogeneous mixture, the components completely mix with each other, meaning particles are uniformly distributed throughout the bulk, and its composition is uniform throughout. An example is sugar solution in water or air.
    • A heterogeneous mixture is one where the components do not completely mix with each other, leading to a non-uniform composition (e.g., sand and water).
• Q2: Explain what is meant by limiting reagent in a chemical reaction.
  • A2: In chemical reactions where reactants are present in amounts different from what a balanced chemical equation requires, the limiting reagent is the reactant that is present in the least amount and gets consumed first. Once the limiting reagent is used up, the reaction stops, and it determines the maximum amount of product that can be formed.

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Unit 2: Structure of Atom

This unit explores the composition of atoms, the models that describe their structure, and the quantum mechanical understanding of electron behaviour.

• Sub-atomic Particles: Atoms are composed of electrons, protons, and neutrons.
• Atomic Models:
  • Dalton's Atomic Theory: Matter consists of indivisible atoms.
  • Rutherford's Nuclear Model (1911):
    • Most of the positive charge and mass of an atom is concentrated in an extremely small region called the nucleus.
    • Electrons move around the nucleus in circular paths called orbits.
    • Electrons and the nucleus are held together by electrostatic forces of attraction.
    • Drawback: Failed to explain the stability of the atom, as orbiting electrons would continuously emit radiation and spiral into the nucleus.
  • Bohr's Model for Hydrogen Atom (1913):
    • Electrons revolve around the nucleus only in certain fixed circular paths called orbits or stationary states, each with a fixed radius and energy.
    • Electrons can move from a lower to a higher stationary state by absorbing a specific amount of energy, or from a higher to a lower state by emitting energy. The energy change is quantised, not continuous.
    • The angular momentum of an electron is quantised, being an integral multiple of h/2π.
    • Energy of a stationary state (for H-atom): Eₙ = –R_H (1/n²). (where R_H is Rydberg constant, 2.18 × 10⁻¹⁸ J).
    • Radius of an orbit (for H-atom): rₙ = n²a₀ (where a₀ = 52.9 pm).
    • Limitations: Could not explain the spectra of multi-electron atoms, the splitting of spectral lines in magnetic (Zeeman effect) or electric (Stark effect) fields, the dual behaviour of matter, or the Heisenberg uncertainty principle.
• Dual Behaviour of Matter (De Broglie, 1924): Proposed that matter, like radiation, exhibits both particle and wave-like properties. The wavelength (λ) associated with a particle of mass (m) and velocity (v) is given by λ = h/mv.
• Heisenberg's Uncertainty Principle (1927): States that it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron. Mathematically, ∆x ⋅ ∆pₓ ≥ h/4π. This implies that the path of an electron in an atom can never be determined accurately.
• Quantum Mechanical Model of Atom: Accounts for the dual behaviour of matter and is consistent with the uncertainty principle.
  • Schrödinger Equation: A fundamental equation in quantum mechanics, whose solution gives the possible energy levels an electron can occupy and their corresponding wave functions (ψ).
  • Atomic Orbital (ψ): The wave function for an electron in an atom. It has no physical meaning by itself.
  • Probability Density (|ψ|²): The square of the wave function (|ψ|²), which gives the probability of finding an electron at a point within an atom.
• Quantum Numbers: A set of four numbers that describe the properties of an electron in an atom.
  • Principal Quantum Number (n): Determines the size and, to a large extent, the energy of the orbital. It identifies the shell (K, L, M, N...). The total number of orbitals in a shell is n².
  • Azimuthal (or Orbital Angular Momentum) Quantum Number (l): Defines the three-dimensional shape of the orbital. It identifies the sub-shell (s, p, d, f...).
    • l = 0 corresponds to an s orbital (spherical shape).
    • l = 1 corresponds to p orbitals (dumbbell shape).
    • l = 2 corresponds to d orbitals.
  • Magnetic Orbital Quantum Number (m_l): Gives information about the spatial orientation of the orbital. For any sub-shell, there are (2l + 1) possible m_l values, hence (2l + 1) orbitals of that type.
  • Spin Quantum Number (m_s): Describes the orientation of the electron's intrinsic spin.
• Rules for Filling Orbitals:
  • Aufbau Principle: In the ground state of atoms, orbitals are filled in order of their increasing energies.
  • Pauli's Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. This means an orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.
  • Hund's Rule of Maximum Multiplicity: For orbitals belonging to the same subshell (degenerate orbitals), pairing of electrons does not take place until each orbital has got one electron each, and these singly occupied orbitals have parallel spins.
• Electronic Configuration: The distribution of electrons into orbitals of an atom.
• Stability of Completely Filled and Half-Filled Subshells: These configurations exhibit extra stability due to factors such as their symmetry, smaller coulombic repulsion energy, and larger exchange energy.

Exam-Oriented Questions & Answers (Unit 2)

• Q1: For an electron in a 3d orbital, what are the possible values for the principal quantum number (n), azimuthal quantum number (l), and magnetic orbital quantum number (m_l)?
  • A1:
    • n (Principal Quantum Number): For a 3d orbital, the principal quantum number is n = 3.
    • l (Azimuthal Quantum Number): For a d orbital, the azimuthal quantum number is l = 2.
    • m_l (Magnetic Orbital Quantum Number): For l = 2, the possible values for m_l are from -l to +l, which are -2, -1, 0, +1, +2.
• Q2: Describe the significance of the Rydberg constant in the context of the hydrogen spectrum.
  • A2: The Rydberg constant for hydrogen is a numerical value that, when used in the Rydberg expression, allows for the calculation of the wavenumbers (and thus wavelengths and frequencies) of all series of lines in the hydrogen spectrum. It quantitatively links the transitions of an electron between different energy levels in a hydrogen atom to the observed spectral lines.

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Unit 3: Classification of Elements and Periodicity in Properties

This unit discusses the historical development of the periodic table, its modern form, and the periodic trends observed in the physical and chemical properties of elements.

• Modern Periodic Law: The physical and chemical properties of the elements are periodic functions of their atomic numbers. This superseded Mendeleev's law, which was based on atomic mass.
• Periodic Table Structure:
  • Periods: The seven horizontal rows. The period number indicates the principal quantum number (n) of the outermost or valence shell.
  • Groups (or Families): The eighteen vertical columns. Elements within the same group typically have similar outer electronic configurations and thus exhibit similar chemical behaviour.
• Blocks of Elements: Classification based on the type of atomic orbital that receives the last electron.
  • s-Block Elements: Groups 1 (alkali metals) and 2 (alkaline earth metals), outer configuration ns¹ or ns². Highly reactive metals with low ionization enthalpies.
  • p-Block Elements: (Not fully detailed in excerpts, but typically Groups 13-18).
  • d-Block Elements (Transition Elements): (Not fully detailed in excerpts).
  • f-Block Elements (Inner-Transition Elements): Lanthanoids (4f series) and Actinoids (5f series), placed separately to maintain table structure.
• Types of Elements:
  • Metals: Comprise more than seventy-eight per cent of known elements. Generally located on the left and centre of the table. Tend to lose electrons.
  • Non-metals: Located at the top right, less than twenty in number. Tend to gain electrons.
  • Metalloids (Semi-metals): Elements that lie at the border line between metals and non-metals (e.g., Si, Ge, As).
• Periodic Trends in Physical Properties:
  • Atomic Radius:
    • Across a Period (left to right): Generally decreases due to increasing effective nuclear charge.
    • Down a Group (top to bottom): Generally increases due to increasing number of electron shells.
  • Ionic Radius: Cations are smaller than their parent atoms, and anions are larger than their parent atoms.
    • Isoelectronic Species: Ions/atoms with the same number of electrons (e.g., Na⁺, Mg²⁺, F⁻). For these, ionic radius decreases with increasing positive nuclear charge.
  • Ionization Enthalpy (∆ᵢH): The energy required to remove an electron from an isolated gaseous atom.
    • Across a Period: Generally increases.
    • Down a Group: Generally decreases.
  • Electron Gain Enthalpy (∆ₑgH): The enthalpy change when an electron is added to a gaseous atom.
    • Across a Period: Generally becomes more negative (greater electron affinity).
    • Down a Group: Generally becomes less negative.
  • Electronegativity: A qualitative measure of the ability of an atom in a chemical compound to attract shared electrons to itself.
    • Across a Period: Generally increases.
    • Down a Group: Generally decreases.
• Valence (or Oxidation States): Reflects the combining capacity of an element. For representative elements, it's often the number of valence electrons or eight minus this number.
• Periodic Trends in Chemical Reactivity:
  • Across a Period: Metallic character decreases and non-metallic character increases from left to right. Reactivity is highest at the two extremes (due to ease of electron loss/gain) and lowest in the centre.
  • Oxides:
    • Elements on the extreme left form the most basic oxides (e.g., Na₂O).
    • Elements on the extreme right form the most acidic oxides (e.g., Cl₂O₇).
    • Elements in the centre form amphoteric (behave as both acidic and basic, e.g., Al₂O₃) or neutral oxides (e.g., CO).

Exam-Oriented Questions & Answers (Unit 3)

• Q1: Explain why cations are smaller and anions are larger in radii than their parent atoms.
  • A1:
    • Cations are smaller than their parent atoms because when an atom loses one or more electrons to form a cation, the number of protons in the nucleus remains the same, but the number of electrons decreases. This leads to a stronger effective nuclear charge per electron, pulling the remaining electrons closer to the nucleus and reducing the ionic radius. Additionally, the removal of the outermost shell may occur.
    • Anions are larger than their parent atoms because when an atom gains one or more electrons to form an anion, the nuclear charge remains the same, but the electron-electron repulsion increases. This increased repulsion spreads the electron cloud further out, leading to a larger ionic radius compared to the neutral atom.
• Q2: How would you justify the presence of 18 elements in the 5th period of the Periodic Table?
  • A2: The 5th period corresponds to the principal quantum number n = 5. For n = 5, the possible values for the azimuthal quantum number (l) are 0, 1, 2, and 3, corresponding to 5s, 5p, 5d, and 5f subshells. However, according to the Aufbau principle, the order of filling energies in the 5th period for the available orbitals is 5s < 4d < 5p.
    • 5s subshell (l=0) has 1 orbital, accommodating 2 electrons.
    • 4d subshell (l=2) has 5 orbitals, accommodating 10 electrons.
    • 5p subshell (l=1) has 3 orbitals, accommodating 6 electrons.
    • The 5f orbitals are not filled in the 5th period.
    • Thus, the total number of electrons that can be accommodated in these orbitals (5s, 4d, 5p) is 2 + 10 + 6 = 18 electrons, which justifies the presence of 18 elements in the 5th period.

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Unit 4: Chemical Bonding and Molecular Structure

This unit delves into the fundamental principles that govern how atoms bond together to form molecules, exploring different types of bonds and theories that explain molecular geometry.

• Chemical Bond: The attractive force that holds various constituent atoms or ions together in different chemical species.
• Kössel-Lewis Approach: Atoms achieve stability by attaining a noble gas electron configuration (an octet of electrons in their valence shell) through transfer or sharing of electrons.
• Octet Rule: Atoms combine by gaining, losing, or sharing valence electrons to achieve eight electrons in their outermost shell.
• Types of Chemical Bonds:
  • Ionic (Electrovalent) Bond: Formed by the complete transfer of one or more valence electrons from one atom to another, resulting in the formation of positively and negatively charged ions, held together by strong electrostatic forces of attraction.
    • Formation depends on ionization enthalpy of metal, electron gain enthalpy of non-metal, and lattice enthalpy (energy released when gaseous ions combine to form a solid crystal lattice).
  • Covalent Bond: Formed by the mutual sharing of one or more pairs of electrons between two atoms.
    • Single Bond: Sharing one electron pair (e.g., Cl-Cl).
    • Double Bond: Sharing two electron pairs (e.g., C=O in CO₂).
    • Triple Bond: Sharing three electron pairs (e.g., N≡N in N₂).
• Limitations of the Octet Rule:
  • Incomplete Octet of the Central Atom: Cases where the central atom has less than eight electrons (e.g., LiCl, BeH₂, BCl₃).
  • Odd-electron Molecules: Molecules with an odd number of valence electrons (e.g., NO, NO₂).
  • Expanded Octet: Elements in or beyond the third period can have more than eight valence electrons around the central atom (e.g., PCl₅, SF₆, H₂SO₄).
  • It does not explain the relative stability or the geometry/shapes of molecules.
• Formal Charge: The charge assigned to an atom in a polyatomic molecule or ion, calculated as: (Total number of valence electrons in free atom) – (Total number of non-bonding electrons) – (1/2 * Total number of bonding electrons).
• Bond Parameters:
  • Bond Length: The equilibrium distance between the nuclei of two bonded atoms in a molecule.
  • Bond Angle: The angle between the orbitals containing bonding electron pairs around the central atom.
  • Bond Enthalpy: The amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state. Higher bond order generally means higher bond enthalpy.
  • Bond Order: The number of bonds between two atoms in a molecule.
• Resonance Structures (Canonical Forms): When a single Lewis structure cannot accurately describe a molecule (e.g., O₃, CO₃²⁻), a number of structures with similar energy, nuclei positions, and electron distribution are considered. These are called canonical forms or resonance structures, and the actual structure is a resonance hybrid of these forms. Resonance stabilises the molecule.
• Polarity of Bonds:
  • Polar Covalent Bond: Forms between atoms of different electronegativity, leading to unequal sharing of electrons and development of partial positive (δ⁺) and negative (δ⁻) charges.
  • Dipole Moment (μ): A measure of the polarity of a molecule, represented as a vector quantity. A molecule can have polar bonds but be non-polar overall if its geometry causes bond dipoles to cancel (e.g., CO₂, BF₃, CCl₄).
• Valence Shell Electron Pair Repulsion (VSEPR) Theory: Predicts the geometrical shapes of covalent molecules based on the principle that electron pairs (both bonding and lone pairs) in the valence shell repel each other and thus tend to arrange themselves as far apart as possible to minimise repulsion. The order of repulsion is LP-LP > LP-BP > BP-BP.
• Valence Bond (VB) Theory: Explains chemical bond formation based on the overlap of atomic orbitals. Greater overlap generally leads to a stronger bond.
  • Types of Overlapping:
    • Sigma (σ) Bond: Formed by end-to-end (axial) overlap of bonding orbitals along the internuclear axis (s-s, s-p, p-p overlaps). It is generally stronger than a pi bond.
    • Pi (π) Bond: Formed by sidewise (lateral) overlap of atomic orbitals whose axes are parallel to each other and perpendicular to the internuclear axis. It is generally weaker than a sigma bond.
• Hybridisation: The process of intermixing of atomic orbitals of slightly different energies to form a new set of equivalent hybrid orbitals of equivalent energies and shape. Hybrid orbitals are used in bond formation.
  • Conditions for Hybridisation: Orbitals in the valence shell are hybridised, they should have almost equal energy, promotion of electron is not essential, even filled orbitals can participate.
  • Types of Hybridisation: sp, sp², sp³, sp³d, sp³d², dsp², d²sp³.
    • sp Hybridisation: One s and one p orbital combine to form two equivalent sp hybrid orbitals (e.g., BeCl₂ linear geometry).
    • sp² Hybridisation: One s and two p orbitals combine to form three equivalent sp² hybrid orbitals (e.g., BCl₃ trigonal planar geometry).
    • sp³ Hybridisation: One s and three p orbitals combine to form four equivalent sp³ hybrid orbitals (e.g., CH₄ tetrahedral, NH₃ pyramidal, H₂O bent/V-shape).
• Molecular Orbital (MO) Theory (Hund and Mulliken, 1932):
  • Electrons in a molecule are present in molecular orbitals that are polycentric (influenced by two or more nuclei).
  • Molecular Orbitals (MOs) are formed by the linear combination of atomic orbitals (LCAO). The number of MOs formed equals the number of combining atomic orbitals.
  • Bonding Molecular Orbitals (BMOs): Have lower energy and greater stability than combining atomic orbitals; increase electron density between nuclei.
  • Antibonding Molecular Orbitals (ABMOs): Have higher energy and less stability; have a region of zero electron density (node) between nuclei.
  • MOs are filled according to Aufbau principle, Pauli's exclusion principle, and Hund's rule.
  • Bond Order (from MO theory): = (Number of electrons in BMOs - Number of electrons in ABMOs) / 2.
  • Magnetic Nature: If all electrons in MOs are paired, the substance is diamagnetic (repelled by magnetic field). If one or more MOs are singly occupied, it is paramagnetic (attracted by magnetic field).
• Hydrogen Bonding: A special type of dipole-dipole interaction. Occurs when a hydrogen atom covalently bonded to a highly electronegative atom (N, O, or F) forms an attractive interaction with another electronegative atom. It is weaker than a covalent bond.
  • Intermolecular Hydrogen Bond: Between different molecules (e.g., in HF, H₂O).
  • Intramolecular Hydrogen Bond: Within the same molecule (e.g., o-nitrophenol).

Exam-Oriented Questions & Answers (Unit 4)

• Q1: Predict the shape of the molecule SF₆ using VSEPR theory and identify any limitations of the octet rule in this molecule.
  • A1:
    • For SF₆, the central atom is Sulphur (S). In SF₆, Sulphur is bonded to six Fluorine atoms, and there are no lone pairs on the central sulphur atom (as sulphur forms an expanded octet).
    • According to VSEPR theory, if there are six electron pairs (all bonding pairs) around the central atom and no lone pairs, the electron pairs arrange themselves in an octahedral geometry.
    • Therefore, the shape of the SF₆ molecule is octahedral.
    • Octet Rule Limitation: In SF₆, the sulphur atom has 12 electrons in its valence shell (6 bonding pairs), which is more than the octet (8 electrons). This is an example of an expanded octet, which is a limitation of the octet rule.
• Q2: Distinguish between a sigma (σ) bond and a pi (π) bond.
  • A2:
    • Sigma (σ) Bond:
      • Formed by the end-to-end (head-on or axial) overlap of atomic orbitals along the internuclear axis.
      • Can be formed by s-s, s-p, or p-p overlapping.
      • It is generally stronger than a pi bond due to a larger extent of overlap.
      • Only one sigma bond can exist between any two atoms.
    • Pi (π) Bond:
      • Formed by the sidewise (lateral) overlap of atomic orbitals, where their axes are parallel to each other and perpendicular to the internuclear axis.
      • Always involves the overlap of p-orbitals (or d-orbitals in some cases).
      • It is generally weaker than a sigma bond due to a smaller extent of overlap.
      • In multiple bonds, one is a sigma bond, and the additional bonds are pi bonds (e.g., a double bond has one σ and one π, a triple bond has one σ and two π).

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Unit 5: States of Matter

This unit explores the microscopic and macroscopic properties of gases and liquids, focusing on intermolecular forces and the laws that govern their behaviour.

• Intermolecular Forces: Attractive and repulsive forces between interacting particles (atoms and molecules). These are distinct from intra-molecular forces (covalent bonds).
  • Van der Waals Forces: General term for various attractive intermolecular forces.
    • Dispersion Forces (London Forces): Weak, short-range attractive forces present in all atoms and molecules (polar or non-polar). Arise from instantaneous dipoles induced by temporary fluctuations in electron distribution.
    • Dipole-Dipole Forces: Attractive forces between molecules possessing permanent dipoles (polar molecules). Stronger than London forces but weaker than ion-ion interactions.
    • Dipole-Induced Dipole Forces: Attractive forces between a polar molecule (permanent dipole) and a non-polar molecule (where the permanent dipole induces a temporary dipole).
  • Hydrogen Bond: A special and particularly strong type of dipole-dipole interaction. Occurs when a hydrogen atom covalently bonded to a highly electronegative atom (N, O, F) interacts with another electronegative atom.
• Thermal Energy: The energy of a body arising from the motion of its atoms or molecules; directly proportional to temperature.
• States of Matter: Determined by the balance between intermolecular forces (tend to keep molecules together) and thermal energy (tend to keep them apart).
• Gaseous State: Characterised by high compressibility, uniform pressure exertion, low density, indefinite volume and shape, and complete mixing. This simplicity is due to negligible intermolecular forces.
• Gas Laws: Describe relationships between measurable properties of gases (pressure (p), volume (V), temperature (T), number of moles (n)).
  • Boyle's Law (p-V relationship): At constant temperature (T) and number of moles (n), the pressure of a fixed amount of gas is inversely proportional to its volume. Mathematically: p₁V₁ = p₂V₂ = constant.
  • Charles's Law (V-T relationship): At constant pressure (p) and number of moles (n), the volume of a fixed mass of gas is directly proportional to its absolute temperature (Kelvin). Mathematically: V₁/T₁ = V₂/T₂ = constant.
    • Absolute Zero: The lowest hypothetical temperature (-273.15 °C) at which gases are theorised to occupy zero volume. The Kelvin scale (Absolute temperature scale) is based on this concept, where K = °C + 273.15.
  • Gay-Lussac's Law (p-T relationship): At constant volume (V) and number of moles (n), the pressure of a fixed amount of gas is directly proportional to its absolute temperature (Kelvin).
  • Avogadro's Law (V-n relationship): At constant temperature (T) and pressure (p), equal volumes of all gases contain equal numbers of molecules. This implies that the volume of a gas is directly proportional to the number of moles (n).
• Ideal Gas Equation: Combines Boyle's, Charles's, and Avogadro's laws into a single equation: pV = nRT.
  • R: The gas constant (or Universal Gas Constant), whose value depends on the units of p, V, and T. (e.g., 8.314 J K⁻¹ mol⁻¹).
  • Combined Gas Law: If the state of a fixed amount of gas changes from (p₁, V₁, T₁) to (p₂, V₂, T₂), then p₁V₁/T₁ = p₂V₂/T₂.
• Dalton's Law of Partial Pressures: The total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of the individual gases.
  • Partial Pressure (p_i): The pressure exerted by an individual gas in a mixture. p_i = x_i ⋅ p_total (where x_i is the mole fraction of gas i).
  • Aqueous Tension: The pressure exerted by saturated water vapour.
• Kinetic Molecular Theory of Gases: A theoretical model based on assumptions to explain gas behaviour.
  • Gases consist of many identical, small particles far apart, so their actual volume is negligible compared to the empty space.
  • There are no intermolecular forces of attraction between gas molecules.
  • Particles are in constant, random motion.
  • Collisions between particles and with container walls are perfectly elastic.
  • The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
• Real Gases: Gases that deviate from ideal behaviour, particularly at high pressures and low temperatures.
  • Reasons for Deviation: The two assumptions of kinetic theory (negligible molecular volume and no intermolecular forces) are not entirely true for real gases.
  • Van der Waals Equation: A modified ideal gas equation that accounts for these deviations: (p + an²/V²)(V - nb) = nRT.
    • 'a' (constant): Accounts for the intermolecular attractive forces.
    • 'b' (constant): Accounts for the volume occupied by the gas molecules themselves.
  • Compressibility Factor (Z): A measure of deviation from ideal behaviour. Z = pV / nRT. For an ideal gas, Z = 1. For real gases, Z deviates from unity.
• Liquefaction of Gases: The process of converting a gas into a liquid.
  • Critical Temperature (T_c): The temperature above which a gas cannot be liquefied, regardless of the pressure applied.
  • Critical Pressure (P_c): The minimum pressure required to liquefy a gas at its critical temperature.
  • Vapour: A gas existing below its critical temperature.
• Properties of Liquids:
  • Vapour Pressure: The pressure exerted by the vapour in equilibrium with its liquid phase at a given temperature.
  • Surface Tension (γ): The force acting per unit length perpendicular to a line drawn on the surface of a liquid. It causes liquids to minimise their surface area, leading to spherical drops.
  • Viscosity (η): A measure of a liquid's resistance to flow.

Exam-Oriented Questions & Answers (Unit 5)

• Q1: A gas occupies 600 mL at 25 °C and 760 mm of Hg pressure. What will be its pressure at a height where the temperature is 10 °C and the volume of the gas is 640 mL?
  • A1: This problem involves changes in pressure, volume, and temperature, so we use the Combined Gas Law: p₁V₁/T₁ = p₂V₂/T₂.
    • Convert temperatures to Kelvin:
      • T₁ = 25 °C + 273 = 298 K
      • T₂ = 10 °C + 273 = 283 K
    • Given: p₁ = 760 mm Hg, V₁ = 600 mL, T₁ = 298 K, V₂ = 640 mL, T₂ = 283 K.
    • Rearrange the formula to solve for p₂: p₂ = (p₁V₁T₂) / (V₂T₁)
    • p₂ = (760 mm Hg × 600 mL × 283 K) / (640 mL × 298 K)
    • p₂ = 676.6 mm Hg.
• Q2: Explain the concept of critical temperature (T_c) and how it relates to the liquefaction of gases.
  • A2: The critical temperature (T_c) is the temperature above which a gas cannot be liquefied, no matter how high the pressure applied.
    • Below its critical temperature, a gas can be liquefied by simply applying sufficient pressure, and in this state, it is often referred to as a vapour.
    • Above T_c, the thermal energy of the gas molecules is too high to be overcome by intermolecular attractive forces, preventing their compression into a liquid state, regardless of pressure. This concept is crucial in industrial processes for gas liquefaction.

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Unit 6: Thermodynamics

This unit introduces the principles of thermodynamics, focusing on energy changes in chemical and physical processes, and the concepts of spontaneity and equilibrium.

• Thermodynamics: The study of energy transformations in macroscopic systems, concerned with the initial and final states of a system undergoing change.
• Thermodynamic Terms:
  • System: The part of the universe under observation.
  • Surroundings: Everything else in the universe that can interact with the system.
  • Boundary: Separates the system from the surroundings.
• Types of Systems:
  • Open System: Exchanges both energy and matter with the surroundings.
  • Closed System: Exchanges energy but not matter with the surroundings.
  • Isolated System: Exchanges neither energy nor matter with the surroundings.
• State Function (or State Variable): A property of the system whose value depends only on the current state of the system, irrespective of the path taken to reach that state (e.g., internal energy (U), enthalpy (H), entropy (S), Gibbs energy (G), pressure (p), volume (V), temperature (T)).
• Internal Energy (U): The total energy contained within a system (sum of all forms of energy). Only changes in internal energy (∆U) can be measured.
• Work (w): Energy transfer resulting from organised motion; in chemistry, often pressure-volume (pV) work.
  • Sign Convention: w > 0 when work is done on the system (compression). w < 0 when work is done by the system (expansion).
• Heat (q): Energy transfer due to a temperature difference between the system and surroundings.
  • Sign Convention: q > 0 when heat is absorbed by the system (endothermic). q < 0 when heat is released by the system (exothermic).
• First Law of Thermodynamics: States that energy can neither be created nor destroyed. Mathematically: ∆U = q + w. For an isolated system, ∆U = 0, meaning its energy is constant.
• Adiabatic Process: A process where no heat (q=0) is exchanged between the system and surroundings.
• Isothermal Process: A process occurring at constant temperature (∆T=0). For an ideal gas, ∆U = 0 for an isothermal process.
• Reversible Process: A process that occurs infinitely slowly through a series of equilibrium states and can be reversed by an infinitesimal change.
• Enthalpy (H): A thermodynamic state function defined as H = U + pV. The heat absorbed or released at constant pressure (q_p) is equal to the change in enthalpy (∆H).
  • ∆H = q_p.
  • Exothermic Reaction: Releases heat, ∆H is negative.
  • Endothermic Reaction: Absorbs heat, ∆H is positive.
  • Relationship between ∆H and ∆U: ∆H = ∆U + ∆n_gRT, where ∆n_g is the change in the number of moles of gaseous products minus gaseous reactants.
• Extensive Property: Depends on the quantity of matter in the system (e.g., mass, volume, internal energy, enthalpy).
• Intensive Property: Does not depend on the quantity of matter (e.g., temperature, density, pressure, molar heat capacity).
• Heat Capacity (C): The quantity of heat required to raise the temperature of a substance by one degree.
  • Specific Heat (c): Heat capacity per unit mass.
  • Molar Heat Capacity (C_m): Heat capacity per mole.
  • Relationship between C_p and C_V (for ideal gas): C_p - C_V = R.
• Calorimetry: Experimental technique to measure heat changes (q_V or q_p).
  • Bomb Calorimeter: Used to measure ∆U (heat at constant volume), typically for combustion reactions.
• Standard Enthalpy of Reaction (∆ᵣH⁰): The enthalpy change for a reaction when all participating substances are in their standard states (pure form at 1 bar pressure, usually 298 K).
  • Standard Enthalpy of Formation (∆_f_H⁰): The enthalpy change when one mole of a compound is formed from its elements in their most stable states of aggregation at standard conditions. By convention, ∆_f_H⁰ of an element in its standard state is zero.
• Hess's Law of Constant Heat Summation: If a reaction takes place in several steps, its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions. It is a consequence of enthalpy being a state function.
• Bond Enthalpy (∆_bond_H⁰): The energy required to break one mole of a specific type of bond in the gaseous state.
• Lattice Enthalpy (∆_lattice_H⁰): The enthalpy change when one mole of an ionic compound dissociates into its gaseous ions.
• Spontaneity: A process is spontaneous if it proceeds without the assistance of an external agency. Spontaneous processes are irreversible.
  • Entropy (S): A thermodynamic function that measures the degree of randomness or disorder in a system. The greater the disorder in an isolated system, the higher the entropy.
    • Second Law of Thermodynamics: States that for a spontaneous process, the total entropy of the system and surroundings (∆S_total) always increases (∆S_total > 0).
    • Third Law of Thermodynamics: States that the entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero (0 K).
  • Gibbs Energy (G) or Gibbs Function: A thermodynamic state function defined as G = H - TS. It represents the net energy available to do useful work.
    • Gibbs Equation: ∆G = ∆H - T∆S.
    • Criteria for Spontaneity (at constant T and P):
      • If ∆G < 0: The process is spontaneous.
      • If ∆G > 0: The process is non-spontaneous (the reverse process is spontaneous).
      • If ∆G = 0: The system is at equilibrium.
• Gibbs Energy and Equilibrium Constant (K): The standard Gibbs energy change (∆G⁰) is related to the equilibrium constant (K) by the equation: ∆G⁰ = -RT ln K or ∆G⁰ = -2.303 RT log K.

Exam-Oriented Questions & Answers (Unit 6)

• Q1: Distinguish between extensive and intensive properties in thermodynamics, providing two examples for each.
  • A1:
    • Extensive properties are those whose values depend on the quantity or size of matter present in the system. Examples include mass, volume, internal energy (U), and enthalpy (H).
    • Intensive properties are those whose values do not depend on the quantity or size of matter present. Examples include temperature, density, pressure, and molar heat capacity.
• Q2: Calculate the change in internal energy (∆U) for the process when 1 mole of water is vaporised at 1 bar pressure and 100 °C, given that the molar enthalpy change for vaporisation (∆_vap_H⁰) is 41 kJ mol⁻¹. Assume water vapour behaves as a perfect gas.
  • A2: The vaporisation process is: H₂O(l) → H₂O(g).
    • We use the relation: ∆H = ∆U + ∆n_gRT.
    • Given: ∆_vap_H⁰ = 41 kJ mol⁻¹ = 41000 J mol⁻¹.
    • For the reaction, ∆n_g = (moles of gaseous products) - (moles of gaseous reactants) = 1 mole (H₂O(g)) - 0 moles (H₂O(l)) = 1 mole.
    • Temperature T = 100 °C + 273.15 = 373.15 K.
    • Gas constant R = 8.314 J K⁻¹ mol⁻¹.
    • Rearrange the equation to solve for ∆U: ∆U = ∆H - ∆n_gRT
    • ∆U = 41000 J mol⁻¹ - (1 mol × 8.314 J K⁻¹ mol⁻¹ × 3 

     

     

    • Chemistry Definition: The science of molecules and their transformations. It studies the preparation, properties, structure, and reactions of material substances. It is also referred to as the science of atoms and molecules.
    • Matter: Anything that possesses mass and occupies space.
        ◦ States of Matter:
            ▪ Solid: Possess definite volume and definite shape.
            ▪ Liquid: Possess definite volume but not definite shape; they take the shape of their container.
            ▪ Gas: Possess neither definite volume nor definite shape; they completely occupy the space of their container.
            ▪ These three states are interconvertible by altering temperature and pressure.
        ◦ Classification of Matter:
            ▪ Pure Substances: Consist of particles that are the same in chemical nature.
                • Elements: Particles consist of only one type of atoms (e.g., sodium, hydrogen, oxygen).
                • Compounds: Formed when two or more atoms of different elements combine in a fixed and definite ratio. The properties of a compound are different from those of its constituent elements, and its constituents cannot be separated by physical methods.
            ▪ Mixtures: Contain particles of two or more pure substances present in any ratio, thus having variable composition.
                • Homogeneous Mixtures: Components completely mix with each other, having a uniform composition throughout (e.g., sugar solution, air).
                • Heterogeneous Mixtures: (Implied as the opposite of homogeneous).
    • Properties of Matter:
        ◦ Physical Properties: Can be measured or observed without changing the identity or composition of the substance (e.g., colour, odour, melting point, density).
        ◦ Chemical Properties: Require a chemical change to occur for measurement or observation (e.g., combustibility, reactivity with acids and bases).
    • Mass vs. Weight: Mass is the amount of matter present and is constant. Weight is the force exerted by gravity on an object and may vary due to changes in gravity.
    • Volume: The amount of space occupied by a substance, with SI units of m³.
    • Density: The mass per unit volume of a substance. Its SI unit is kg m⁻³.
    • Temperature Scales: Celsius (°C), Fahrenheit (°F), and Kelvin (K), which is the SI unit. The relationship between Kelvin and Celsius is K = °C + 273.15.
    • Scientific Notation: A method to represent very large or very small numbers in the form N × 10ⁿ, where N is a number between 1.000... and 9.999....
    • Significant Figures: The meaningful digits in a measurement which are known with certainty plus one which is estimated or uncertain.
    • Precision vs. Accuracy:
        ◦ Precision: Refers to the closeness of various measurements for the same quantity.
        ◦ Accuracy: Is the agreement of a particular value to the true value of the result.
    • Dimensional Analysis: A method used to convert units from one system to another.
    • Laws of Chemical Combination:
        ◦ Law of Conservation of Mass: States that mass can neither be created nor destroyed in a chemical reaction.
        ◦ Law of Definite Proportions: States that a given compound always contains exactly the same proportion of elements by weight.
        ◦ Law of Multiple Proportions: States that if two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
        ◦ Avogadro's Law: States that equal volumes of all gases at the same temperature and pressure should contain equal number of molecules.
    • Dalton's Atomic Theory (1808): Proposed that matter consists of indivisible atoms; atoms of a given element have identical properties; compounds are formed when atoms of different elements combine in fixed ratios; chemical reactions involve the reorganisation of atoms.
    • Atomic Mass Unit (amu or u): Defined as one-twelfth of the mass of one carbon-12 atom.
    • Molecular Mass: The sum of atomic masses of the elements present in a molecule.
    • Formula Mass: Used for ionic compounds (e.g., NaCl) where discrete molecules do not exist; it is the sum of atomic masses in the formula unit.
    • Mole: The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. This number is known as the Avogadro constant (N_A), approximately 6.022 × 10²³.
    • Molar Mass: The mass of one mole of a particular substance.
    • Percentage Composition: Provides information regarding the percentage of a particular element present in a compound.
    • Empirical Formula: Represents the simplest whole number ratio of various atoms present in a compound.
    • Molecular Formula: Shows the exact number of different types of atoms present in a molecule of a compound.
    • Stoichiometry: Deals with the calculation of masses (and sometimes volumes) of reactants and products involved in a chemical reaction.
    • Limiting Reagent: The reactant which gets consumed first in a chemical reaction, thereby limiting the amount of product formed.
    • Concentration of a Solution: Can be expressed in various ways when substances are present in solution:
        ◦ Mass per cent (w/w %): (Mass of solute / Mass of solution) × 100.
        ◦ Mole Fraction: Ratio of the number of moles of a particular component to the total number of moles of the solution.
        ◦ Molarity (M): The number of moles of the solute in 1 litre of the solution. (Note: depends on temperature due to volume dependence).
        ◦ Molality (m): The number of moles of solute present in 1 kg of solvent. (Note: does not change with temperature as mass is unaffected).
    Exam-Oriented Questions & Answers (Unit 1)
    • Q1: Distinguish between a homogeneous mixture and a heterogeneous mixture. Provide an example for each.
        ◦ A1:
            ▪ In a homogeneous mixture, the components completely mix with each other, meaning particles are uniformly distributed throughout the bulk, and its composition is uniform throughout. An example is sugar solution in water or air.
            ▪ A heterogeneous mixture is one where the components do not completely mix with each other, leading to a non-uniform composition (e.g., sand and water).
    • Q2: Explain what is meant by limiting reagent in a chemical reaction.
        ◦ A2: In chemical reactions where reactants are present in amounts different from what a balanced chemical equation requires, the limiting reagent is the reactant that is present in the least amount and gets consumed first. Once the limiting reagent is used up, the reaction stops, and it determines the maximum amount of product that can be formed.
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    Unit 2: Structure of Atom
    This unit explores the composition of atoms, the models that describe their structure, and the quantum mechanical understanding of electron behaviour.
    • Sub-atomic Particles: Atoms are composed of electrons, protons, and neutrons.
    • Atomic Models:
        ◦ Dalton's Atomic Theory: Matter consists of indivisible atoms.
        ◦ Rutherford's Nuclear Model (1911):
            ▪ Most of the positive charge and mass of an atom is concentrated in an extremely small region called the nucleus.
            ▪ Electrons move around the nucleus in circular paths called orbits.
            ▪ Electrons and the nucleus are held together by electrostatic forces of attraction.
            ▪ Drawback: Failed to explain the stability of the atom, as orbiting electrons would continuously emit radiation and spiral into the nucleus.
        ◦ Bohr's Model for Hydrogen Atom (1913):
            ▪ Electrons revolve around the nucleus only in certain fixed circular paths called orbits or stationary states, each with a fixed radius and energy.
            ▪ Electrons can move from a lower to a higher stationary state by absorbing a specific amount of energy, or from a higher to a lower state by emitting energy. The energy change is quantised, not continuous.
            ▪ The angular momentum of an electron is quantised, being an integral multiple of h/2π.
            ▪ Energy of a stationary state (for H-atom): Eₙ = –R_H (1/n²). (where R_H is Rydberg constant, 2.18 × 10⁻¹⁸ J).
            ▪ Radius of an orbit (for H-atom): rₙ = n²a₀ (where a₀ = 52.9 pm).
            ▪ Limitations: Could not explain the spectra of multi-electron atoms, the splitting of spectral lines in magnetic (Zeeman effect) or electric (Stark effect) fields, the dual behaviour of matter, or the Heisenberg uncertainty principle.
    • Dual Behaviour of Matter (De Broglie, 1924): Proposed that matter, like radiation, exhibits both particle and wave-like properties. The wavelength (λ) associated with a particle of mass (m) and velocity (v) is given by λ = h/mv.
    • Heisenberg's Uncertainty Principle (1927): States that it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron. Mathematically, ∆x ⋅ ∆pₓ ≥ h/4π. This implies that the path of an electron in an atom can never be determined accurately.
    • Quantum Mechanical Model of Atom: Accounts for the dual behaviour of matter and is consistent with the uncertainty principle.
        ◦ Schrödinger Equation: A fundamental equation in quantum mechanics, whose solution gives the possible energy levels an electron can occupy and their corresponding wave functions (ψ).
        ◦ Atomic Orbital (ψ): The wave function for an electron in an atom. It has no physical meaning by itself.
        ◦ Probability Density (|ψ|²): The square of the wave function (|ψ|²), which gives the probability of finding an electron at a point within an atom.
    • Quantum Numbers: A set of four numbers that describe the properties of an electron in an atom.
        ◦ Principal Quantum Number (n): (n = 1, 2, 3...) Determines the size and, to a large extent, the energy of the orbital. It identifies the shell (K, L, M, N...). The total number of orbitals in a shell is n².
        ◦ Azimuthal (or Orbital Angular Momentum) Quantum Number (l): (l = 0, 1, ..., n-1) Defines the three-dimensional shape of the orbital. It identifies the sub-shell (s, p, d, f...).
            ▪ l = 0 corresponds to an s orbital (spherical shape).
            ▪ l = 1 corresponds to p orbitals (dumbbell shape).
            ▪ l = 2 corresponds to d orbitals.
        ◦ Magnetic Orbital Quantum Number (m_l): (m_l = -l, ..., 0, ..., +l) Gives information about the spatial orientation of the orbital. For any sub-shell, there are (2l + 1) possible m_l values, hence (2l + 1) orbitals of that type.
        ◦ Spin Quantum Number (m_s): (+½ or -½) Describes the orientation of the electron's intrinsic spin.
    • Rules for Filling Orbitals:
        ◦ Aufbau Principle: In the ground state of atoms, orbitals are filled in order of their increasing energies.
        ◦ Pauli's Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. This means an orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.
        ◦ Hund's Rule of Maximum Multiplicity: For orbitals belonging to the same subshell (degenerate orbitals), pairing of electrons does not take place until each orbital has got one electron each, and these singly occupied orbitals have parallel spins.
    • Electronic Configuration: The distribution of electrons into orbitals of an atom.
    • Stability of Completely Filled and Half-Filled Subshells: These configurations exhibit extra stability due to factors such as their symmetry, smaller coulombic repulsion energy, and larger exchange energy.
    Exam-Oriented Questions & Answers (Unit 2)
    • Q1: For an electron in a 3d orbital, what are the possible values for the principal quantum number (n), azimuthal quantum number (l), and magnetic orbital quantum number (m_l)?
        ◦ A1:
            ▪ n (Principal Quantum Number): For a 3d orbital, the principal quantum number is n = 3.
            ▪ l (Azimuthal Quantum Number): For a d orbital, the azimuthal quantum number is l = 2.
            ▪ m_l (Magnetic Orbital Quantum Number): For l = 2, the possible values for m_l are from -l to +l, which are -2, -1, 0, +1, +2.
    • Q2: Describe the significance of the Rydberg constant in the context of the hydrogen spectrum.
        ◦ A2: The Rydberg constant for hydrogen (109,677 cm⁻¹) is a numerical value that, when used in the Rydberg expression, allows for the calculation of the wavenumbers (and thus wavelengths and frequencies) of all series of lines in the hydrogen spectrum. It quantitatively links the transitions of an electron between different energy levels (n₁ and n₂) in a hydrogen atom to the observed spectral lines.
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    Unit 3: Classification of Elements and Periodicity in Properties
    This unit discusses the historical development of the periodic table, its modern form, and the periodic trends observed in the physical and chemical properties of elements.
    • Modern Periodic Law: The physical and chemical properties of the elements are periodic functions of their atomic numbers. This superseded Mendeleev's law, which was based on atomic mass.
    • Periodic Table Structure:
        ◦ Periods: The seven horizontal rows. The period number indicates the principal quantum number (n) of the outermost or valence shell.
        ◦ Groups (or Families): The eighteen vertical columns. Elements within the same group typically have similar outer electronic configurations and thus exhibit similar chemical behaviour.
    • Blocks of Elements: Classification based on the type of atomic orbital that receives the last electron.
        ◦ s-Block Elements: Groups 1 (alkali metals) and 2 (alkaline earth metals), outer configuration ns¹ or ns². Highly reactive metals with low ionization enthalpies.
        ◦ p-Block Elements: (Not fully detailed in excerpts, but typically Groups 13-18).
        ◦ d-Block Elements (Transition Elements): (Not fully detailed in excerpts).
        ◦ f-Block Elements (Inner-Transition Elements): Lanthanoids (4f series) and Actinoids (5f series), placed separately to maintain table structure.
    • Types of Elements:
        ◦ Metals: Comprise more than seventy-eight per cent of known elements. Generally located on the left and centre of the table. Tend to lose electrons.
        ◦ Non-metals: Located at the top right, less than twenty in number. Tend to gain electrons.
        ◦ Metalloids (Semi-metals): Elements that lie at the border line between metals and non-metals (e.g., Si, Ge, As).
    • Periodic Trends in Physical Properties:
        ◦ Atomic Radius:
            ▪ Across a Period (left to right): Generally decreases due to increasing effective nuclear charge.
            ▪ Down a Group (top to bottom): Generally increases due to increasing number of electron shells.
        ◦ Ionic Radius: Cations are smaller than their parent atoms, and anions are larger than their parent atoms.
            ▪ Isoelectronic Species: Ions/atoms with the same number of electrons (e.g., Na⁺, Mg²⁺, F⁻). For these, ionic radius decreases with increasing positive nuclear charge.
        ◦ Ionization Enthalpy (∆ᵢH): The energy required to remove an electron from an isolated gaseous atom.
            ▪ Across a Period: Generally increases.
            ▪ Down a Group: Generally decreases.
        ◦ Electron Gain Enthalpy (∆ₑgH): The enthalpy change when an electron is added to a gaseous atom.
            ▪ Across a Period: Generally becomes more negative (greater electron affinity).
            ▪ Down a Group: Generally becomes less negative.
        ◦ Electronegativity: A qualitative measure of the ability of an atom in a chemical compound to attract shared electrons to itself.
            ▪ Across a Period: Generally increases.
            ▪ Down a Group: Generally decreases.
    • Valence (or Oxidation States): Reflects the combining capacity of an element. For representative elements, it's often the number of valence electrons or eight minus this number.
    • Periodic Trends in Chemical Reactivity:
        ◦ Across a Period: Metallic character decreases and non-metallic character increases from left to right. Reactivity is highest at the two extremes (due to ease of electron loss/gain) and lowest in the centre.
        ◦ Oxides:
            ▪ Elements on the extreme left form the most basic oxides (e.g., Na₂O).
            ▪ Elements on the extreme right form the most acidic oxides (e.g., Cl₂O₇).
            ▪ Elements in the centre form amphoteric (behave as both acidic and basic, e.g., Al₂O₃) or neutral oxides (e.g., CO).
    Exam-Oriented Questions & Answers (Unit 3)
    • Q1: Explain why cations are smaller and anions are larger in radii than their parent atoms.
        ◦ A1:
            ▪ Cations are smaller than their parent atoms because when an atom loses one or more electrons to form a cation, the number of protons in the nucleus remains the same, but the number of electrons decreases. This leads to a stronger effective nuclear charge per electron, pulling the remaining electrons closer to the nucleus and reducing the ionic radius. Additionally, the removal of the outermost shell may occur.
            ▪ Anions are larger than their parent atoms because when an atom gains one or more electrons to form an anion, the nuclear charge remains the same, but the electron-electron repulsion increases. This increased repulsion spreads the electron cloud further out, leading to a larger ionic radius compared to the neutral atom.
    • Q2: How would you justify the presence of 18 elements in the 5th period of the Periodic Table?
        ◦ A2: The 5th period corresponds to the principal quantum number n = 5. For n = 5, the possible values for the azimuthal quantum number (l) are 0, 1, 2, and 3, corresponding to 5s, 5p, 5d, and 5f subshells. However, according to the Aufbau principle, the order of filling energies in the 5th period for the available orbitals is 5s < 4d < 5p.
            ▪ 5s subshell (l=0) has 1 orbital, accommodating 2 electrons.
            ▪ 4d subshell (l=2) has 5 orbitals, accommodating 10 electrons.
            ▪ 5p subshell (l=1) has 3 orbitals, accommodating 6 electrons.
            ▪ The 5f orbitals are not filled in the 5th period.
            ▪ Thus, the total number of electrons that can be accommodated in these orbitals (5s, 4d, 5p) is 2 + 10 + 6 = 18 electrons, which justifies the presence of 18 elements in the 5th period.
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    Unit 4: Chemical Bonding and Molecular Structure
    This unit delves into the fundamental principles that govern how atoms bond together to form molecules, exploring different types of bonds and theories that explain molecular geometry.
    • Chemical Bond: The attractive force that holds various constituent atoms or ions together in different chemical species.
    • Kössel-Lewis Approach: Atoms achieve stability by attaining a noble gas electron configuration (an octet of electrons in their valence shell) through transfer or sharing of electrons.
    • Octet Rule: Atoms combine by gaining, losing, or sharing valence electrons to achieve eight electrons in their outermost shell.
    • Types of Chemical Bonds:
        ◦ Ionic (Electrovalent) Bond: Formed by the complete transfer of one or more valence electrons from one atom to another, resulting in the formation of positively and negatively charged ions, held together by strong electrostatic forces of attraction.
            ▪ Formation depends on ionization enthalpy of metal, electron gain enthalpy of non-metal, and lattice enthalpy (energy released when gaseous ions combine to form a solid crystal lattice).
        ◦ Covalent Bond: Formed by the mutual sharing of one or more pairs of electrons between two atoms. Can be:
            ▪ Single Bond: Sharing one electron pair (e.g., Cl-Cl).
            ▪ Double Bond: Sharing two electron pairs (e.g., C=O in CO₂).
            ▪ Triple Bond: Sharing three electron pairs (e.g., N≡N in N₂).
    • Limitations of the Octet Rule:
        ◦ Incomplete Octet of the Central Atom: Cases where the central atom has less than eight electrons (e.g., LiCl, BeH₂, BCl₃).
        ◦ Odd-electron Molecules: Molecules with an odd number of valence electrons (e.g., NO, NO₂).
        ◦ Expanded Octet: Elements in or beyond the third period can have more than eight valence electrons around the central atom (e.g., PCl₅, SF₆, H₂SO₄).
        ◦ It does not explain the relative stability or the geometry/shapes of molecules.
    • Formal Charge: The charge assigned to an atom in a polyatomic molecule or ion, calculated as: (Total number of valence electrons in free atom) – (Total number of non-bonding electrons) – (1/2 * Total number of bonding electrons).
    • Bond Parameters:
        ◦ Bond Length: The equilibrium distance between the nuclei of two bonded atoms in a molecule.
        ◦ Bond Angle: The angle between the orbitals containing bonding electron pairs around the central atom.
        ◦ Bond Enthalpy: The amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state. Higher bond order generally means higher bond enthalpy.
        ◦ Bond Order: The number of bonds between two atoms in a molecule.
    • Resonance Structures (Canonical Forms): When a single Lewis structure cannot accurately describe a molecule (e.g., O₃, CO₃²⁻), a number of structures with similar energy, nuclei positions, and electron distribution are considered. These are called canonical forms or resonance structures, and the actual structure is a resonance hybrid of these forms. Resonance stabilises the molecule.
    • Polarity of Bonds:
        ◦ Polar Covalent Bond: Forms between atoms of different electronegativity, leading to unequal sharing of electrons and development of partial positive (δ⁺) and negative (δ⁻) charges.
        ◦ Dipole Moment (μ): A measure of the polarity of a molecule, represented as a vector quantity. A molecule can have polar bonds but be non-polar overall if its geometry causes bond dipoles to cancel (e.g., CO₂, BF₃, CCl₄).
    • Valence Shell Electron Pair Repulsion (VSEPR) Theory: Predicts the geometrical shapes of covalent molecules based on the principle that electron pairs (both bonding and lone pairs) in the valence shell repel each other and thus tend to arrange themselves as far apart as possible to minimise repulsion. The order of repulsion is LP-LP > LP-BP > BP-BP.
    • Valence Bond (VB) Theory: Explains chemical bond formation based on the overlap of atomic orbitals. Greater overlap generally leads to a stronger bond.
        ◦ Types of Overlapping:
            ▪ Sigma (σ) Bond: Formed by end-to-end (axial) overlap of bonding orbitals along the internuclear axis (s-s, s-p, p-p overlaps). It is generally stronger than a pi bond.
            ▪ Pi (π) Bond: Formed by sidewise (lateral) overlap of atomic orbitals whose axes are parallel to each other and perpendicular to the internuclear axis. It is generally weaker than a sigma bond.
    • Hybridisation: The process of intermixing of atomic orbitals of slightly different energies to form a new set of equivalent hybrid orbitals of equivalent energies and shape. Hybrid orbitals are used in bond formation.
        ◦ Conditions for Hybridisation: Orbitals in the valence shell are hybridised, they should have almost equal energy, promotion of electron is not essential, even filled orbitals can participate.
        ◦ Types of Hybridisation: sp, sp², sp³, sp³d, sp³d², dsp², d²sp³.
            ▪ sp Hybridisation: One s and one p orbital combine to form two equivalent sp hybrid orbitals (e.g., BeCl₂ linear geometry).
            ▪ sp² Hybridisation: One s and two p orbitals combine to form three equivalent sp² hybrid orbitals (e.g., BCl₃ trigonal planar geometry).
            ▪ sp³ Hybridisation: One s and three p orbitals combine to form four equivalent sp³ hybrid orbitals (e.g., CH₄ tetrahedral, NH₃ pyramidal, H₂O bent/V-shape).
    • Molecular Orbital (MO) Theory (Hund and Mulliken, 1932):
        ◦ Electrons in a molecule are present in molecular orbitals that are polycentric (influenced by two or more nuclei).
        ◦ Molecular Orbitals (MOs) are formed by the linear combination of atomic orbitals (LCAO). The number of MOs formed equals the number of combining atomic orbitals.
        ◦ Bonding Molecular Orbitals (BMOs): Have lower energy and greater stability than combining atomic orbitals; increase electron density between nuclei.
        ◦ Antibonding Molecular Orbitals (ABMOs): Have higher energy and less stability; have a region of zero electron density (node) between nuclei.
        ◦ MOs are filled according to Aufbau principle, Pauli's exclusion principle, and Hund's rule.
        ◦ Bond Order (from MO theory): = (Number of electrons in BMOs - Number of electrons in ABMOs) / 2.
        ◦ Magnetic Nature: If all electrons in MOs are paired, the substance is diamagnetic (repelled by magnetic field). If one or more MOs are singly occupied, it is paramagnetic (attracted by magnetic field).
    • Hydrogen Bonding: A special type of dipole-dipole interaction. Occurs when a hydrogen atom covalently bonded to a highly electronegative atom (N, O, or F) forms an attractive interaction with another electronegative atom. It is weaker than a covalent bond.
        ◦ Intermolecular Hydrogen Bond: Between different molecules (e.g., in HF, H₂O).
        ◦ Intramolecular Hydrogen Bond: Within the same molecule (e.g., o-nitrophenol).
    Exam-Oriented Questions & Answers (Unit 4)
    • Q1: Predict the shape of the molecule SF₆ using VSEPR theory and identify any limitations of the octet rule in this molecule.
        ◦ A1:
            ▪ For SF₆, the central atom is Sulphur (S). In SF₆, Sulphur is bonded to six Fluorine atoms, and there are no lone pairs on the central sulphur atom (as sulphur forms an expanded octet).
            ▪ According to VSEPR theory, if there are six electron pairs (all bonding pairs) around the central atom and no lone pairs, the electron pairs arrange themselves in an octahedral geometry [275, Table 4.6].
            ▪ Therefore, the shape of the SF₆ molecule is octahedral.
            ▪ Octet Rule Limitation: In SF₆, the sulphur atom has 12 electrons in its valence shell (6 bonding pairs), which is more than the octet (8 electrons). This is an example of an expanded octet, which is a limitation of the octet rule.
    • Q2: Distinguish between a sigma (σ) bond and a pi (π) bond.
        ◦ A2:
            ▪ Sigma (σ) Bond:
                • Formed by the end-to-end (head-on or axial) overlap of atomic orbitals along the internuclear axis.
                • Can be formed by s-s, s-p, or p-p overlapping.
                • It is generally stronger than a pi bond due to a larger extent of overlap.
                • Only one sigma bond can exist between any two atoms.
            ▪ Pi (π) Bond:
                • Formed by the sidewise (lateral) overlap of atomic orbitals, where their axes are parallel to each other and perpendicular to the internuclear axis.
                • Always involves the overlap of p-orbitals (or d-orbitals in some cases).
                • It is generally weaker than a sigma bond due to a smaller extent of overlap.
                • In multiple bonds, one is a sigma bond, and the additional bonds are pi bonds (e.g., a double bond has one σ and one π, a triple bond has one σ and two π).
    --------------------------------------------------------------------------------
    Unit 5: States of Matter
    This unit explores the microscopic and macroscopic properties of gases and liquids, focusing on intermolecular forces and the laws that govern their behaviour.
    • Intermolecular Forces: Attractive and repulsive forces between interacting particles (atoms and molecules). These are distinct from intra-molecular forces (covalent bonds).
        ◦ Van der Waals Forces: General term for various attractive intermolecular forces.
            ▪ Dispersion Forces (London Forces): Weak, short-range attractive forces present in all atoms and molecules (polar or non-polar). Arise from instantaneous dipoles induced by temporary fluctuations in electron distribution.
            ▪ Dipole-Dipole Forces: Attractive forces between molecules possessing permanent dipoles (polar molecules). Stronger than London forces but weaker than ion-ion interactions.
            ▪ Dipole-Induced Dipole Forces: Attractive forces between a polar molecule (permanent dipole) and a non-polar molecule (where the permanent dipole induces a temporary dipole).
        ◦ Hydrogen Bond: A special and particularly strong type of dipole-dipole interaction. Occurs when a hydrogen atom covalently bonded to a highly electronegative atom (N, O, F) interacts with another electronegative atom.
    • Thermal Energy: The energy of a body arising from the motion of its atoms or molecules; directly proportional to temperature.
    • States of Matter: Determined by the balance between intermolecular forces (tend to keep molecules together) and thermal energy (tend to keep them apart).
    • Gaseous State: Characterised by high compressibility, uniform pressure exertion, low density, indefinite volume and shape, and complete mixing. This simplicity is due to negligible intermolecular forces.
    • Gas Laws: Describe relationships between measurable properties of gases (pressure (p), volume (V), temperature (T), number of moles (n)).
        ◦ Boyle's Law (p-V relationship): At constant temperature (T) and number of moles (n), the pressure of a fixed amount of gas is inversely proportional to its volume. Mathematically: p₁V₁ = p₂V₂ = constant.
        ◦ Charles's Law (V-T relationship): At constant pressure (p) and number of moles (n), the volume of a fixed mass of gas is directly proportional to its absolute temperature (Kelvin). Mathematically: V₁/T₁ = V₂/T₂ = constant.
            ▪ Absolute Zero: The lowest hypothetical temperature (-273.15 °C) at which gases are theorised to occupy zero volume. The Kelvin scale (Absolute temperature scale) is based on this concept, where K = °C + 273.15.
        ◦ Gay-Lussac's Law (p-T relationship): At constant volume (V) and number of moles (n), the pressure of a fixed amount of gas is directly proportional to its absolute temperature (Kelvin).
        ◦ Avogadro's Law (V-n relationship): At constant temperature (T) and pressure (p), equal volumes of all gases contain equal numbers of molecules. This implies that the volume of a gas is directly proportional to the number of moles (n).
    • Ideal Gas Equation: Combines Boyle's, Charles's, and Avogadro's laws into a single equation: pV = nRT.
        ◦ R: The gas constant (or Universal Gas Constant), whose value depends on the units of p, V, and T. (e.g., 8.314 J K⁻¹ mol⁻¹).
        ◦ Combined Gas Law: If the state of a fixed amount of gas changes from (p₁, V₁, T₁) to (p₂, V₂, T₂), then p₁V₁/T₁ = p₂V₂/T₂.
    • Dalton's Law of Partial Pressures: The total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of the individual gases.
        ◦ Partial Pressure (p_i): The pressure exerted by an individual gas in a mixture. p_i = x_i ⋅ p_total (where x_i is the mole fraction of gas i).
        ◦ Aqueous Tension: The pressure exerted by saturated water vapour.
    • Kinetic Molecular Theory of Gases: A theoretical model based on assumptions to explain gas behaviour:
        ◦ Gases consist of many identical, small particles far apart, so their actual volume is negligible compared to the empty space.
        ◦ There are no intermolecular forces of attraction between gas molecules.
        ◦ Particles are in constant, random motion.
        ◦ Collisions between particles and with container walls are perfectly elastic.
        ◦ The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
    • Real Gases: Gases that deviate from ideal behaviour, particularly at high pressures and low temperatures.
        ◦ Reasons for Deviation: The two assumptions of kinetic theory (negligible molecular volume and no intermolecular forces) are not entirely true for real gases.
        ◦ Van der Waals Equation: A modified ideal gas equation that accounts for these deviations: (p + an²/V²)(V - nb) = nRT.
            ▪ 'a' (constant): Accounts for the intermolecular attractive forces.
            ▪ 'b' (constant): Accounts for the volume occupied by the gas molecules themselves.
        ◦ Compressibility Factor (Z): A measure of deviation from ideal behaviour. Z = pV / nRT. For an ideal gas, Z = 1. For real gases, Z deviates from unity.
    • Liquefaction of Gases: The process of converting a gas into a liquid.
        ◦ Critical Temperature (T_c): The temperature above which a gas cannot be liquefied, regardless of the pressure applied.
        ◦ Critical Pressure (P_c): The minimum pressure required to liquefy a gas at its critical temperature.
        ◦ Vapour: A gas existing below its critical temperature.
    • Properties of Liquids:
        ◦ Vapour Pressure: The pressure exerted by the vapour in equilibrium with its liquid phase at a given temperature.
        ◦ Surface Tension (γ): The force acting per unit length perpendicular to a line drawn on the surface of a liquid. It causes liquids to minimise their surface area, leading to spherical drops.
        ◦ Viscosity (η): A measure of a liquid's resistance to flow.
    Exam-Oriented Questions & Answers (Unit 5)
    • Q1: A gas occupies 600 mL at 25 °C and 760 mm of Hg pressure. What will be its pressure at a height where the temperature is 10 °C and the volume of the gas is 640 mL?
        ◦ A1: This problem involves changes in pressure, volume, and temperature, so we use the Combined Gas Law: p₁V₁/T₁ = p₂V₂/T₂.
            ▪ Convert temperatures to Kelvin:
                • T₁ = 25 °C + 273 = 298 K
                • T₂ = 10 °C + 273 = 283 K
            ▪ Given: p₁ = 760 mm Hg, V₁ = 600 mL, T₁ = 298 K, V₂ = 640 mL, T₂ = 283 K.
            ▪ Rearrange the formula to solve for p₂: p₂ = (p₁V₁T₂) / (V₂T₁)
            ▪ p₂ = (760 mm Hg × 600 mL × 283 K) / (640 mL × 298 K)
            ▪ p₂ = 676.6 mm Hg.
    • Q2: Explain the concept of critical temperature (T_c) and how it relates to the liquefaction of gases.
        ◦ A2: The critical temperature (T_c) is the temperature above which a gas cannot be liquefied, no matter how high the pressure applied.
            ▪ Below its critical temperature, a gas can be liquefied by simply applying sufficient pressure, and in this state, it is often referred to as a vapour.
            ▪ Above T_c, the thermal energy of the gas molecules is too high to be overcome by intermolecular attractive forces, preventing their compression into a liquid state, regardless of pressure. This concept is crucial in industrial processes for gas liquefaction.
    --------------------------------------------------------------------------------
    Unit 6: Thermodynamics
    This unit introduces the principles of thermodynamics, focusing on energy changes in chemical and physical processes, and the concepts of spontaneity and equilibrium.
    • Thermodynamics: The study of energy transformations in macroscopic systems, concerned with the initial and final states of a system undergoing change.
    • Thermodynamic Terms:
        ◦ System: The part of the universe under observation.
        ◦ Surroundings: Everything else in the universe that can interact with the system.
        ◦ Boundary: Separates the system from the surroundings.
    • Types of Systems:
        ◦ Open System: Exchanges both energy and matter with the surroundings.
        ◦ Closed System: Exchanges energy but not matter with the surroundings.
        ◦ Isolated System: Exchanges neither energy nor matter with the surroundings.
    • State Function (or State Variable): A property of the system whose value depends only on the current state of the system, irrespective of the path taken to reach that state (e.g., internal energy (U), enthalpy (H), entropy (S), Gibbs energy (G), pressure (p), volume (V), temperature (T)).
    • Internal Energy (U): The total energy contained within a system (sum of all forms of energy). Only changes in internal energy (∆U) can be measured.
    • Work (w): Energy transfer resulting from organised motion; in chemistry, often pressure-volume (pV) work.
        ◦ Sign Convention: w > 0 when work is done on the system (compression). w < 0 when work is done by the system (expansion).
    • Heat (q): Energy transfer due to a temperature difference between the system and surroundings.
        ◦ Sign Convention: q > 0 when heat is absorbed by the system (endothermic). q < 0 when heat is released by the system (exothermic).
    • First Law of Thermodynamics: States that energy can neither be created nor destroyed. Mathematically: ∆U = q + w. For an isolated system, ∆U = 0, meaning its energy is constant.
    • Adiabatic Process: A process where no heat (q=0) is exchanged between the system and surroundings.
    • Isothermal Process: A process occurring at constant temperature (∆T=0). For an ideal gas, ∆U = 0 for an isothermal process.
    • Reversible Process: A process that occurs infinitely slowly through a series of equilibrium states and can be reversed by an infinitesimal change.
    • Enthalpy (H): A thermodynamic state function defined as H = U + pV. The heat absorbed or released at constant pressure (q_p) is equal to the change in enthalpy (∆H).
        ◦ ∆H = q_p.
        ◦ Exothermic Reaction: Releases heat, ∆H is negative.
        ◦ Endothermic Reaction: Absorbs heat, ∆H is positive.
        ◦ Relationship between ∆H and ∆U: ∆H = ∆U + ∆n_gRT, where ∆n_g is the change in the number of moles of gaseous products minus gaseous reactants.
    • Extensive Property: Depends on the quantity of matter in the system (e.g., mass, volume, internal energy, enthalpy).
    • Intensive Property: Does not depend on the quantity of matter (e.g., temperature, density, pressure, molar heat capacity).
    • Heat Capacity (C): The quantity of heat required to raise the temperature of a substance by one degree.
        ◦ Specific Heat (c): Heat capacity per unit mass.
        ◦ Molar Heat Capacity (C_m): Heat capacity per mole.
        ◦ Relationship between C_p and C_V (for ideal gas): C_p - C_V = R.
    • Calorimetry: Experimental technique to measure heat changes (q_V or q_p).
        ◦ Bomb Calorimeter: Used to measure ∆U (heat at constant volume), typically for combustion reactions.
    • Standard Enthalpy of Reaction (∆ᵣH⁰): The enthalpy change for a reaction when all participating substances are in their standard states (pure form at 1 bar pressure, usually 298 K).
        ◦ Standard Enthalpy of Formation (∆_f_H⁰): The enthalpy change when one mole of a compound is formed from its elements in their most stable states of aggregation at standard conditions. By convention, ∆_f_H⁰ of an element in its standard state is zero.
    • Hess's Law of Constant Heat Summation: If a reaction takes place in several steps, its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions. It is a consequence of enthalpy being a state function.
    • Bond Enthalpy (∆_bond_H⁰): The energy required to break one mole of a specific type of bond in the gaseous state.
    • Lattice Enthalpy (∆_lattice_H⁰): The enthalpy change when one mole of an ionic compound dissociates into its gaseous ions.
    • Spontaneity: A process is spontaneous if it proceeds without the assistance of an external agency. Spontaneous processes are irreversible.
        ◦ Entropy (S): A thermodynamic function that measures the degree of randomness or disorder in a system. The greater the disorder in an isolated system, the higher the entropy.
            ▪ Second Law of Thermodynamics: States that for a spontaneous process, the total entropy of the system and surroundings (∆S_total) always increases (∆S_total > 0).
            ▪ Third Law of Thermodynamics: States that the entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero (0 K).
        ◦ Gibbs Energy (G) or Gibbs Function: A thermodynamic state function defined as G = H - TS. It represents the net energy available to do useful work.
            ▪ Gibbs Equation: ∆G = ∆H - T∆S.
            ▪ Criteria for Spontaneity (at constant T and P):
                • If ∆G < 0: The process is spontaneous.
                • If ∆G > 0: The process is non-spontaneous (the reverse process is spontaneous).
                • If ∆G = 0: The system is at equilibrium.
    • Gibbs Energy and Equilibrium Constant (K): The standard Gibbs energy change (∆G⁰) is related to the equilibrium constant (K) by the equation: ∆G⁰ = -RT ln K or ∆G⁰ = -2.303 RT log K.
    Exam-Oriented Questions & Answers (Unit 6)
    • Q1: Distinguish between extensive and intensive properties in thermodynamics, providing two examples for each.
        ◦ A1:
            ▪ Extensive properties are those whose values depend on the quantity or size of matter present in the system. Examples include mass, volume, internal energy (U), and enthalpy (H).
            ▪ Intensive properties are those whose values do not depend on the quantity or size of matter present. Examples include temperature, density, pressure, and molar heat capacity.
    • Q2: Calculate the change in internal energy (∆U) for the process when 1 mole of water is vaporised at 1 bar pressure and 100 °C, given that the molar enthalpy change for vaporisation (∆_vap_H⁰) is 41 kJ mol⁻¹. Assume water vapour behaves as a perfect gas.
        ◦ A2: The vaporisation process is: H₂O(l) → H₂O(g).
            ▪ We use the relation: ∆H = ∆U + ∆n_gRT.
            ▪ Given: ∆_vap_H⁰ = 41 kJ mol⁻¹ = 41000 J mol⁻¹.
            ▪ For the reaction, ∆n_g = (moles of gaseous products) - (moles of gaseous reactants) = 1 mole (H₂O(g)) - 0 moles (H₂O(l)) = 1 mole.
            ▪ Temperature T = 100 °C + 273.15 = 373.15 K.
            ▪ Gas constant R = 8.314 J K⁻¹ mol⁻¹.
            ▪ Rearrange the equation to solve for ∆U: ∆U = ∆H - ∆n_gRT
            ▪ ∆U = 41000 J mol⁻¹ - (1 mol × 8.314 J K⁻¹ mol⁻¹ × 373.15 K)
            ▪ ∆U = 41000 J mol⁻¹ - 3101.3 J mol⁻¹
            ▪ ∆U = 37898.7 J mol⁻¹ or 37.90 kJ mol⁻¹.
    --------------------------------------------------------------------------------
    Unit 7: Equilibrium
    This unit explores the concept of equilibrium in both physical and chemical systems, the factors influencing it, and delves into ionic equilibrium, including acid-base theories and pH.
    • Equilibrium: A state where the rates of opposing processes become equal, leading to constant concentrations of reactants and products. Equilibrium is dynamic, meaning the processes continue to occur, but with no net change.
        ◦ Physical Equilibrium: Occurs in physical processes like phase changes (e.g., liquid-vapour equilibrium, H₂O(l) ⇌ H₂O(vap)) or dissolution (e.g., Sugar(s) ⇌ Sugar(solution)).
        ◦ Chemical Equilibrium: Occurs in reversible chemical reactions (e.g., H₂(g) + I₂(g) ⇌ 2HI(g)).
    • Equilibrium Constant (K):
        ◦ Law of Chemical Equilibrium: At a given temperature, the product of concentrations of the reaction products (each raised to its stoichiometric coefficient) divided by the product of concentrations of the reactants (each raised to its stoichiometric coefficient) is a constant value.
        ◦ K_c (Concentration Equilibrium Constant): Expressed in terms of molar concentrations (mol L⁻¹). For aA + bB ⇌ cC + dD, K_c = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ.
        ◦ K_p (Partial Pressure Equilibrium Constant): Expressed in terms of partial pressures for gaseous reactions.
        ◦ Relationship between K_p and K_c: K_p = K_c(RT)^∆n, where ∆n = (moles of gaseous products) - (moles of gaseous reactants).
        ◦ Units of K: K_c and K_p can have units depending on ∆n, but are often considered dimensionless if standard states are defined.
    • Homogeneous Equilibrium: All reactants and products are in the same phase (e.g., N₂(g) + 3H₂(g) ⇌ 2NH₃(g)).
    • Heterogeneous Equilibrium: Reactants and products are in different phases (e.g., CaCO₃(s) ⇌ CaO(s) + CO₂(g)). Concentrations of pure solids and pure liquids are considered constant and are omitted from the equilibrium constant expression.
    • Reaction Quotient (Q): An expression identical to K, but calculated using non-equilibrium concentrations.
        ◦ Predicting Reaction Direction using Q:
            ▪ If Q < K: Net reaction proceeds in the forward direction (towards products) to reach equilibrium.
            ▪ If Q > K: Net reaction proceeds in the reverse direction (towards reactants) to reach equilibrium.
            ▪ If Q = K: The system is already at equilibrium; no net reaction occurs.
    • Le Chatelier's Principle: States that if a change (stress) is applied to a system at equilibrium, the system will shift in a direction that tends to counteract (minimise) the effect of that change.
        ◦ Effect of Concentration Change:
            ▪ Adding a reactant/removing a product: Shifts equilibrium to the right (forward direction).
            ▪ Removing a reactant/adding a product: Shifts equilibrium to the left (reverse direction).
        ◦ Effect of Pressure Change (for gaseous reactions with ∆n ≠ 0):
            ▪ Increasing pressure (decreasing volume): Shifts equilibrium towards the side with fewer moles of gas.
            ▪ Decreasing pressure (increasing volume): Shifts equilibrium towards the side with more moles of gas.
            ▪ Adding an inert gas at constant volume has no effect on equilibrium.
        ◦ Effect of Temperature Change:
            ▪ For Exothermic Reactions (∆H < 0): Increasing temperature shifts equilibrium to the left (reactants), decreasing K.
            ▪ For Endothermic Reactions (∆H > 0): Increasing temperature shifts equilibrium to the right (products), increasing K.
        ◦ Effect of Catalyst: A catalyst increases the rate of both forward and reverse reactions equally. It does not change the equilibrium composition or the value of K. It only helps the system reach equilibrium faster.
    • Ionic Equilibrium: Equilibria involving ions in aqueous solutions.
        ◦ Electrolytes: Substances that produce ions in solution and thus conduct electricity.
            ▪ Strong Electrolytes: Almost completely dissociate/ionise in solution.
            ▪ Weak Electrolytes: Partially dissociate/ionise in solution (e.g., weak acids, weak bases).
        ◦ Acid-Base Concepts:
            ▪ Arrhenius Concept:
                • Acid: Produces H⁺ (aq) ions in water.
                • Base: Produces OH⁻ (aq) ions in water.
                • Limitation: Applicable only to aqueous solutions.
            ▪ Brønsted-Lowry Concept (Proton Concept):
                • Acid: A proton (H⁺) donor.
                • Base: A proton (H⁺) acceptor.
                • Conjugate Acid-Base Pair: Two species that differ by a single proton (e.g., HCl is acid, Cl⁻ is its conjugate base; H₂O is base, H₃O⁺ is its conjugate acid).
                • Water can act as both a Brønsted acid and a base (amphoteric).
            ▪ Lewis Concept (Electron Pair Concept):
                • Acid: An electron pair acceptor (e.g., BF₃, H⁺, metal cations).
                • Base: An electron pair donor (e.g., NH₃, H₂O, OH⁻).
        ◦ Ionization of Water: Water undergoes auto-ionisation: H₂O(l) + H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq).
            ▪ Ionic Product of Water (K_w): K_w = [H⁺][OH⁻]. At 298 K, K_w = 1.0 × 10⁻¹⁴ M².
        ◦ pH Scale: A logarithmic scale to express hydrogen ion concentration.
            ▪ pH = -log₁₀[H⁺].
            ▪ pOH = -log₁₀[OH⁻].
            ▪ Relationship: pH + pOH = pK_w = 14 (at 298 K).
            ▪ pH < 7: Acidic solution. pH = 7: Neutral solution. pH > 7: Basic solution (at 298 K).
        ◦ Ionization Constants for Weak Acids (K_a) and Weak Bases (K_b): Measures of their strengths.
            ▪ K_a = [H⁺][A⁻] / [HA] for HA ⇌ H⁺ + A⁻. pK_a = -logK_a.
            ▪ K_b = [BH⁺][OH⁻] / [B] for B + H₂O ⇌ BH⁺ + OH⁻. pK_b = -logK_b.
            ▪ Relationship for Conjugate Acid-Base Pairs: K_a × K_b = K_w. Consequently, pK_a + pK_b = pK_w = 14. A strong acid has a weak conjugate base and vice-versa.
        ◦ Common Ion Effect: The suppression of the dissociation of a weak electrolyte by the addition of a strong electrolyte containing a common ion. It is an application of Le Chatelier's Principle.
        ◦ Hydrolysis of Salts: The interaction of cations/anions of a salt with water, which can affect the pH of the solution.
        ◦ Buffer Solutions: Solutions that resist significant changes in pH upon dilution or the addition of small amounts of strong acid or alkali. They are typically mixtures of a weak acid and its salt with a strong base (e.g., CH₃COOH/CH₃COONa) or a weak base and its salt with a strong acid (e.g., NH₃/NH₄Cl).
            ▪ Henderson-Hasselbalch Equation (Acidic Buffer): pH = pK_a + log([Salt]/[Acid]).
        ◦ Solubility Product Constant (K_sp): The equilibrium constant for the dissolution of a sparingly soluble salt (e.g., AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), K_sp = [Ag⁺][Cl⁻]).
    Exam-Oriented Questions & Answers (Unit 7)
    • Q1: The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10⁻³ M. What is its pH? Is it acidic or basic?
        ◦ A1: The pH of a solution is defined as pH = -log₁₀[H⁺].
            ▪ Given [H⁺] = 3.8 × 10⁻³ M.
            ▪ pH = -log(3.8 × 10⁻³)
            ▪ pH = -(log 3.8 + log 10⁻³)
            ▪ pH = -(0.58 + (-3))
            ▪ pH = -(-2.42) = 2.42.
            ▪ Since the pH (2.42) is less than 7, the soft drink is acidic.
    • Q2: Explain the common ion effect with an example. How does it relate to Le Chatelier's Principle?
        ◦ A2: The common ion effect is defined as a shift in equilibrium on adding a substance that provides more of an ionic species already present in the dissociation equilibrium of a weak electrolyte.
            ▪ Example: Consider the dissociation of acetic acid (a weak acid) in water: CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq) If sodium acetate (CH₃COONa), a strong electrolyte, is added to this solution, it dissociates completely to provide more acetate ions (CH₃COO⁻). These acetate ions are common to the acetic acid dissociation equilibrium. CH₃COONa(aq) → Na⁺(aq) + CH₃COO⁻(aq) The increased concentration of CH₃COO⁻ ions causes the equilibrium of acetic acid dissociation to shift to the left (reverse direction), according to Le Chatelier's Principle. This results in a decrease in the concentration of H⁺ ions and thus an increase in the pH of the solution.
            ▪ Relation to Le Chatelier's Principle: The common ion effect is a direct application of Le Chatelier's Principle. When the concentration of a product (or reactant) is increased, the system responds by shifting the equilibrium in the direction that consumes the added substance to relieve the stress, thereby re-establishing equilibrium.