Course Title: General Chemistry I (Physical & Inorganic Chemistry)

Course Description

General Chemistry I provides students with a foundational understanding of the fundamental principles of chemistry, with emphasis on physical chemistry and inorganic chemistry concepts. The course introduces atomic structure, chemical bonding, stoichiometry, states of matter, periodicity, and the quantitative relationships that govern chemical reactions. Students will develop problem-solving skills, analytical reasoning, and an appreciation for the role of chemistry in scientific and technological advancements. This course is essential for students in science, engineering, medical, agricultural, and environmental disciplines.

Course Objectives

By the end of this course, students should be able to:

1. Explain basic chemical principles and apply them to physical and inorganic systems.
2. Understand the structure of atoms, periodic trends, and how these determine chemical properties.
3. Apply the laws of chemical combination and perform stoichiometric calculations.
4. Describe chemical bonding theories and use them to predict molecular geometry and properties.
5. Explain the behavior of matter in different states (solid, liquid, gas) using physical chemistry principles.
6. Interpret and solve numerical problems involving gas laws, energy changes, and thermodynamic processes.
7. Demonstrate understanding of chemical equilibrium, acidity, and basic inorganic reactions.
8. Develop laboratory skills, safety awareness, and scientific reporting (if practicals are included).

CHAPTER 1: Introduction to Chemistry and Stoichiometry

1.1 Nature and Scope of Chemistry

• Definition and branches of chemistry
• Importance of chemistry in medicine, agriculture, engineering, and daily life
• Scientific method and chemical experimentation

1.2 Measurements in Chemistry

• SI units and conversions
• Accuracy, precision, and significant figures
• Density and its applications

1.3 Matter and Its Classification

• States of matter
• Elements, compounds, and mixtures
• Physical vs chemical changes

1.4 Chemical Laws

• Law of Conservation of Mass
• Law of Definite Proportions
• Law of Multiple Proportions

1.5 Chemical Formulas and Equations

• Writing and balancing chemical equations
• Types of chemical reactions: synthesis, decomposition, combustion, displacement, redox

1.6 Stoichiometry

• Mole concept and Avogadro’s number
• Molar mass and empirical formula
• Limiting reagents
• Percentage yield and theoretical yield

CHAPTER 2: Atomic Structure and Periodicity

2.1 Historical Development of Atomic Theory

• Dalton, Thomson, Rutherford, Bohr models
• Wave-particle duality (de Broglie)
• Quantum mechanical model

2.2 Structure of the Atom

• Subatomic particles: electrons, protons, neutrons
• Isotopes, ions, and atomic mass
• Electronic configuration and orbital notation

2.3 Quantum Numbers

• Principal, azimuthal, magnetic, and spin quantum numbers
• Shapes of s, p, d orbitals

2.4 Periodic Table and Periodicity

• Modern periodic table
• Periodic trends:
  • Atomic radius
  • Ionization energy
  • Electron affinity
  • Electronegativity
• Metallic and non-metallic character trends

2.5 Classification of Elements

• Groups and periods
• Representative elements, transition metals, lanthanides, actinides

CHAPTER 3: Chemical Bonding and Molecular Structure

3.1 Types of Chemical Bonds

• Ionic bonding and lattice energy
• Covalent bonding
• Polar and non-polar molecules
• Coordinate (dative) bond
• Metallic bonding

3.2 Valence Shell Electron Pair Repulsion (VSEPR) Theory

• Predicting molecular shapes:
  • Linear, bent, trigonal planar, tetrahedral, trigonal pyramidal, trigonal bipyramidal, octahedral

3.3 Valence Bond Theory (VBT)

• Hybridization:
  • sp, sp², sp³, sp³d, sp³d²
• Sigma and pi bonds

3.4 Molecular Orbital Theory (MOT)

• Bond order
• Paramagnetism and diamagnetism

3.5 Intermolecular Forces

• Hydrogen bonding
• Dipole-dipole interactions
• London dispersion forces
• Importance in boiling/melting points and solubility

CHAPTER 4: States of Matter and Gas Laws

4.1 Properties of the States of Matter

• Molecular arrangement in solids, liquids, gases
• Crystalline vs amorphous solids
• Phase changes and phase diagrams

4.2 Kinetic Molecular Theory of Gases

• Assumptions
• Relationship between molecular motion and temperature

4.3 Gas Laws

• Boyle’s law
• Charles’ law
• Gay-Lussac’s law
• Avogadro’s law
• Ideal gas law (PV = nRT)
• Dalton's law of partial pressures
• Graham’s law of diffusion and effusion

4.4 Real Gases

• Deviations from ideal gas behavior
• Van der Waals equation

4.5 Liquids and Solutions

• Vapour pressure
• Surface tension
• Viscosity
• Types of solutions and solubility

LECTURE NOTES: CHAPTER ONE

Introduction to Chemistry and Stoichiometry

1.0 Introduction

Chemistry is often described as the “central science” because it links the physical sciences with the life sciences and applied sciences such as engineering, agriculture, medicine, pharmacy, and environmental studies. Every substance around you—air, water, soil, foods, metals, plastics, even your own body—is made of chemicals. Understanding chemistry means understanding matter, its composition, structure, and the changes it undergoes.

Chapter One introduces the basic foundations of chemistry: what chemistry is, how chemists study matter, the measurement systems used in scientific work, the classification of matter, the laws that govern chemical behavior, and the quantitative relationships known as stoichiometry. These ideas form the backbone of all higher-level chemistry topics, from physical chemistry to inorganic chemistry, biochemistry, organic chemistry, and analytical chemistry.

1.1 Nature, Scope, and Importance of Chemistry

1.1.1 What is Chemistry?

Chemistry is the scientific study of matter—its composition, structure, properties—and the changes it undergoes during chemical reactions. It attempts to answer fundamental questions such as:

• What substances are made of
• Why substances behave the way they do
• How substances can combine or break apart
• How energy interacts with matter
• How new materials can be created

In essence, chemistry helps us understand the building blocks of everything around us.

1.1.2 Branches of Chemistry

Chemistry is broadly divided into several branches:

1. Physical Chemistry – deals with the laws and theories governing energy, thermodynamics, kinetics, and states of matter.
2. Inorganic Chemistry – studies all elements and inorganic compounds, including metals, minerals, and coordination complexes.
3. Organic Chemistry – focuses on carbon-containing compounds.
4. Analytical Chemistry – deals with qualitative and quantitative analysis of substances.
5. Biochemistry – studies chemical processes in living organisms.
6. Industrial Chemistry – application of chemical principles in industry.

1.1.3 Importance of Chemistry

Chemistry influences nearly every aspect of modern life:

• Medicine & Pharmacy: development of drugs, vaccines, and diagnostic chemicals
• Agriculture: fertilizers, pesticides, herbicides, soil testing
• Engineering & Technology: materials science, polymers, metals, semiconductors
• Environmental Science: pollution control, water purification, green chemistry
• Household Uses: soaps, detergents, cleaners, food preservation
• Energy: batteries, fuels, renewable energy systems

From cooking to breathing, everything involves chemistry.

1.1.4 The Scientific Method

Chemists rely on the scientific method—a systematic approach to studying natural phenomena.

1. Observation – noticing a pattern or problem
2. Hypothesis – proposing an explanation
3. Experimentation – testing the hypothesis
4. Analysis – interpreting data
5. Theory – a well–supported explanation
6. Law – a statement describing consistent behaviors

This method ensures that chemical knowledge is based on evidence.

1.2 Measurements in Chemistry

Chemical science depends heavily on accurate measurements, since chemistry is quantitative.

1.2.1 The SI System of Units

Chemists use the International System of Units (SI) for standardization.

Some basic SI units:

Commonly used derived units include liters (L), milliliters (mL), and grams (g).

1.2.2 Significant Figures

Significant figures reflect the precision of a measurement.

Rules:

• Non-zero digits are significant
• Zeros between non-zero digits are significant
• Leading zeros are not significant
• Trailing zeros are significant only if a decimal is present

1.2.3 Accuracy vs Precision

• Accuracy – how close a measurement is to the true value
• Precision – how reproducible measurements are

Example:
If a scale consistently gives values close to the same number but far from the true value → precise but not accurate.

1.2.4 Scientific Notation

Large and small numbers are expressed conveniently using scientific notation:

• 0.00025 = 2.5 × 10⁻⁴
• 120,000 = 1.2 × 10⁵

1.2.5 Density

Density is the mass per unit volume:

\text{Density (ρ)} = \frac{\text{Mass}}{\text{Volume}}

Units: g/cm³ or kg/m³
Density helps identify substances and predict how they interact (e.g., floating, mixing).

1.3 Matter and Its Classification

1.3.1 Definition of Matter

Matter is anything that has mass and occupies space. It exists in different states:

1.3.2 States of Matter

1.3.3 Physical vs Chemical Changes

Physical changes

• Do not alter the composition of matter
• Examples: melting, boiling, dissolving, breaking

Chemical changes

• New substances are formed
• Evidence: color change, gas production, heat release

1.3.4 Classification of Matter

Matter is divided into:

1. Pure Substances

   • Elements: cannot be broken down (e.g., O₂, Fe)
   • Compounds: chemically bonded elements (e.g., H₂O, NaCl)

2. Mixtures

   • Homogeneous mixtures (solutions): uniform composition (salt water)
   • Heterogeneous mixtures: non-uniform (sand + water)

1.4 Laws Governing Chemical Combinations

Chemistry is governed by foundational laws that describe how substances combine.

1.4.1 Law of Conservation of Mass (Lavoisier, 1789)

Matter is neither created nor destroyed during chemical reactions.

Example:
2H₂ + O₂ → 2H₂O
Mass of reactants = Mass of products.

1.4.2 Law of Definite Proportions (Proust’s Law)

A chemical compound always contains the same elements in the same proportion by mass.

Example:
Water always contains H and O in a mass ratio of 1:8.

1.4.3 Law of Multiple Proportions (Dalton’s Law)

If two elements form more than one compound, the masses combine in simple whole-number ratios.

Example: Carbon & oxygen:

• CO → 12g C combines with 16g O
• CO₂ → 12g C combines with 32g O

Ratio 16:32 = 1:2 (simple whole numbers)

1.4.4 Dalton’s Atomic Theory

Dalton proposed that:

• matter is composed of indivisible atoms
• atoms combine in whole-number ratios
• atoms of same element are identical

Although modern modifications exist, the theory remains foundational.

1.5 Chemical Formulas and Equations

1.5.1 Chemical Symbols and Formulas

• Chemical symbols represent elements (H, O, Na, Cl).
• Chemical formulas represent compounds (H₂O, CO₂, NH₃).
• Subscripts show the number of atoms.

1.5.2 Chemical Equations

A chemical equation represents a chemical reaction:

Reactants → Products

Example:
2H₂ + O₂ → 2H₂O

1.5.3 Balancing Chemical Equations

Equations must obey the Law of Conservation of Mass.
Balance using coefficients, not subscripts.

Steps:

1. List atoms on both sides
2. Balance metals
3. Balance non-metals
4. Balance hydrogen and oxygen last
5. Check all atoms again

1.5.4 Types of Chemical Reactions

1. Combination:
   A + B → AB
2. Decomposition:
   AB → A + B
3. Single displacement:
   A + BC → AC + B
4. Double displacement:
   AB + CD → AD + CB
5. Combustion:
   Hydrocarbon + O₂ → CO₂ + H₂O
6. Redox reactions: involve electron transfer.

1.6 Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction.

It allows chemists to calculate:

• the amount of product formed
• the amount of reactant required
• percentage yield
• limiting reactant

1.6.1 The Mole Concept

A mole (mol) is the amount of substance containing 6.022 × 10²³ particles (Avogadro’s number).

1 mole of:

• atoms = 6.022 × 10²³ atoms
• molecules = 6.022 × 10²³ molecules
• ions = 6.022 × 10²³ ions

1.6.2 Molar Mass

The molar mass is the mass of 1 mole of a substance.

Examples:

• H = 1 g/mol
• O = 16 g/mol
• H₂O = (2 × 1) + 16 = 18 g/mol

1.6.3 Mole–Mass Conversions

\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}

\text{Mass} = \text{Moles} \times \text{Molar Mass}

1.6.4 Empirical and Molecular Formulas

• Empirical formula: simplest whole-number ratio of atoms
• Molecular formula: actual number of atoms

Example:
Glucose: C₆H₁₂O₆
Empirical formula: CH₂O

1.6.5 Stoichiometric Calculations Using Balanced Equations

If the equation is:
N₂ + 3H₂ → 2NH₃

The mole ratios are:

• 1 mol N₂ reacts with 3 mol H₂
• 2 mol NH₃ produced

These ratios help determine the required quantities.

1.6.6 Limiting and Excess Reactants

The limiting reactant is the one that is completely consumed first and determines the amount of product formed.

Steps:

1. Convert reactants to moles
2. Use mole ratio to determine product
3. The reactant that produces the least product is limiting

1.6.7 Theoretical, Actual, and Percentage Yield

• Theoretical yield: maximum product predicted by stoichiometry
• Actual yield: amount obtained in experiment
• Percentage yield:

\text{Percentage Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100

High yield indicates an efficient reaction.

1.7 Applications of Stoichiometry in Real Life

Stoichiometry is crucial in:

1.7.1 Industrial Production

• Fertilizers (urea, ammonia)
• Cement, glass, plastics
• Pharmaceuticals (drug synthesis)
• Petroleum refining

Companies calculate exact quantities to avoid waste.

1.7.2 Environmental Chemistry

• Predicting pollutant formation
• Treating wastewater
• Calculating emission levels

1.7.3 Energy Production

• Fuel combustion calculations
• Battery reactions
• Food energy (calorimetry)

1.7.4 Medicine and Biology

• Drug dosage calculations
• Metabolism pathways
• Blood chemistry

1.8 Summary of Key Points

• Chemistry is the study of matter and its changes.
• The SI system provides standard units for measurements.
• Significant figures represent measurement precision.
• Matter exists as elements, compounds, and mixtures.
• Laws of chemical combination describe how substances form compounds.
• Chemical equations must be balanced to obey conservation of mass.
• Stoichiometry uses mole relationships to predict quantities of reactants and products.
• Limiting reactants determine the maximum amount of product formed.
• Stoichiometry is essential in industry, environment, medicine, and daily life.

1.9 Conclusion

Chapter One provides the foundational building blocks for studying chemistry. Understanding measurements, matter, chemical laws, chemical equations, and stoichiometry enables students to navigate more advanced topics such as chemical bonding, thermodynamics, kinetics, inorganic reactions, gas behavior, and equilibrium. A strong grasp of these basic concepts improves problem-solving skills and prepares students for laboratory work, scientific reasoning, and higher-level courses.

LECTURE NOTES: CHAPTER TWO 

Atomic Structure and Periodicity

2.0 Introduction

The structure of the atom and the periodic behavior of elements form the theoretical backbone of modern chemistry. Understanding how atoms are built, how electrons are arranged, and how these arrangements influence chemical reactivity enables us to predict and explain a wide range of chemical phenomena. This chapter explores the historical development of atomic theory, the quantum mechanical model of the atom, electron configuration, periodic trends, and how these concepts provide a unified framework for understanding the properties of elements.

While Chapter One dealt with matter in a broad sense, Chapter Two digs deeper into the smallest units that make up matter—the atoms. The journey begins with early models of the atom, transitions into quantum theory, and culminates in our modern interpretation of the periodic table.

2.1 Historical Development of Atomic Theory

Understanding the atom has been a centuries-long scientific endeavor. Each model built upon previous knowledge, moving closer to the modern understanding.

2.1.1 Ancient Concepts of the Atom

The idea of the atom originated in ancient Greece by philosophers such as Democritus, who proposed that matter was made of tiny, indivisible particles called atomos. However, this idea lacked experimental evidence and was overshadowed by Aristotle’s belief that matter was continuous.

It wasn’t until the 18th and 19th centuries that the atomic theory re-emerged as a result of new experimental data from chemistry.

2.1.2 Dalton’s Atomic Theory (1803)

John Dalton proposed the first scientifically based atomic theory to explain the laws of chemical combination.

Key postulates:

1. Matter consists of indivisible atoms.
2. Atoms of the same element are identical in mass and properties.
3. Atoms of different elements differ in mass and properties.
4. Atoms combine in simple whole-number ratios to form compounds.
5. Atoms cannot be created or destroyed in chemical reactions.

Modern updates:

• Atoms are divisible (existence of subatomic particles).
• Atoms of the same element can differ in mass (isotopes).

Regardless, Dalton’s theory laid the foundation for modern chemistry.

2.1.3 Discovery of the Electron: J.J. Thomson (1897)

Thomson used the cathode ray tube experiment to discover the electron.

Findings:

• Cathode rays were streams of negatively charged particles.
• Calculated charge-to-mass ratio of the electron.

Thomson proposed the Plum Pudding Model:

• Atom is a positively charged sphere with negatively charged electrons embedded within.

This model was revolutionary but later disproven.

2.1.4 Discovery of the Nucleus: Rutherford (1911)

Ernest Rutherford’s gold foil experiment involved bombarding thin gold foil with alpha particles.

Observations:

• Most particles passed through → atoms are mostly empty space.
• Some deflected → existence of a dense, positively charged nucleus.

Conclusions:

• Atom has a tiny central nucleus containing protons.
• Electrons orbit the nucleus.
• Most of the atom is empty space.

The Rutherford Model resembled a mini solar system.

2.1.5 Bohr’s Atomic Model (1913)

Niels Bohr built on Rutherford’s work to address the stability of electron orbits.

Postulates:

1. Electrons orbit in fixed energy levels without radiating energy.
2. Electrons can jump between energy levels by absorbing or emitting photons.
3. Energy of emitted/absorbed light is quantized.

Bohr’s model explained the hydrogen emission spectrum perfectly, but failed for multi-electron atoms.

2.1.6 Quantum Mechanical Model

In the early 20th century, scientists like de Broglie, Heisenberg, and Schrödinger revolutionized atomic theory.

Key ideas:

• Electrons exhibit both wave and particle nature (wave-particle duality).
• Electron behavior described by probability, not fixed orbits.
• Schrödinger’s equation describes electron wave functions.
• Electrons occupy atomic orbitals, not circular orbits.

This forms the modern quantum mechanical model, which is more accurate than any previous model.

2.2 Structure of the Atom

Atoms consist of three fundamental particles:

The nucleus contains protons and neutrons, with electrons occupying regions around the nucleus called orbitals.

2.2.1 Atomic Number, Mass Number, and Isotopes

1. Atomic Number (Z): number of protons.
2. Mass Number (A): number of protons + neutrons.
3. Isotopes: atoms with same Z but different A.

Example:

• Carbon-12
• Carbon-13
• Carbon-14

All are isotopes of carbon.

2.2.2 Atomic Mass and Average Atomic Mass

Atomic mass = weighted average of isotopes.

\text{Average atomic mass} = \sum (\text{mass of isotope} \times \text{abundance})

This explains why chlorine’s atomic mass is 35.5 (mixture of Cl-35 and Cl-37).

2.2.3 Ions

• Cations: positively charged (lost electrons)
• Anions: negatively charged (gained electrons)

2.3 Quantum Mechanical Model of the Atom

This model replaced circular orbits with orbitals.

2.3.1 Wave-Particle Duality (de Broglie)

De Broglie proposed that all matter exhibits wave-like properties.

\lambda = \frac{h}{mv}

Electrons behave as standing waves, not particles orbiting like planets.

2.3.2 Heisenberg Uncertainty Principle

Impossible to know both the exact position and exact momentum of an electron simultaneously.

This principle indicates that electrons are found in probability clouds known as orbitals.

2.3.3 Schrödinger Wave Equation

Schrödinger used wave functions (ψ) to describe electrons as wave-like entities.

Solutions to his equation give rise to:

• Energy levels
• Sublevels
• Atomic orbitals

These orbitals describe regions where electrons are most likely found.

2.3.4 Quantum Numbers

Quantum numbers describe the unique address of an electron.

1. Principal Quantum Number (n)

• Determines energy level.
• Values: n = 1, 2, 3, 4…
• Larger n → higher energy and larger orbital.

2. Azimuthal Quantum Number (l)

Defines sublevel/orbital shape.

3. Magnetic Quantum Number (mᵢ)

Defines orientation in space.
Values: –l → +l

4. Spin Quantum Number (mₛ)

Values: +½ or –½

Electrons must have opposite spins when sharing the same orbital.

2.3.5 Shapes of Orbitals

• s-orbitals: spherical
• p-orbitals: 3 orientations (px, py, pz)
• d-orbitals: 5 orientations
• f-orbitals: 7 orientations

Understanding shapes helps explain bonding and geometries.

2.4 Electron Configuration and Aufbau Principle

Electron configuration indicates how electrons are arranged in orbitals.

Electrons fill orbitals based on three rules:

2.4.1 Aufbau (Build-Up) Principle

Electrons fill orbitals from lowest to highest energy.

Order (up to Z = 36):

1s
2s
2p
3s
3p
4s
3d
4p
5s
4d
5p…

2.4.2 Pauli Exclusion Principle

No two electrons can have the same set of four quantum numbers.
Hence, an orbital holds a maximum of 2 electrons with opposite spins.

2.4.3 Hund’s Rule of Maximum Multiplicity

Electrons fill degenerate orbitals singly before pairing occurs.

Example:In the p-sublevel, electrons occupy the three p orbitals one-by-one.

2.4.4 Writing Electron Configurations

Example: Phosphorus (Z = 15)
Electron configuration:

1s² 2s² 2p⁶ 3s² 3p³

Orbital notation places electrons into orbitals with arrows.

2.4.5 Condensed (Noble Gas) Notation

Using noble gases:

P: [Ne] 3s² 3p³

This makes configurations shorter and easier.

2.4.6 Exceptions to Expected Configurations

Some transition metals have irregular configurations due to stability of half-filled or fully filled orbitals.

Examples:

• Cr: [Ar] 4s¹ 3d⁵
• Cu: [Ar] 4s¹ 3d¹⁰

These exceptions play important roles in inorganic chemistry.

2.5 The Periodic Table and Periodicity

The periodic table organizes elements based on their properties.

2.5.1 Development of the Periodic Table

Mendeleev’s Contribution

• Arranged elements by increasing atomic mass
• Predicted unknown elements and their properties

Henry Moseley

• X-ray experiments revealed atomic number, leading to the modern arrangement.

2.5.2 Structure of the Modern Periodic Table

• Groups (vertical columns): 1–18
• Periods (horizontal rows): 1–7
• Blocks: s, p, d, f

Major Element Families

• Group 1: Alkali metals
• Group 2: Alkaline earth metals
• Group 17: Halogens
• Group 18: Noble gases
• d-block: Transition metals
• f-block: Lanthanides & actinides

2.6 Periodic Trends

Periodic trends arise from electron configuration and effective nuclear charge.

2.6.1 Atomic Radius

Distance from nucleus to outermost electron shell.

Trend:

• ↓ down a group = increases
• → across a period = decreases

Reason: increasing nuclear charge pulls electrons closer.

2.6.2 Ionic Radius

• Cations are smaller than parent atoms.
• Anions are larger than parent atoms.

Isoelectronic ions decrease in radius with increasing nuclear charge.

2.6.3 Ionization Energy (IE)

Energy required to remove one electron.

Trend:

• ↑ across a period
• ↓ down a group

Noble gases have highest IE.

2.6.4 Electron Affinity (EA)

Energy change when an atom gains an electron.

Non-metals (like halogens) have higher EA than metals.

2.6.5 Electronegativity

Ability of an atom to attract electrons in a bond.

Most electronegative: Fluorine
Least electronegative: Cesium

Trend:

• ↑ across a period
• ↓ down a group

2.6.6 Metallic Character

Metals lose electrons easily.

Trend:

• ↑ down a group
• ↓ across a period

2.6.7 Reactivity

• Metals: increase down a group, decrease across
• Non-metals: decrease down a group, increase across

2.7 Connection Between Atomic Structure and Periodicity

The periodic table is not arbitrary—it reflects electron configuration patterns.

Examples:

• Noble gases: stable full-shell configurations
• Alkali metals: one s-electron → highly reactive
• Halogens: 7 valence electrons → strong oxidizers
• Transition metals: partially filled d-orbitals → variable oxidation states

Atomic structure explains chemical behavior.

2.8 Applications of Atomic Structure and Periodicity

Understanding the atom and periodic trends helps explain:

1. Chemical Reactivity

Predicting which reactions occur and why.

2. Bonding

Electron configuration determines bonding type.

3. Material Science

Metallic, ionic, and covalent properties depend on atomic structure.

4. Biochemistry

Elements like Na, K, Mg, Ca behave differently due to periodic trends.

5. Environmental Chemistry

Reactivity of pollutants, metals, and gases.

2.9 Summary of Key Ideas

• Atomic theory evolved through experiments by Dalton, Thomson, Rutherford, Bohr, and quantum physicists.
• Atoms consist of protons, neutrons, and electrons.
• Quantum mechanics defines electron behavior using orbitals.
• Four quantum numbers describe electron locations.
• Electron configuration follows Aufbau, Pauli, and Hund’s rules.
• The periodic table organizes elements by atomic number and electron configuration.
• Periodic trends arise from shielding, effective nuclear charge, and orbital sizes.
• Atomic structure predicts chemical properties and reactivities.

2.10 Conclusion

Atomic structure and periodicity form the theoretical basis for understanding all chemical behavior. Whether studying chemical bonding, reactivity, thermodynamics, metals, inorganic complexes, or biochemical systems, these principles remain essential. A solid grasp of these concepts enables students to navigate advanced topics and apply chemical knowledge effectively in scientific and industrial contexts.

LECTURE NOTES — CHAPTER THREE 

Chemical Bonding and Molecular Structure

3.0 Introduction

Chemical bonding is one of the most important concepts in chemistry because almost all physical and chemical properties of matter—including hardness, melting point, electrical conductivity, solubility, colour, and reactivity—are determined by the type of bonding holding atoms together. Everything around us, from water to diamonds, from proteins to plastics, is the result of atoms bonding in specific ways.

Atoms bond because they achieve greater stability when their outermost (valence) electron shells are either filled or reach a more energetically favorable configuration. Chemical bonding explains why certain elements readily combine while others resist reaction, why molecules adopt particular shapes, and how the forces between molecules determine states of matter.

In this chapter, we explore the different types of chemical bonds, theories that explain bonding, molecular geometry, intermolecular forces, and how molecular structure affects chemical and physical properties.

3.1 Why Atoms Form Bonds

Atoms form bonds to lower their potential energy and achieve stable electronic configurations, often resembling noble gases.

The main driving forces in bonding are:

1. Electrostatic attraction between positive and negative charges
2. Lowering of energy through sharing or transferring electrons
3. Fulfillment of the octet rule (most main-group elements aim for 8 valence electrons)

Some exceptions exist (H, He, B, expanded octets), but the principle remains a helpful guideline.

Two major categories of bonding include:

1. Intramolecular bonds — occur within a molecule (ionic, covalent, metallic)
2. Intermolecular forces — occur between molecules (hydrogen bonding, dipole interactions, dispersion forces)

Understanding the nature of these interactions is key to explaining molecular behavior.

3.2 Ionic Bonding

An ionic bond forms through complete transfer of electrons from one atom to another, resulting in:

• A positively charged ion (cation)
• A negatively charged ion (anion)

The bond arises from the strong electrostatic attraction between these oppositely charged ions.

3.2.1 Formation of Ionic Bonds

Ionic bonds usually form between:

• Metals (electron donors)
• Nonmetals (electron acceptors)

Example: Formation of sodium chloride

Na (2,8,1) → loses 1 electron → Na⁺
Cl (2,8,7) → gains 1 electron → Cl⁻

They combine to form NaCl.

3.2.2 Properties of Ionic Compounds

Ionic substances have distinct properties:

1. High melting and boiling points
   — result of strong electrostatic attractions.

2. Hard and brittle
   — shifting layers cause repulsion between like charges.

3. Conduct electricity when molten or dissolved
   — ions become mobile.

4. Soluble in polar solvents (like water)

5. Form crystal lattice structures

The strength of the ionic bond is measured by lattice energy, which is the energy required to separate one mole of ionic solid into gaseous ions.

3.2.3 Lattice Energy Factors

Lattice energy increases when:

• Ion charges increase
• Ion sizes decrease
• Lattice structure becomes more compact

Ca²⁺ and O²⁻ produce stronger lattice interactions than Na⁺ and Cl⁻.

3.3 Covalent Bonding

A covalent bond forms when two atoms share electrons to achieve stable configurations.

Covalent bonding typically occurs between:

• Nonmetals + nonmetals
• Nonmetals + metalloids

3.3.1 Types of Covalent Bonds

1. Single Bonds

Sharing one pair of electrons
Example: H–H, H–Cl, CH₄

2. Double Bonds

Sharing two pairs of electrons
Example: O=O, C=O

3. Triple Bonds

Sharing three pairs of electrons
Example: N≡N, C≡C

Bond order increases → bond strength increases → bond length decreases.

3.3.2 Polar vs Nonpolar Covalent Bonds

Bond polarity depends on electronegativity difference.

• Nonpolar covalent (0 – 0.4 difference): equal sharing
• Polar covalent (0.5 – 1.7 difference): unequal sharing

Example:

• H₂ (nonpolar)
• H–Cl (polar)

Polarity creates dipoles, which influence molecular behavior.

3.3.3 Coordinate (Dative) Covalent Bond

Already-shared electron pair comes entirely from one atom.

Example:
NH₃ + H⁺ → NH₄⁺
Here, nitrogen donates both electrons for bonding.

3.4 Metallic Bonding

Metal atoms share a “sea of electrons” that move freely throughout the lattice.

Features of metallic bonding:

1. Electrical conductivity — due to mobile electrons
2. Thermal conductivity
3. Malleability and ductility — layers slide easily
4. Lustrous appearance — electrons absorb and re-emit light
5. Variable bond strength — depends on electron density

Metallic bonding explains why metals exhibit unique physical properties.

3.5 Valence Shell Electron Pair Repulsion (VSEPR) Theory

VSEPR theory predicts molecular shapes based on electron pair repulsion.

Basic principle:

Electron pairs (bonding and lone pairs) around the central atom repel one another and arrange themselves to minimize repulsion.

3.5.1 Electron Domain Geometry vs Molecular Geometry

• Electron geometry considers all electron domains.
• Molecular geometry considers only bonded atoms.

3.5.2 Common VSEPR Shapes

Lone pairs reduce angles due to greater repulsion.

Examples:

• NH₃ → trigonal pyramidal
• H₂O → bent
• CO₂ → linear
• CH₄ → tetrahedral

3.6 Valence Bond Theory (VBT)

VBT explains covalent bonding as the overlap of atomic orbitals.

When two atomic orbitals overlap:

• A bond forms
• Electrons become shared
• Energy decreases

3.6.1 Types of Overlap

Sigma (σ) Bonds

• End-on overlap
• Strongest type of bond
• Present in all covalent bonds
• Single bonds = pure σ-bonds

Pi (π) Bonds

• Side-on overlap
• Weaker than σ-bonds
• Present only in double/triple bonds

Bond structure:

• Double bond = 1 σ + 1 π
• Triple bond = 1 σ + 2 π

3.7 Hybridization Theory

Hybridization involves mixing atomic orbitals to form new hybrid orbitals with equal energy.

3.7.1 Types of Hybridization

sp Hybridization

• 2 electron domains
• Linear geometry
• 180° bond angle
• Example: C in CO₂

sp² Hybridization

• 3 electron domains
• Trigonal planar geometry
• 120°
• Example: C in C₂H₄ (ethylene)

sp³ Hybridization

• 4 electron domains
• Tetrahedral geometry
• 109.5°
• Example: C in CH₄

sp³d Hybridization

• 5 domains
• Trigonal bipyramidal
• Example: P in PCl₅

sp³d² Hybridization

• 6 domains
• Octahedral
• Example: S in SF₆

Hybridization explains molecular shapes more precisely than VSEPR alone.

3.8 Molecular Orbital Theory (MOT)

MOT treats electrons as belonging to the whole molecule, not individual atoms.

3.8.1 Bonding vs Antibonding Orbitals

When atomic orbitals combine:

1. Bonding molecular orbital (σ or π)
   — lowers energy, stabilizes molecule

2. Antibonding molecular orbital (σ or π*)*
   — higher energy, destabilizing

Bond order:

\text{Bond Order} = \frac{(N_{\text{bonding}} - N_{\text{antibonding}})}{2}

Bond order predicts:

• Stability
• Bond length
• Bond strength

Example:
O₂ has bond order 2, and MOT explains its paramagnetism (presence of unpaired electrons).

3.9 Intermolecular Forces (IMFs)

IMFs determine the physical properties of substances.

3.9.1 Types of IMFs

1. London Dispersion Forces (LDF)

• Weakest
• Due to temporary dipoles
• Present in all molecules
• Increase with molecular size

Explain:

• Boiling points of noble gases
• Softness of waxes

2. Dipole–Dipole Interactions

• Occur between permanent dipoles
• Stronger than LDF
• Found in polar molecules

Example: HCl, SO₂

3. Hydrogen Bonding

Strongest IMF
Occurs when H bonds to N, O, or F.

Explains:

• High boiling point of water
• DNA double helix
• Protein folding

4. Ion–Dipole Forces

Strong interactions between ions and polar molecules.

Example: Na⁺ interacting with water molecules during dissolution.

3.10 Molecular Polarity

Molecular polarity depends on:

1. Bond polarity
2. Molecular geometry

A molecule can have polar bonds but still be nonpolar if dipoles cancel.

Examples:

• CO₂ → nonpolar (linear symmetry)
• H₂O → polar (bent geometry)
• CH₄ → nonpolar
• NH₃ → polar

Polarity affects:

• Solubility
• Boiling points
• Intermolecular interactions

3.11 Relationship Between Bonding and Physical Properties

The type of bonding determines many physical properties:

3.11.1 Electrical Conductivity

• Ionic compounds: conduct when molten or in solution
• Metals: excellent conductors
• Covalent compounds: generally poor conductors

3.11.2 Solubility

• Polar solutes dissolve in polar solvents (“like dissolves like”)
• Nonpolar solutes dissolve in nonpolar solvents

3.11.3 Melting and Boiling Points

• Ionic compounds: very high
• Covalent molecules: lower
• Metallic solids: variable
• Network covalent solids (diamond, SiO₂): extremely high

3.12 Lewis Structures and Resonance

Lewis structures show valence electrons as dots.

3.12.1 Rules for Drawing Lewis Structures

1. Count total valence electrons
2. Arrange atoms (central atom is least electronegative)
3. Form bonds (2 electrons each)
4. Complete octets around outer atoms
5. Place remaining electrons on central atom
6. Use multiple bonds if needed

3.12.2 Resonance Structures

Some molecules cannot be represented by a single structure.

Examples:

• O₃
• NO₃⁻
• SO₃
• Benzene (C₆H₆)

Actual structure = resonance hybrid, which is more stable than any single form.

3.13 Bond Energy, Length, and Strength

• Bond energy: energy needed to break a bond
• Bond length: distance between nuclei
• Bond strength: inversely related to bond length

General trends:

• Triple bond > Double bond > Single bond (strength)
• Single bond > Double bond > Triple bond (length)

This explains differences in reactivity and stability.

3.14 Molecular Geometry and Chemical Reactivity

Shape and polarity influence how molecules interact.

Examples:

1. CO₂ is linear → nonpolar → weak interactions → gas at room temperature
2. H₂O is bent → highly polar → hydrogen bonding → liquid at room temperature
3. NH₃ trigonal pyramidal → good electron donor → forms complex ions

Molecular structure determines:

• Reaction mechanisms
• Solubility
• Acid-base behavior
• Redox tendencies
• Biological activity

3.15 Applications of Chemical Bonding

1. Biology

• DNA hydrogen bonding
• Protein folding (IMFs)
• Enzyme–substrate interactions

2. Medicine

• Drug–receptor binding
• Interaction of metal ions with biomolecules

3. Materials Science

• Polymers
• Semiconductors
• Ceramics
• Superconductors

4. Environment

• Water purification
• Atmospheric chemistry

5. Industry

• Production of fertilizers, plastics, metals, and pharmaceuticals

Bonding theories explain why materials behave as they do and how they can be engineered for specific uses.

3.16 Summary of Key Concepts

• Chemical bonding results from atoms seeking stability.
• Ionic bonds involve electron transfer; covalent bonds involve sharing.
• Metallic bonding features delocalized “sea of electrons.”
• VSEPR theory predicts molecular shapes.
• Hybridization explains the geometry of molecules.
• Molecular Orbital Theory gives deeper insight into bonding.
• Intermolecular forces determine physical properties.
• Polarity affects solubility and reactivity.
• Resonance structures provide stability through delocalization.
• Bond strength, length, and energy influence chemical reactions.

3.17 Conclusion

Chemical bonding and molecular structure represent the heart of chemical science. They explain why matter forms the structures we observe, why substances have particular properties, and how molecules behave during reactions. A full understanding of bonding prepares students to tackle advanced chemistry topics such as thermodynamics, kinetics, inorganic chemistry, organic chemistry, and biological chemistry.

Mastery of this chapter not only enhances scientific literacy but also provides the conceptual tools needed for careers in medicine, engineering, biotechnology, environmental science, and industrial chemistry.

CHAPTER FOUR LECTURE NOTES

States of Matter and Gas Laws

4.0 INTRODUCTION

Matter exists in three major physical states: solid, liquid, and gas, and each state displays distinct properties that arise from the arrangement, motion, and interaction of particles. Understanding the behavior of matter in these states is foundational to physical chemistry, particularly when examining how substances respond to temperature, pressure, and intermolecular forces.

In this chapter, we explore in depth the states of matter, the kinetic molecular theory, the laws governing gases, and the behavior of real vs. ideal gases. We also examine the properties of liquids and solids, phase changes, phase diagrams, and the nature of solutions. The chapter integrates both qualitative explanations and quantitative relationships, giving students a strong conceptual and mathematical understanding of physical changes in matter.

4.1 STATES OF MATTER

Matter is anything that has mass and occupies space. On a macroscopic level, matter exists in three principal states:

1. Solid
2. Liquid
3. Gas

These states differ in molecular arrangement, intermolecular forces, compressibility, and movement of particles.

4.1.1 The Solid State

Solids are substances with definite shape and definite volume. Their particles are held close together in a fixed arrangement due to strong intermolecular forces.

Characteristics of Solids

• High density
• Low compressibility
• Extremely limited molecular motion—only vibrational
• Strong intermolecular forces
• Defined melting point (in crystalline solids)

Types of Solids

1. Crystalline Solids
2. Amorphous Solids

i. Crystalline Solids

Crystalline solids have particles arranged in an ordered, repeating three-dimensional pattern known as a crystal lattice.

Examples:

• Sodium chloride (NaCl)
• Quartz (SiO₂)
• Diamond
• Metals

Properties of Crystalline Solids

• Sharp melting point
• Long-range order
• Well-defined geometric shape

ii. Amorphous Solids

Amorphous solids lack long-range order. Their particles are arranged randomly.

Examples:

• Glass
• Rubber
• Plastic

Properties

• Do not have a sharp melting point
• Gradually soften upon heating
• No specific geometric pattern

4.1.2 The Liquid State

Liquids have definite volume but no definite shape, taking the shape of their container. Intermolecular forces in liquids are moderate—stronger than in gases but weaker than in solids.

Characteristics of Liquids

• Free movement of particles but still close together
• Moderate density
• Incompressible
• Exhibit flow
• Surface tension, viscosity, and capillarity

Important Properties of Liquids

a. Surface Tension

Surface tension is the resistance of a liquid surface to external force due to cohesive forces among molecules.

Examples:

• Water droplets forming spheres
• Insects walking on water

b. Viscosity

Viscosity refers to the resistance to flow.

• Honey is highly viscous
• Water has low viscosity

Viscosity decreases with temperature.

c. Vapor Pressure

Vapor pressure is the pressure exerted by vapor molecules at equilibrium with their liquid at a given temperature.

High vapor pressure → boils easily (e.g., ether)

4.1.3 The Gaseous State

Gases have neither definite shape nor definite volume. Their particles are far apart with negligible intermolecular forces, and they move freely at high speeds.

Characteristics of Gases

• Easily compressible
• Expand to fill their container
• Low density
• Rapid diffusion
• Particles move randomly

The behavior of gases is best explained by the kinetic molecular theory, discussed later in the chapter.

4.2 KINETIC MOLECULAR THEORY OF GASES

The kinetic molecular theory (KMT) describes the physical behavior of gases based on molecular motion.

Postulates of KMT

1. Gases consist of extremely small particles (atoms or molecules).
2. The distance between gas particles is large compared to their size.
3. Gas particles move randomly and continuously in straight lines.
4. Collisions between particles and container walls are perfectly elastic.
5. There are no attractive or repulsive forces between gas particles.
6. The average kinetic energy of gas particles is directly proportional to the absolute temperature (Kelvin).

Implications of KMT

• Temperature determines molecular speed.
• Pressure arises from collisions of gas molecules with container walls.
• Gases behave ideally under low pressure and high temperature.

4.3 GAS LAWS

Gas laws relate pressure (P), volume (V), temperature (T), and amount of gas (n). They were discovered through experiments by early scientists such as Boyle, Charles, and Avogadro.

4.3.1 Boyle’s Law (Pressure–Volume Relationship)

At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

PV = k

P_1V_1 = P_2V_2

Graphical Representation

• P vs 1/V → straight line
• P vs V → hyperbola

Example

A gas at 2 atm has a volume of 4 L. What is the volume at 4 atm?

V_2 = \frac{P_1V_1}{P_2} = \frac{2 \times 4}{4} = 2 L

4.3.2 Charles’ Law (Temperature–Volume Relationship)

At constant pressure, the volume of a gas is directly proportional to its absolute temperature.

\frac{V}{T} = k

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

Key Point

Temperature must be in Kelvin (K).

K = ^\circ C + 273

4.3.3 Gay-Lussac’s Law (Pressure–Temperature Relationship)

At constant volume, pressure is directly proportional to absolute temperature.

\frac{P}{T} = k

\frac{P_1}{T_1} = \frac{P_2}{T_2}

4.3.4 Avogadro’s Law (Volume–Mole Relationship)

Equal volumes of gases at the same temperature and pressure contain equal number of molecules.

V \propto n

\frac{V_1}{n_1} = \frac{V_2}{n_2}

Molar Volume

At STP (0°C, 1 atm):

1 \text{ mole of gas} = 22.4 \text{ L}

4.3.5 Ideal Gas Law

Combining all simple gas laws gives:

PV = nRT

Where:

• P = Pressure
• V = Volume
• n = Moles
• R = Gas constant
• T = Temperature (K)

Values of R:

• 0.0821 L·atm·mol⁻¹·K⁻¹
• 8.314 J·mol⁻¹·K⁻¹

4.3.6 Dalton’s Law of Partial Pressures

In a mixture of gases, the total pressure is the sum of partial pressures.

P_{total} = P_1 + P_2 + P_3 + \ldots

Partial pressure is proportional to mole fraction.

P_i = X_i P_{total}

4.3.7 Graham’s Law of Diffusion and Effusion

The rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass.

\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}

Where:

•  = diffusion/effusion rate
•  = molar mass

4.4 REAL GASES VS. IDEAL GASES

Ideal gases obey gas laws under all conditions—but real gases do not.

Ideal Gas Assumptions

• No intermolecular forces
• Gas molecules occupy no volume

These assumptions break down at:

• High pressures
• Low temperatures

4.4.1 Causes of Non-Ideality

1. Gas molecules attract one another (intermolecular forces).
2. Gas molecules occupy space (finite molecular volume).

4.4.2 Van der Waals Equation

Corrects for non-ideal behavior:

\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT

Where:

• a accounts for intermolecular forces
• b accounts for molecular volume

Gases like CO₂ and NH₃ deviate more due to polarity.

4.5 PHASE CHANGES

Substances can change from one physical state to another when temperature or pressure changes.

Important Phase Transitions

• Melting (solid → liquid)
• Freezing (liquid → solid)
• Vaporization (liquid → gas)
• Condensation (gas → liquid)
• Sublimation (solid → gas)
• Deposition (gas → solid)

Latent Heat

Energy needed for phase transitions without temperature change.

4.6 PHASE DIAGRAMS

A phase diagram represents the relationship between temperature, pressure, and physical states.

Important Features

1. Triple Point – all three phases coexist
2. Critical Point – beyond which a gas cannot be liquefied
3. Phase Boundaries – equilibrium curves

Water and CO₂ have different phase behaviors due to molecular structure.

4.7 PROPERTIES OF SOLUTIONS

A solution is a homogeneous mixture of two or more substances.

Components

• Solvent – major component
• Solute – minor component

4.7.1 Types of Solutions

• Gas in gas (air)
• Gas in liquid (soda water)
• Liquid in liquid (alcohol in water)
• Solid in liquid (saltwater)
• Solid in solid (alloys)

4.7.2 Solubility

Solubility is the amount of solute that dissolves in a given amount of solvent at a specific temperature.

Factors Affecting Solubility

1. Temperature
2. Pressure (gases)
3. Nature of solute and solvent
   • “Like dissolves like”

Henry’s Law (Gas Solubility)

C = kP

Where:

• C = solubility
• P = pressure
• k = constant

4.7.3 Colligative Properties

Depend only on the number of solute particles.

1. Boiling point elevation
2. Freezing point depression
3. Osmotic pressure
4. Vapor pressure lowering

Boiling Point Elevation

\Delta T_b = K_b m

Freezing Point Depression

\Delta T_f = K_f m

Osmotic Pressure

\Pi = MRT

4.7.3 Colligative Properties

Depend only on the number of solute particles.

1. Boiling point elevation

2. Freezing point depression

3. Osmotic pressure

4. Vapor pressure lowering

Boiling Point Elevation

\Delta T_b = K_b m

Freezing Point Depression

\Delta T_f = K_f m

Osmotic Pressure

\Pi = MRT

These properties help determine molar masses of compounds experimentally.

4.8 APPLICATIONS OF GAS LAWS AND STATES OF MATTER

1. Breathing Mechanism

Boyle’s law explains how lungs expand and contract.

2. Refrigeration and Air Conditioning

Phase changes of refrigerants absorb and release heat.

3. Weather and Atmospheric Science

Gas laws describe pressure variations and gas mixing.

4. Industrial Gas Production

Liquefaction of air uses real gas deviations.

5. Medicine

Oxygen cylinders rely on pressure-volume relationships.

4.9 SUMMARY OF KEY POINTS

Matter exists as solid, liquid, and gas, each with unique properties.

Kinetic molecular theory explains gas motion and pressure.

Gas laws relate temperature, pressure, volume, and moles.

Real gases deviate at high pressure and low temperature.

Phase diagrams show equilibrium among phases.

Solutions exhibit colligative properties that depend on particle concentration.