Chapter 3: Periodic Properties

Chapter 3: Periodic Properties of the Elements

Introduction

The periodic table organizes elements based on recurring chemical and physical properties, which are determined by atomic structure and electron configurations. Understanding periodic trends is essential for predicting element behavior and chemical reactivity.

Learning Outcomes

• Electron Configurations: Distribution of electrons among atomic orbitals.

• Orbital Diagrams: Visual representation of electron arrangements.

• Valence vs. Core Electrons: Differentiation between electrons involved in bonding and those that are not.

• Periodic Table and Electron Configuration: Relationship between table position and electron arrangement.

• Predicting Ion Charges: Using periodic trends to determine likely ion charges.

• Periodic Trends: Trends in atomic size, ionization energy, and electron affinity.

3.1 Aluminum: Low-Density Atoms Result in Low-Density Metal

Comparison of Densities

• Aluminum is used in airplanes due to its low density ($2.70\,\text{g/cm}^3$).

• Iron: $7.87\,\text{g/cm}^3$; Platinum: $21.4\,\text{g/cm}^3$.

• Low density of aluminum is attributed to its low mass-to-volume ratio.

Group 13 Elements

• Boron (B): Atomic number 5, radius 85 pm, density $2.34\,\text{g/cm}^3$

• Aluminum (Al): Atomic number 13, radius 143 pm, density $2.70\,\text{g/cm}^3$

• Gallium (Ga): Atomic number 31, radius 135 pm, density $5.91\,\text{g/cm}^3$

• Indium (In): Atomic number 49, radius 166 pm, density $7.31\,\text{g/cm}^3$

Reason for Increasing Density

• As you move down a column, atomic mass increases more than atomic volume, leading to higher density.

3.2 The Periodic Law and the Periodic Table

Early Organization of Elements

• Johann Döbereiner: Grouped elements into triads based on similar properties.

• John Newlands: Arranged elements into octaves, noting periodic repetition of properties.

Mendeleev’s Periodic Table

• Arranged elements by increasing mass, observed periodicity.

• Periodic Law: When elements are arranged in order of increasing mass, certain sets of properties recur periodically.

• Predicted properties of undiscovered elements.

Modern Periodic Table

• Arranged by increasing atomic number (Henry Moseley).

• Main-group elements (groups 1A, 2A, 3A-8A) have predictable properties.

Periodic Table Structure

• Main-group elements: labeled with a number and letter A.

• Transition elements: labeled with a number and letter B.

• Alternative numbering: 1–18 left to right.

• Each column (group) contains elements with similar properties.

Scientific Approach and Quantum Mechanics

• Periodic law is based on observed properties, but quantum mechanics explains the underlying reasons.

• Similar properties in elements are due to similarities in electron configurations.

3.3 Electron Configurations: How Electrons Occupy Orbitals

Electron Configuration and Orbital Diagrams

• Electron configuration shows the specific orbitals that electrons occupy in an atom.

• For hydrogen: 1 electron in 1s orbital (lowest energy).

• Electrons generally occupy the lowest energy orbitals available.

Schrödinger Equation and Quantum Numbers

• Describes atomic orbitals and their energies.

• For multielectron atoms, includes electron interaction terms.

Electron Spin and the Pauli Exclusion Principle

• Electron Spin: Fundamental property; two possible values ($+\frac{1}{2}$, $-\frac{1}{2}$).

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.

Example: Helium Atom

• Electron 1: $n=1, l=0, m_l=0, m_s=+\frac{1}{2}$

• Electron 2: $n=1, l=0, m_l=0, m_s=-\frac{1}{2}$

Sublevel Energy Splitting in Multielectron Atoms

• Energy of orbitals depends on principal quantum number ($n$) and angular momentum quantum number ($l$).

• Orbitals with same $n$ but different $l$ are not degenerate.

• Key concepts: Coulomb’s Law, Shielding, Penetration.

Coulomb’s Law

• Describes interactions between charged particles: $E = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r}$

• Potential energy is negative for opposite charges, positive for like charges.

Shielding

• Electrons shield each other from nuclear charge, reducing effective nuclear charge felt by outer electrons.

Penetration

• Electrons in orbitals that penetrate closer to the nucleus experience greater nuclear charge, lowering their energy.

Electron Configuration Rules

• Aufbau Principle: Electrons occupy lowest energy orbitals first.

• Hund’s Rule: Electrons fill degenerate orbitals singly first, with parallel spins.

• Pauli Exclusion Principle: No two electrons in an atom have the same set of quantum numbers.

Summarizing Orbital Filling

• Order of orbital filling: $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p$

• Each orbital holds max two electrons, with opposite spins.

Electron Configurations for Selected Elements

• Mg (12 electrons): $1s^2 2s^2 2p^6 3s^2$

• P (15 electrons): $1s^2 2s^2 2p^6 3s^2 3p^3$

• S (16 electrons): $1s^2 2s^2 2p^6 3s^2 3p^4$

3.4 Electron Configurations, Valence Electrons, and the Periodic Table

Valence Electrons

• Electrons in the outermost principal energy level.

• Determine chemical properties and reactivity.

• For main-group elements, number of valence electrons equals group number.

Example: Silicon (Si)

• Electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^2$

• Valence electrons: 4 ($3s^2 3p^2$)

Orbital Blocks in the Periodic Table

• s-block: Groups 1A and 2A; outer electron configurations end in $ns^1$ or $ns^2$.

• p-block: Groups 3A–8A; outer electron configurations end in $ns^2 np^1$ to $ns^2 np^6$.

• d-block: Transition elements; outer electron configurations end in $ns^2 (n-1)d^1$ to $ns^2 (n-1)d^{10}$.

• f-block: Inner transition elements; outer electron configurations end in $ns^2 (n-2)f^1$ to $ns^2 (n-2)f^{14}$.

Summarizing Periodic Table Organization

• Number of valence electrons for main-group elements equals group number.

• Highest principal quantum number ($n$) equals row number.

3.5 Electron Configurations and Elemental Properties

Metals, Nonmetals, and Metalloids

• Metals: Lower left and middle of periodic table; good conductors, ductile, malleable, tend to lose electrons.

• Nonmetals: Upper right; poor conductors, tend to gain electrons.

• Metalloids: Stair-stepped section; intermediate properties.

General Trends

• Metals lose electrons to achieve noble gas configurations.

• Nonmetals gain electrons to achieve noble gas configurations.

Families of Elements

• Noble Gases (Group 8A): $ns^2 np^6$; unreactive.

• Alkali Metals (Group 1A): $ns^1$; lose one electron.

• Alkaline Earth Metals (Group 2A): $ns^2$; lose two electrons.

• Halogens (Group 7A): $ns^2 np^5$; gain one electron.

The Formation of Ions

• Atoms lose or gain electrons to form ions: metals form cations, nonmetals form anions.

• Group 1A: $1^+$ cations; Group 2A: $2^+$ cations; Group 7A: $1^-$ anions.

Electron Configurations and Ion Charge

• Main-group elements form ions with electron configurations of noble gases.

• Example: $\text{Na}^+$ has configuration $1s^2 2s^2 2p^6$ (like Ne).

3.6 Periodic Trends in Atomic Size and Effective Nuclear Charge

Atomic Radius Trends

• Atomic radius increases down a column, decreases across a period.

• Van der Waals radius: Half the distance between adjacent nuclei in a solid of nonbonding atoms.

• Covalent radius: Half the distance between two bonded atoms.

Examples

• Krypton: $220\,\text{pm}$

• Iodine chloride: $232\,\text{pm}$

Effective Nuclear Charge ($Z_{\text{eff}}$)

• Increases left to right across a period.

• Trend: Atomic radius decreases as $Z_{\text{eff}}$ increases.

Example: Li and He

• Li: $1s^2 2s^1$; $2s$ electron is shielded by $1s$ electrons.

• He: $1s^2$; both electrons experience full nuclear charge.

Electron Configurations and Magnetic Properties of Ions

• Electron configurations for ions: Remove electrons from highest $n$ orbital for cations, add for anions.

• Paramagnetic: Unpaired electrons; attracted to magnetic field.

• Diamagnetic: All electrons paired; not attracted to magnetic field.

Example

• Zn: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10}$; diamagnetic.

Ionization Energy

• Ionization energy (IE): Energy required to remove an electron from an atom in the gaseous state.

• First ionization energy ($IE_1$): $\text{Na}(g) \rightarrow \text{Na}^+(g) + e^-$

• Second ionization energy ($IE_2$): $\text{Na}^+(g) \rightarrow \text{Na}^{2+}(g) + e^-$

Trends in Ionization Energy

• Increases across a period (higher $Z_{\text{eff}}$).

• Decreases down a group (electrons farther from nucleus).

Examples

• Alkali metals: $IE_1$ decreases down the group.

• Noble gases: $IE_1$ at a maximum.

Electron Affinities and Metallic Character

• Electron affinity (EA): Energy change when an atom gains an electron.

• EA is usually negative (energy released).

• EA becomes more negative across a period, less negative down a group.

Example

• Chlorine: $\text{Cl}(g) + e^- \rightarrow \text{Cl}^-(g); \Delta E = -349\,\text{kJ/mol}$

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Becomes more negative	Becomes less negative
Metallic Character	Decreases	Increases

Key Equations

• Coulomb’s Law: $E = \frac{1}{4\pi\varepsilon_0} \frac{q_1q_2}{r}$

• Effective Nuclear Charge: $Z_{\text{eff}} = Z - S$

Conclusion

Understanding periodic properties and electron configurations is fundamental to predicting chemical behavior and reactivity. The periodic table is a powerful tool for organizing elements and understanding their properties based on atomic structure.