Chapter 3: Periodic Properties of the Elements – Study Notes

Periodic Properties of the Elements

Introduction

This chapter explores the periodic trends and properties of elements as organized in the periodic table. Understanding these trends is essential for predicting the chemical and physical behavior of elements and their compounds.

The Periodic Law and the Periodic Table

Development of the Periodic Table

• Periodic Law: The properties of elements are periodic functions of their atomic numbers. This means that elements with similar properties recur at regular intervals when arranged by increasing atomic number.

• Dmitri Mendeleev: Developed the first widely recognized periodic table, arranging elements by atomic mass and predicting the existence and properties of undiscovered elements.

• Modern Periodic Table: Elements are arranged by increasing atomic number, which better reflects periodicity in properties.

Example: Mendeleev's Predictions

Element	Predicted Properties (Mendeleev)	Actual Properties
Gallium (eka-aluminum)	Atomic mass: ~68 amu Density: Low Formula of oxide: X2O3 Formula of chloride: XCl3	Atomic mass: 69.72 amu Density: 5.9 g/cm3 Formula of oxide: Ga2O3 Formula of chloride: GaCl3
Germanium (eka-silicon)	Atomic mass: ~72 amu Density: 5.5 g/cm3 Formula of oxide: XO2 Formula of chloride: XCl4	Atomic mass: 72.6 amu Density: 5.3 g/cm3 Formula of oxide: GeO2 Formula of chloride: GeCl4

Electron Configuration

Quantum Numbers and Orbitals

• Principal Quantum Number (n): Indicates the main energy level or shell.

• Angular Momentum Quantum Number (l): Defines the subshell (s, p, d, f).

• Magnetic Quantum Number (ml): Specifies the orientation of the orbital.

• Spin Quantum Number (ms): Indicates the spin direction of the electron (+1/2 or -1/2).

Aufbau Principle, Pauli Exclusion Principle, and Hund's Rule

• Aufbau Principle: Electrons fill orbitals starting with the lowest available energy levels before filling higher levels.

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

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing up.

Writing Electron Configurations

• Use the order of orbital energies: $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p$

• Shorthand notation uses the previous noble gas in brackets, e.g., [Ne] 3s2 3p4 for sulfur.

• Valence electrons: Electrons in the outermost shell, important for chemical reactivity.

• Core electrons: Electrons in inner shells, not involved in bonding.

Example: Electron Configuration of Carbon

• Full: $1s^2 2s^2 2p^2$

• Shorthand: [He] $2s^2 2p^2$

• Valence electrons: 4 (2 in 2s, 2 in 2p)

Periodic Trends

Effective Nuclear Charge (Zeff)

• Definition: The net positive charge experienced by valence electrons, accounting for shielding by core electrons.

• Calculated approximately as $Z_{eff} = Z - S$, where Z is the atomic number and S is the number of core electrons.

• Trend: Increases across a period (left to right), remains relatively constant down a group.

Atomic and Ionic Radii

• Atomic radius: Half the distance between nuclei of two bonded atoms of the same element.

• Trend: Decreases across a period (due to increasing Zeff), increases down a group (due to additional shells).

• Cation radius: Smaller than the neutral atom (loss of electrons reduces electron-electron repulsion).

• Anion radius: Larger than the neutral atom (gain of electrons increases electron-electron repulsion).

Ionization Energy (IE)

• Definition: The energy required to remove an electron from a gaseous atom or ion.

• First ionization energy: $X(g) \rightarrow X^+(g) + e^-$

• Trend: Increases across a period, decreases down a group.

• Successive ionization energies increase for the same atom.

Example: Ionization Energies of Magnesium

• First IE: $Mg(g) \rightarrow Mg^+(g) + e^-$, $\Delta E = +735$ kJ/mol

• Second IE: $Mg^+(g) \rightarrow Mg^{2+}(g) + e^-$, $\Delta E = +1445$ kJ/mol

Electron Affinity (EA)

• Definition: The energy change when an electron is added to a gaseous atom.

• $X(g) + e^- \rightarrow X^-(g)$

• Trend: Becomes more negative (greater affinity) across a period; less clear trend down a group.

• Halogens have the most negative electron affinities.

Metallic Character

• Definition: The tendency of an element to exhibit properties of metals (e.g., conductivity, malleability, luster).

• Trend: Increases down a group, decreases across a period.

Summary Table: Periodic Trends

Property	Trend Down a Group	Trend Across a Period	Reason
Atomic Radius	Increases	Decreases	More shells down a group; higher Zeff across a period
Ionization Energy	Decreases	Increases	Electrons farther from nucleus down a group; higher Zeff across a period
Electron Affinity	No clear trend	Becomes more negative	Atoms more eager to gain electrons across a period
Metallic Character	Increases	Decreases	Metals are on the left and bottom of the table

Key Terms

• Valence electrons: Outermost electrons involved in bonding.

• Core electrons: Inner electrons not involved in bonding.

• Isoelectronic: Species with the same electron configuration.

• Paramagnetic: Atoms/ions with unpaired electrons; attracted to magnetic fields.

• Diamagnetic: Atoms/ions with all electrons paired; weakly repelled by magnetic fields.

Conclusion

Understanding periodic trends allows chemists to predict and explain the properties and reactivity of elements. Mastery of electron configurations and periodic law is foundational for further study in chemistry.