Study Guide for Periodic Properties of Elements

Chapter 9: Periodic Properties of the Elements

Organizing the Periodic Table

• Elements are organized in the periodic table by:
    - Increasing atomic number - This is the definitive order and is preferred over atomic mass.
    - Each column is referred to as a family or group which has similar properties. Some groups have specific names; for example:
      - Noble gases
      - Halogens
    - Rows are referred to as periods.
  

A Brief History of the Periodic Table

• Dmitri Mendeleev (1834-1907):
    - Developed the modern periodic table.
    - Argued that the properties of elements are periodic functions of their atomic weights.

• Henry Moseley (1887-1915):
    - Improved Mendeleev's table by proposing elements should be arranged by atomic number instead of atomic mass.
    - This arrangement provided better correlations regarding physical and chemical properties.
  
  Periodic Law: Elements are arranged in order of increasing atomic mass, with sets of properties recurring periodically.

• Similar physical and chemical properties fall within the same column or family, allowing for predictions of undiscovered elements based on their predicted properties.

Review of the Quantum-Mechanical Model

• The quantum-mechanical theory explains electron behavior in atoms via four quantum numbers:
    - Principal quantum number (𝑛): Determines the size and energy of an orbital. Integer values include 1, 2, 3,…
    - Angular momentum quantum number (𝓵): Determines the shape of the orbital. Values are integers from 0 to (𝑛−1) corresponding to orbital types: s, p, d, f.
    - Magnetic quantum number (𝑚𝓵): Specifies the orientation of orbitals; ranges from -𝓵 to +𝓵.
    - Spin quantum number (𝑚𝑠): Indicates the orientation of electron spin (
      - 𝑚𝑠 = +½ for spin up     - 𝑚𝑠 = -½ for spin down

How Electrons Occupy Orbitals

• Electron configurations are essential for understanding chemical bonding as they govern how electrons are transferred or shared during bonding.

• The filling of orbitals in multielectron atoms is influenced by:
    - Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers. Therefore, orbitals can hold no more than two electrons with opposite spins (↿⇂).
    - Electrons tend to occupy the lowest energy orbitals available, following the established order of orbital filling and energy levels.

Electron Configurations

• Orbital Diagram: Visual representation of orbitals occupied by electrons:
    - Example: The orbital diagram for lithium (Li) shows the arrangement of its three electrons: 1s² 2s¹.
  

• Energy Levels and Order of Filling:
    1. Electrons occupy orbitals to minimize the energy of the atom, filling lower-energy orbitals before higher-energy orbitals.
    2. Orbital filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.

Reasons for Sublevel Energy Splitting

• Energy splitting occurs in sublevels due to:
    - Coulomb's Law: Governs the potential energy between charged particles.
    - Shielding: Inner electrons shield outer electrons from the full nuclear charge; the effective nuclear charge decreases for outer electrons.
    - Penetration: Determines how close outer electrons can come to the nucleus. S-orbitals penetrate more effectively than P-orbitals, which penetrate more than D-orbitals, affecting energy levels.

Trends in Atomic Size

• Atomic Size increases:
     - Down a column (group) due to an increase in principal quantum number (n).
     - From left to right decreases because the effective nuclear charge (Z_eff) increases, pulling electrons closer.
     

Effective Nuclear Charge (Z_eff)

• Definition: The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom.

• Calculated as follows:
    $Z_{eff} = Z - S$ where:
     - Z = atomic number (total protons)
     - S = shielding electrons (inner electron count)

• Z_eff increases across a period and decreases down a group, affecting ionization energy and atomic radius.
   

Ionization Energy

• Definition: The energy required to remove an electron from an atom or ion in the gas state.
    - Reaction: $X(g) <br>ightarrow X^+(g) + e^-$

• Ionization energy trends:
    - Increases from left to right across a period due to increasing Z_eff.
    - Decreases down a group due to increasing atomic size and thus effective nuclear charge.

Electron Affinity

• Definition: A measure of the energy change when an atom accepts an electron to form an anion.
    - Reaction: $X(g) + e^- <br>ightarrow X^-(g)$

• Most periodic groups show no clear trend, but electron affinity becomes more negative across a period and more positive down a group.

Summary of Element Properties Based on Electron Configuration

• The chemical properties of elements are primarily determined by the number of valence electrons:
    - Elements with configurations nearing the noble gas configuration are particularly reactive.
    - Trends in metallic character and reactivity also correlate with groups in the periodic table, with alkali metals (Group 1A) being the most reactive.