Chapter 8: Periodic Properties of the Elements – Study Notes

Periodic Properties of the Elements

Introduction

The periodic table is a powerful tool for understanding the properties of elements. Periodic properties are those that repeat or show predictable trends as you move across or down the table. These trends arise from the arrangement of electrons in atoms and the structure of the periodic table itself.

The Development of the Periodic Table

Historical Background

• Periodic Property: A property of an element that is predictable based on its position in the periodic table.

• Dmitri Mendeleev (1834–1907) and Julius Meyer (1830–1895) independently developed early versions of the periodic table, arranging elements by increasing mass and recurring properties.

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

• The modern periodic table is arranged so that elemental mass increases from left to right, and elements with similar properties fall in the same column.

The Periodic Table and Electron Configurations

Atomic Number and Electron Configuration

• Henry Moseley (1913) established that elements are best arranged by atomic number (number of protons), not atomic mass.

• Using atomic number sequence to order elements better correlates with elemental properties.

• Electron configurations of elements can be superimposed on the periodic table, showing a connection between position and configuration.

Electron Configurations, Valence Electrons, and the Periodic Table

Core and Valence Electrons

• Core electrons: Electrons in complete principal energy levels and those in complete d and f sublevels.

• Valence electrons: Most important bonding electrons; for main group elements, these are in the outermost principal energy level.

• For transition elements, valence electrons include outermost d electrons, even if not in the highest principal energy level.

• Examples:

  • Si: $1s^2 2s^2 2p^6 3s^2 3p^2$

  • Ge: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2$

  • V: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3$

Orbital Blocks in the Periodic Table

Sublevels and Electron Capacity

• s sublevel: 1 orbital, 2 electrons

• p sublevel: 3 orbitals, 6 electrons

• d sublevel: 5 orbitals, 10 electrons

• f sublevel: 7 orbitals, 14 electrons

• Row number: Equal to the number of the highest principal energy level.

Writing Electron Configurations from the Periodic Table

Methodology

• The periodic table's organization allows us to write electron configurations for any element based on its position.

• Inner electron configuration: Describes electrons of the noble gas that precedes the element (core electrons).

• Outer electron configuration: Describes electrons beyond the previous noble gas (valence electrons).

• Example: Cl: [Ne] $3s^2 3p^5$

The d-Block and f-Block Elements

Transition and Inner Transition Metals

• d-Block (Transition metals): Electron configuration trends differ from main-group elements. The principal quantum number of the d orbital being filled is the row number minus one.

• 1st row: Most configurations are $4s^2 3d^n$ except for Cr and Cu (which have anomalous configurations).

• 2nd row: More difficult to predict; actual configurations determined experimentally.

• f-Block (Inner transition metals): Principal quantum number of the f orbital being filled is the row number minus two. For the sixth row, 4f orbitals are filled; for the seventh row, 5f orbitals are filled.

• Close energy spacing of 5d and 4f allows electrons to enter 5d orbital instead of expected 4f orbital.

Periodic Trends in Atomic Size and Effective Nuclear Charge

Defining Atomic Size

• Nonbonding atomic radius (van der Waals radius): Half the distance between atoms in direct contact but not bonded.

• Bonding atomic radius (covalent radius): Half the distance between two bonded atoms.

• Atomic radius: Average bonding radii determined from measurements on many elements and compounds.

Trends in Atomic Radius

• Down a group (column): Atomic radius increases due to addition of electron shells.

• Across a period (row): Atomic radius decreases due to increased effective nuclear charge ($Z_{eff}$), pulling electrons closer to the nucleus.

• Transition elements: Size trends are less consistent; small increase from Period 4 to 5, no increase from Period 5 to 6 (lanthanoid contraction).

Effective Nuclear Charge ($Z_{eff}$)

Definition and Calculation

• Effective nuclear charge: The net positive charge experienced by an electron in a multi-electron atom.

• For a particle electron: $Z_{eff} = Z - S$ where $Z$ is the actual nuclear charge and $S$ is the shielding constant.

• Slater's Rules: Used to calculate the shielding constant ($S$) for a given electron.

Element	Na	Mg	Al	P	S	Cl	Ar
$Z_{eff}$	2.20	3.25	4.45	5.50	6.45	7.65	8.60
Radius (pm)	186	160	141	121	107	102	106

Additional info: There is an inverse relationship between $Z_{eff}$ and atomic size.

Ionic Radii

Comparison to Atomic Radii

• Cations: Smaller than their corresponding atoms due to loss of electrons and increased effective nuclear charge.

• Anions: Larger than their corresponding atoms due to gain of electrons and decreased effective nuclear charge.

Isoelectronic Series

• Isoelectronic species have the same electron configuration but different nuclear charges.

• Example: $S^{2-}$, $Cl^-$, $K^+$, $Ca^{2+}$ all have $3s^2 3p^6$ configuration, but their radii differ due to varying numbers of protons.

Ion	Radius (pm)
$S^{2-}$	184
$Cl^-$	181
$K^+$	133
$Ca^{2+}$	99

Ionization Energy

Definition and Trends

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

• Always positive; the lower the IE, the easier it is to remove an electron.

• Trends:

  • IE increases from left to right across a period.

  • IE decreases from top to bottom down a group.

Exceptions to Trends

• Between Be to B (Mg to Al, Ca to Ga): IE decreases unexpectedly due to electron entering a new sublevel.

• Between N to O (and P to S, As to Se): IE decreases due to electron pairing and increased repulsion.

• Example:

  • N: $2s^2 2p^3$ (no repulsions in same orbital)

  • O: $2s^2 2p^4$ (pairing of electrons; electronic repulsion)

Ionization Energies in Transition Metals

• Small decrease in IE from d-block to p-block (e.g., Cd to In).

• Successive removal of electrons shows a large jump when removing a core electron after all valence electrons are gone.

Summary Table: Key Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Effective Nuclear Charge ($Z_{eff}$)	Increases	Decreases slightly
Metallic Character	Decreases	Increases

Practice and Application

• Determine the number of valence electrons for nitrogen: 5 (Group 15).

• Write the full electron configuration for aluminum (Al): $1s^2 2s^2 2p^6 3s^2 3p^1$.

• Arrange Br, Br-, Cl, Se2- in order of increasing atomic or ionic radius: Cl < Br < Br- < Se2-.

Additional info:

• Periodic trends are foundational for predicting chemical reactivity, bonding, and physical properties of elements.

• Understanding electron configurations is essential for rationalizing these trends.