Chapter 9: Periodic Properties of the Elements – General Chemistry Study Notes

Periodic Properties of the Elements

Introduction

This chapter explores the periodic properties of elements, focusing on electron configurations, periodic trends, and the chemical behavior of groups in the periodic table. Understanding these concepts is essential for predicting and explaining the properties of elements and their compounds.

Electron Configuration

Definition and Notation

• Electron configuration describes the arrangement of electrons in an atom's orbitals.

• Notation example: H: 1s1 ("1s" is the orbital, "1" is the number of electrons in that orbital).

Rules for Electron Configuration

• Aufbau Principle: Electrons fill orbitals starting with the lowest energy first.

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

• Each orbital can hold a maximum of 2 electrons, with opposite spins ($m_s = +1/2$ and $m_s = -1/2$).

Sublevel Splitting in Multielectron Atoms

• In multielectron atoms, subshell orbitals are no longer degenerate (not equal in energy).

• For the same principal quantum number $n$, orbitals with higher angular momentum quantum number $l$ have higher energy: $s < p < d < f$.

• The 4s orbital is slightly lower in energy than the 3d orbital.

Writing Electron Configurations

• Sequence to remember: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...

• Each shell contains: one s orbital (2 electrons), three p orbitals (6 electrons), five d orbitals (10 electrons).

• Example: Nitrogen (N, atomic number 7): $1s^2 2s^2 2p^3$

Orbital Diagrams

• Each box represents an orbital; half-arrows represent electrons and their spins.

• Boxes for orbitals in the same subshell are attached.

• Hund's Rule: For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized. Place one electron in each orbital before pairing.

Condensed Electron Configuration and Valence Electrons

Core and Valence Electrons

• Valence electrons are those in the outermost shell (largest $n$); they determine chemical properties.

• Core electrons are those in inner shells.

• Condensed electron configuration: Use the noble gas symbol to represent core electrons, followed by the configuration of valence electrons. Example: Na: [Ne] 3s1; Mn: [Ar] 4s2 3d5

Valence Electrons by Group

Group	Valence Electrons
1A	1
2A	2
3A	3
4A	4
5A	5
6A	6
7A	7
8A (Noble gases)	0 (full shell)

Irregular Electron Configurations

Exceptions in Transition Metals

• Some transition metals have electron configurations that differ from the expected order due to extra stabilization of half-filled or fully-filled d subshells.

Element	Expected	Actual
Cr	[Ar] 4s2 3d4	[Ar] 4s1 3d5
Cu	[Ar] 4s2 3d9	[Ar] 4s1 3d10
Mo	[Kr] 5s2 4d4	[Kr] 5s1 4d5
Ru	[Kr] 5s2 4d6	[Kr] 5s1 4d7
Pd	[Kr] 5s2 4d8	[Kr] 4d10

Cations of Transition Metals

Electron Removal in Cation Formation

• When transition metals form cations, electrons are first removed from the outermost shell (highest $n$), even if they were filled before inner d electrons.

• Example: Fe atom: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6$ Fe2+: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6$ Fe3+: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^5$

Magnetic Properties of Transition Metal Atoms and Ions

Paramagnetism and Diamagnetism

• Paramagnetism: Atoms/ions with unpaired electrons are attracted to a magnetic field.

• Diamagnetism: Atoms/ions with all electrons paired are slightly repelled by a magnetic field.

Counting Unpaired Electrons

• Use Hund's rule and electron configuration to determine the number of unpaired electrons.

• Example: Fe2+ ([Ar] 3d6) has 4 unpaired electrons.

Periodic Table and Periodic Trends

Understanding Group Properties

• Elements in the same group have similar chemical properties due to similar valence electron configurations.

• Noble gases are inert due to full valence shells.

• Metals (groups 1, 2, 3) tend to lose electrons; nonmetals (groups 6, 7) tend to gain electrons.

Trends in the Periodic Table

• Trends are analyzed both across periods (left to right) and down groups (top to bottom).

Effective Nuclear Charge ($Z_{eff}$)

Definition and Calculation

• Effective nuclear charge ($Z_{eff}$) is the net positive charge experienced by valence electrons.

• Calculated as: $Z_{eff} = Z - S$, where $Z$ is atomic number and $S$ is the screening constant (approximate number of inner electrons).

• Attraction to valence electrons: $F = k \frac{eZ_{eff}}{r^2}$

Trends in $Z_{eff}$

• Across a period: $Z_{eff}$ increases (more protons, similar shielding).

• Down a group: $Z_{eff}$ increases slightly, but increased shell number ($r$) reduces attraction.

Atomic Radius

Trend of Atomic Radius

• Across a period (left to right): atomic radius decreases (increased $Z_{eff}$ pulls electrons closer).

• Down a group (top to bottom): atomic radius increases (more electron shells).

Size of Ions

Cations vs. Anions

• Cations (positive ions) are smaller than their parent atoms due to loss of electrons and reduced electron repulsion.

• Anions (negative ions) are larger than their parent atoms due to gain of electrons and increased electron repulsion.

Ionization Energy

Definition and Trends

• Ionization energy (IE): Minimum energy required to remove an electron from an atom or ion in the gas phase.

• First IE: removal from neutral atom; second IE: removal from 1+ ion, etc.

• Across a period: first IE increases (higher $Z_{eff}$).

• Down a group: first IE decreases (valence electrons farther from nucleus).

• Exceptions exist due to subshell stability (e.g., Be > B, N > O).

Element	I1	I2	I3	I4	I5
Na	495	4562	--	--	--
Mg	738	1451	7733	--	--
Al	578	1817	2745	11577	--
Si	786	1577	3232	4356	16091

Electron Affinity

Definition and Trends

• Electron affinity (EA): Energy released when a neutral atom gains an electron (usually exothermic).

• Across a period: EA increases (more negative values, especially for group 7).

• Down a group: EA decreases (less negative values).

• Exceptions exist due to subshell stability and electron repulsion.

Group	Electron Affinity (kJ/mol)
1A (H)	-73
2A (Be)	>0
3A (B)	-27
4A (C)	-122
5A (N)	>0
6A (O)	-328
7A (F)	-328
8A (Ne)	>0

Trends in Metallic Character

Metallic vs. Nonmetallic Properties

• Across a period: metallic character decreases.

• Down a group: metallic character increases.

Properties of Typical Groups

Alkali Metals (Group 1)

• Electron configuration: ns1

• Very reactive, good reducing agents, easily oxidized.

• React with nonmetals to form salts. Example: $2Na + Cl_2 \rightarrow 2NaCl$

Halogens (Group 7)

• Electron configuration: ns2np5

• Very reactive, not found uncombined in nature.

• React with metals to form salts. Example: $2Na + Cl_2 \rightarrow 2NaCl$

Noble Gases (Group 8)

• Electron configuration: ns2np6

• Very unreactive, found uncombined in nature.

• Used as "inert" atmospheres in chemical reactions.

• Only react with F under extreme conditions. Example: $Kr + F_2 \rightarrow KrF_2$

Summary of Periodic Trends

• Across a period (left to right): Effective nuclear charge increases First ionization energy increases Electron affinity increases Atomic size decreases Metallic property decreases

• Down a group (top to bottom): First ionization energy decreases Electron affinity decreases Atomic size increases Metallic property increases

• Exceptions exist for all trends due to subshell effects and electron repulsion.

Additional info:

• All equations are provided in LaTeX format for clarity.

• Tables have been recreated to summarize group properties and periodic trends.