Chapter 7: Periodic Properties & Effective Nuclear Charge

Effective Nuclear Charge (Zeff)

The effective nuclear charge (Zeff) is the net positive charge experienced by a valence electron in a multi-electron atom. It accounts for the shielding effect of core electrons, which reduce the full attractive force of the nucleus.

• Definition: The actual net positive charge attracting a valence electron toward the nucleus.

• Formula: where = total number of protons, = number of core (inner) electrons.

• Core Electrons: Calculated as total electrons minus valence electrons.

• Period Trend: Zeff increases from left to right across a period (row) due to increasing nuclear charge with minimal additional shielding.

• Group Trend: Zeff remains roughly constant down a group (column) because added shells increase both and similarly.

Example: For chlorine (Cl, Z = 17), with 10 core electrons (1s22s22p6), .

The Four Key Periodic Trends

Periodic trends describe how certain atomic properties change across the periodic table.

• 1. Atomic Radius (Size):

  • Decreases across a period (left to right) due to increasing Zeff pulling electrons closer.

  • Increases down a group as higher principal quantum numbers (n) add electron shells.

• 2. Metallic Character:

  • Decreases across a period as Zeff increases, making it harder to lose electrons.

  • Increases down a group as outer electrons are farther from the nucleus and more easily lost.

• 3. Ionization Energy (IE):

  • Increases across a period due to stronger attraction between nucleus and electrons.

  • Decreases down a group as valence electrons are farther from the nucleus and less tightly held.

• 4. Electron Affinity (EA):

  • Becomes more negative (more exothermic) across a period as atoms more readily accept electrons.

  • Becomes less negative down a group as added electrons are farther from the nucleus.

Chapter 8: Chemical Bonding & Lewis Structures

Electronegativity & Bond Polarity

Electronegativity is the ability of an atom in a molecule to attract shared electrons to itself. It determines the type of bond formed between atoms.

• Trend: Electronegativity increases up and to the right on the periodic table (highest in fluorine).

• Bond Types by Electronegativity Difference:

  • Nonpolar Covalent: Electrons shared equally; difference < 0.4.

  • Polar Covalent: Electrons shared unequally; difference = 0.4 to 1.8.

  • Ionic Bond: Electrons transferred; difference > 1.8.

• Dipole Arrow: Points toward the more electronegative atom, indicating bond polarity.

Example: In HCl, Cl is more electronegative, so the dipole arrow points toward Cl.

Step-by-Step Lewis Structures

Lewis structures represent the arrangement of valence electrons in molecules. Follow these steps:

1. Sum all valence electrons (adjust for polyatomic ion charges).

2. Choose the central atom (usually the least electronegative, never hydrogen).

3. Connect outer atoms to the central atom with single bonds.

4. Distribute remaining electrons as lone pairs to complete octets on outer atoms first.

5. Place any leftover electrons on the central atom.

6. If the central atom lacks an octet, form multiple bonds as needed.

Example: For CO2 (carbon dioxide):

• Total valence electrons: 4 (C) + 2 × 6 (O) = 16

• Central atom: C

• Each O forms a double bond with C to complete octets.

Resonance Structures

Some molecules have more than one valid Lewis structure, called resonance structures. The actual structure is a hybrid of these forms.

• Definition: Multiple valid Lewis structures for a single molecule or ion.

• Formal Charge (FC) Formula:

• Best Structure: Minimizes formal charges; negative charges should be on the most electronegative atoms.

Example: The thiocyanate ion (SCN-) has several resonance structures, with the most stable one placing the negative charge on nitrogen.

Lattice Energy & Size

Lattice energy is the energy released when gaseous ions form an ionic solid. It is a measure of the strength of the ionic bonds in a crystal lattice.

• Formula: where and are the charges of the ions, is the distance between ion centers, and is a proportionality constant.

• Rule 1 (Charge First): Higher ionic charges result in much higher lattice energy.

• Rule 2 (Size Second): Smaller ionic radii allow ions to pack closer, increasing lattice energy.

Example: MgO (Mg2+ and O2-) has a much higher lattice energy than NaCl (Na+ and Cl-) due to higher charges.

Practice Questions (Selected with Academic Context)

Periodic Properties

• Q1: Calculate the Zeff for a valence electron in Cl (Z = 17). Solution: Core electrons = 10 (1s22s22p6), so .

• Q2: Which element has the highest first ionization energy? (Na, Cl, F, Ne) Answer: Ne (noble gases have the highest IE in a period).

• Q3: Rank by increasing metallic character: Ca, Ba, Mg. Answer: Mg < Ca < Ba (metallic character increases down a group).

• Q4: Arrange by decreasing lattice energy: MgO, NaCl, NaF, MgS. Answer: MgO > MgS > NaF > NaCl (higher charges and smaller ions increase lattice energy).

Lewis Structures and Resonance

• Q5: Draw the Lewis structure for CO2 and calculate formal charges.

  • Lewis structure: O=C=O, each O has two lone pairs.

  • Formal charge on C: 4 (valence) - 0 (lone pairs) - 4 (bonds) = 0

  • Formal charge on each O: 6 (valence) - 4 (lone pairs) - 2 (bonds) = 0

• Q6: Draw all resonance structures for SCN- and identify the most stable.

  • Possible resonance forms:

    1. S=C=N- (negative charge on N)

    2. S--C≡N (negative charge on S)

    3. S≡C-N- (less common, negative charge on N)

  • Most stable: S=C=N- (negative charge on the most electronegative atom, N).

Summary Table: Periodic Trends