Periodic Trends, Ionic Bonds, and Lattice Energy: Study Notes for General Chemistry

Periodic Trends, Ionic Bonds, and Lattice Energy

Atomic Structure and Ion Formation

Atoms can gain or lose electrons to form ions, a process governed by their electronic structure and periodic trends. Understanding how main-group and transition metals form cations, and how nonmetals form anions, is fundamental to predicting chemical behavior.

• Main-group metals form cations by losing electrons from their highest-energy shell.

• Main-group nonmetals form anions by gaining enough electrons to fill their highest-energy shell.

• Transition metals form cations by first losing electrons from their highest-energy s-subshell, then from their d-subshell if necessary.

• Periodic trend in atomic radii:

  • Size increases down a group.

  • Size decreases across a period.

  • Cations are smaller than their parent atoms.

  • Anions are larger than their parent atoms.

  • Ion size increases down a group.

Ionization Energy

Ionization energy is the energy required to remove an electron from a gas-phase atom. It is a key property that influences chemical reactivity and periodic trends.

• Definition: The energy required to remove an electron from a neutral atom in the gas phase.

• General equation:

$X(g) \rightarrow X^+(g) + e^-$

• Ionization energies are always positive; energy input is required.

Periodic Trends in Ionization Energy

Ionization energy varies predictably across the periodic table.

• Increases across a period (left to right).

• Decreases down a group (top to bottom).

• Maximum values for noble gases; minimum values for alkali metals.

Reason: Across a period, effective nuclear charge ($Z_{\text{eff}}$) increases, making electrons harder to remove. Down a group, increased distance from the nucleus makes electrons easier to remove.

Ionization Energy at Period Extremes

• Noble gases have very high ionization energies because removing an electron destroys a filled valence shell.

• Alkali metals have low ionization energies because removing an electron creates a filled valence shell.

Examples:

• $\text{Ne}(1s^22s^22p^6) \rightarrow \text{Ne}^+(1s^22s^22p^5) + e^-$

• $\text{Na}(1s^22s^22p^63s^1) \rightarrow \text{Na}^+(1s^22s^22p^6) + e^-$

Irregularities in Ionization Energy Trends

• Subshell energies cause exceptions (e.g., Mg has higher ionization energy than expected due to filled 3s subshell).

• Hund’s rule: Pairing electrons is energetically unfavorable, so removing a paired electron (easier) can cause lower ionization energy than expected (e.g., O vs. N).

Higher Order Ionization Energies

Atoms can lose more than one electron, each subsequent ionization requiring more energy.

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

• Second ionization: $X^+(g) \rightarrow X^{2+}(g) + e^-$

• Third ionization: $X^{2+}(g) \rightarrow X^{3+}(g) + e^-$

• Each successive ionization energy is larger than the previous.

There is always one ionization energy that is much larger than the previous, corresponding to the removal of an electron from a filled valence shell.

Electron Affinity

Electron affinity is the energy change when an electron is added to a gas-phase atom. It reflects an atom’s tendency to accept electrons and form anions.

• Definition: The energy change when a neutral atom gains an electron.

• General equation:

$X(g) + e^- \rightarrow X^-(g)$

• Electron affinities are generally negative (energy released).

• Large negative values indicate a strong tendency to accept electrons.

• Zero electron affinity means no measurable energy change.

Periodic Trends in Electron Affinity

• Halogens: Large, negative electron affinities (form stable anions with filled valence shells).

• Noble gases: Positive electron affinities (adding an electron destroys a filled shell).

• Alkaline earth metals: Electron affinities approximately zero (added electron goes into a higher energy subshell).

Examples:

• Halogen: $\text{Br}([Ar]4s^23d^{10}4p^5) + e^- \rightarrow \text{Br}^-([Ar]4s^23d^{10}4p^6)$

• Noble gas: $\text{Ne}(1s^22s^22p^6) + e^- \rightarrow \text{Ne}^-(1s^22s^22p^63s^1)$

• Alkaline earth: $\text{Be}(1s^22s^2) + e^- \rightarrow \text{Be}^-(1s^22s^22p^1)$

The Octet Rule

The octet rule states that main-group elements tend to react to achieve a filled valence shell (usually 8 electrons), which is associated with chemical stability.

• Atoms with filled valence shells are unreactive (e.g., noble gases).

• Atoms without filled valence shells react by gaining or losing electrons.

• Alkali metals are good reducing agents; halogens are good oxidizing agents.

Ionic Bond Formation

Ionic bonds form when electrons are transferred from one atom (usually a metal) to another (usually a nonmetal), resulting in the formation of cations and anions. The process is governed by ionization energy, electron affinity, and the octet rule.

• Electrons are lost by atoms with low ionization energy.

• Electrons are gained by atoms with large, negative electron affinity.

• The number of electrons lost or gained is determined by the octet rule.

Example: Formation of NaCl

• $\text{Na}(1s^22s^22p^63s^1) + \text{Cl}(1s^22s^22p^63s^23p^5) \rightarrow \text{Na}^+(1s^22s^22p^6) + \text{Cl}^-(1s^22s^22p^63s^23p^6)$

Energetics of Ionic Bond Formation: The Born-Haber Cycle

The formation of an ionic compound like NaCl involves several steps, each with associated energy changes. The overall energy change is determined by the sum of these steps, known as the Born-Haber cycle.

• Step 1: Sublimation of Na(s) to Na(g): $E_1 = 107.3$ kJ/mol

• Step 2: Dissociation of Cl2(g) to Cl(g): $E_2 = 122$ kJ/mol

• Step 3: Ionization of Na(g): $E_3 = 495.8$ kJ/mol

• Step 4: Electron affinity of Cl(g): $E_4 = -348.6$ kJ/mol

• Step 5: Formation of NaCl(s) from gaseous ions (lattice energy): $E_5 = -787$ kJ/mol

Net energy change:

$E_{\text{net}} = E_1 + E_2 + E_3 + E_4 + E_5 = 107.3 + 122 + 495.8 + (-348.6) + (-787) = -411$ kJ/mol

The driving force for ionic bond formation is the large, negative lattice energy.

The Ionic Bond

An ionic bond is the electrostatic attraction between cations and anions in an ionic solid. The strength of the bond depends on the charges and sizes of the ions.

• Bond strength equation:

$\text{Ionic bond strength} \propto \frac{(\text{cation charge})(\text{anion charge})}{\text{cation radius} + \text{anion radius}}$

• Larger charges lead to stronger ionic bonds.

• Larger ions lead to weaker ionic bonds.

• Soluble ionic compounds tend to have weaker ionic bonds (large ions, small charges).

Solubility Guidelines for Ionic Compounds in Water

Solubility of ionic compounds depends on the nature of the ions. The following table summarizes common solubility rules and exceptions:

Ionic Compound	Common Exceptions
Group 1A cations	None
NH4+ (ammonium)	None
Halides (Cl-, Br-, I-)	Halides of Ag+, Hg22+, Pb2+
NO3- (nitrate)	None
SO42- (sulfate)	Sulfates of Sr2+, Hg22+, Ba2+
CO32- (carbonate)	Carbonates of group 1A cations, NH4+
S2- (sulfide)	Sulfides of group 1A cations, NH4+, Ca2+, Sr2+, Ba2+
PO43- (phosphate)	Phosphates of group 1A cations, NH4+
OH- (hydroxide)	Hydroxides of group 1A cations, NH4+, Ca2+, Sr2+, Ba2+

Factors Affecting Lattice Energy

Lattice energy is the energy released when gaseous ions form an ionic solid. It is a measure of ionic bond strength and is affected by ion charge and size.

• Lattice energy equation:

$\text{Lattice energy} \propto \frac{(\text{cation charge})(\text{anion charge})}{\text{cation radius} + \text{anion radius}}$

• Larger charges lead to larger lattice energies.

• Larger ions lead to smaller lattice energies.

• Lattice energies are easier to measure than ionic bond strengths and are commonly reported in reference texts.

Estimating Lattice Energies

Known lattice energies can be used to estimate unknown values using the proportionality above.

• Example: For MgO and NaCl:

$E_{\text{lattice}} \propto \frac{(+2)(-2)}{66\,\text{pm} + 140\,\text{pm}}$ for MgO

$E_{\text{lattice}} \propto \frac{(+1)(-1)}{102\,\text{pm} + 181\,\text{pm}}$ for NaCl

MgO has a much larger lattice energy than NaCl due to higher charges and smaller ionic radii.

Summary of Key Concepts

• Ionization energy: Energy required to remove an electron from a gas-phase atom.

• Electron affinity: Energy change when an electron is added to a gas-phase atom.

• Octet rule: Main-group elements react to achieve filled valence shells (8 electrons).

• Ionic bond formation: Driven by the negative lattice energy, not just electron transfer.

• Lattice energy: Directly proportional to ionic bond strength; can be estimated using ion charges and radii.