DAT General Chemistry: Comparing Solid Properties and Lattice Energy

DAT High-Yield Concept

Solid Categories: Crystalline solids are grouped into four types based on constituent units and interparticle forces: molecular, covalent network, metallic, and ionic.
Dominant Lattice Energy Factor: Ionic charge exerts a primary influence over lattice energy compared to ionic radius ( $U \propto \frac{|Q_1 Q_2|}{r_0}$ ).
Coulomb's Law Scale: Doubling both ion charges increases electrostatic lattice energy by approximately a factor of four.
Conductivity Rules: Ionic solids conduct electricity only when molten or dissolved in water, metallic solids conduct in all states, and covalent network solids are typically non-conductive insulators (except graphite).

1. Classification and Physical Properties of Crystalline Solids

Crystalline solids are classified by the nature of the forces holding their structural units together. Understanding these structural differences allows quick comparisons of hardness, melting point, and electrical conductivity on the DAT.

Categories of Crystalline Solids

Molecular Solids: Composed of neutral atoms or molecules held together by weak intermolecular forces (London dispersion forces, dipole-dipole interactions, or hydrogen bonds). Examples include $\ce{H2O}$ (ice), $\ce{CO2}$ (dry ice), and $\ce{I2}$ . Because intermolecular forces are relatively weak, molecular solids display low melting points, soft texture, and poor electrical conductivity.
Covalent Network Solids: Composed of atoms connected by a continuous three-dimensional network of strong covalent bonds. Examples include diamond (carbon), quartz ( $\ce{SiO2}$ ), and silicon carbide ( $\ce{SiC}$ ). The continuous network gives these solids extreme hardness and exceptionally high melting points. Due to localized valence electrons separated by a wide band gap, most covalent network solids act as electrical insulators.

Diagram illustrating how electronic band structure of a solid comes about by the hypothetical example of a large number of carbon atoms coming together to form a diamond crystal lattice. The graph (right) shows the energy levels of the atoms as a function of the spacing between atoms. When the atoms are far apart (right side of graph) each atom has valence atomic orbitals p and s which have the same energy. However when the atoms come closer together their orbitals begin to overlap. The Pauli Exclusion Principle dictates that no two atoms in a molecule can have electrons with the same quantum numbers, so each atomic orbital splits into N molecular orbitals each with a different energy, where N is the number of atoms in the crystal. Since N is such a large number (~10 22 ) adjacent orbitals are extremely close together in energy (~10 -22 eV) so the orbitals can be considered a continuous energy band. a is the atomic spacing (lattice constant) found in an actual crystal lattice of carbon atoms (diamond lattice) so the band structure at that spacing is the one found in diamond. At that spacing the orbitals form two bands, called the valence band and conduction band, with an energy gap of 5.5 electron volts (eV) between them. The valence electrons fill the lower band. Electrons in this band are not mobile; while electrons in the higher conduction band can travel through the crystal from atom to atom, and thus serve as charge carriers to conduct electricity. Since the 5.5 eV band gap is much larger than the thermal energy of most electrons in the crystal, very few electrons acquire the energy to jump the gap and become conduction electrons. This is why diamond is an electrical insulator. The shape of the graph (right) is only approximately correct. It also only shows the band structure of the outer (valence) electrons of the atoms (in carbon the 4 2p and 2s electrons). The orbitals of the inner electrons do not overlap to a significant degree, so their bands are much narrower. (Source: Chetvorno · CC0 · Wikimedia Commons)
Metallic Solids: Metallic solids consist of metal cations held together by a delocalized sea of valence electrons, leading to high electrical and thermal conductivity, malleability, ductility, and variable melting points. Examples include $\ce{Fe}$ , $\ce{Cu}$ , and $\ce{Na}$ .
Ionic Solids: Composed of repeating three-dimensional arrays of alternating cations and anions bound by strong electrostatic attractions. Examples include $\ce{NaCl}$ and $\ce{MgO}$ . Ionic solids exhibit high melting points and hard, brittle structures (impact causes like-charged ions to align and repel). They do not conduct electricity in the solid state because ions are fixed in position, but they conduct readily when molten or dissolved in aqueous solution.

Solid Type	Structural Units	Attractive Forces	Hardness & Mechanical	Conductivity	Melting Point	Examples
Molecular	Molecules / Atoms	Intermolecular forces	Soft, brittle	Non-conducting	Low	$\ce{H2O}$ , $\ce{CO2}$ , $\ce{I2}$
Covalent Network	Atoms	Covalent bonds	Very hard	Non-conducting*	Very High	Diamond, $\ce{SiO2}$ , $\ce{SiC}$
Metallic	Metal Cations + Electrons	Metallic bonding	Variable, malleable	High (solid & liquid)	Variable to High	$\ce{Fe}$ , $\ce{Cu}$ , $\ce{Mg}$
Ionic	Cations & Anions	Ionic / Electrostatic	Hard, brittle	Conducts in molten/aq	High to Very High	$\ce{NaCl}$ , $\ce{MgO}$ , $\ce{CaF2}$

2. Qualitative Lattice Energy Trends

Lattice energy ( $U$ ) is the energy released when isolated gaseous ions combine to form one mole of an ionic crystalline solid. It measures electrostatic stability and directly correlates with melting points in ionic compounds.

Coulomb's Law and Lattice Energy

Qualitatively, lattice energy follows Coulomb's law:

U \propto \frac{|Q_1 Q_2|}{r_0}

where $Q_1$ and $Q_2$ represent ionic charges and $r_0$ represents the inter-ionic distance (the sum of cation radius $r_+$ and anion radius $r_-$ ).

Key Determinants of Lattice Energy

Ionic Charge (Primary Effect): Larger magnitude of ionic charge product ( $|Q_1 Q_2|$ ) produces significantly greater lattice energy.
Ionic Radius (Secondary Effect): Smaller ionic radii shorten the inter-ionic distance ( $r_0$ ), increasing electrostatic attraction and lattice energy.

DAT Mnemonic — COR: First compare Charge product; if charges are equal, compare ionic Radius! Charge magnitude always outweighs size differences on exams.

Worked Examples

Worked Example 1 (Charge Factor): Compare the relative lattice energies and melting points of $\ce{NaCl}$ and $\ce{MgO}$ .

Step 1: Identify charges. $\ce{NaCl}$ contains $\ce{Na^+}$ and $\ce{Cl^-}$ ( $|Q_1 Q_2| = 1 \times 1 = 1$ ). $\ce{MgO}$ contains $\ce{Mg^{2+}}$ and $\ce{O^{2-}}$ ( $|Q_1 Q_2| = 2 \times 2 = 4$ ).
Step 2: Evaluate radii. $\ce{Na^+}$ and $\ce{Mg^{2+}}$ are isoelectronic, as are $\ce{O^{2-}}$ and $\ce{F^-}$ . Inter-ionic distances are comparable.
Conclusion: Because $|Q_1 Q_2|$ is 4 times larger in $\ce{MgO}$ , $\ce{MgO}$ has a dramatically higher lattice energy and melting point ( $\pu{2852 degC}$ ) than $\ce{NaCl}$ ( $\pu{801 degC}$ ).

Worked Example 2 (Radius Factor): Rank $\ce{LiF}$ , $\ce{LiCl}$ , $\ce{LiBr}$ , and $\ce{LiI}$ in order of decreasing lattice energy.

Step 1: Identify charges. All four salts have identical $|Q_1 Q_2| = 1 \times 1 = 1$ .
Step 2: Evaluate radii. Halide ionic radii increase down Group 17: $\ce{F^-}$ < $\ce{Cl^-}$ < $\ce{Br^-}$ < $\ce{I^-}$ .
Conclusion: Shorter inter-ionic distance yields higher lattice energy. The lattice energy decreases in the order: $\ce{LiF}$ > $\ce{LiCl}$ > $\ce{LiBr}$ > $\ce{LiI}$ .

Critical Thinking Questions

Why does graphite conduct electricity effectively along its planes, while diamond acts as an insulator, even though both are covalent network solids of pure carbon?
Although $\ce{CaO}$ and $\ce{NaCl}$ form identical crystal lattice geometries, $\ce{CaO}$ melts at $\pu{2572 degC}$ whereas $\ce{NaCl}$ melts at $\pu{801 degC}$ . Which factor drives this difference?
Why do ionic solids shatter when hit with a mechanical force, whereas metallic solids deform malleably?

References

Sources returned by Google Search grounding during lesson verification.

8.3: Lattice Energies in Ionic Solids - Chemistry LibreTexts — chem.libretexts.org
12.7: Types of Crystalline Solids - Chemistry LibreTexts — chem.libretexts.org

Comparing Solid Properties and Lattice Energy

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