Solids
Solids are characterized by definite shape and volume, very low compressibility, and constituent particles held in fixed positions by strong cohesive forces. For the MCAT you should be able to distinguish crystalline from amorphous solids, classify crystals by bonding type, and reason about lattice energy and the geometry of ionic crystals.
Crystalline Solids
A crystalline solid has a regular, repeating internal arrangement of particles (atoms, ions or molecules) extending in three dimensions. It has a sharp melting point, definite geometric shape, and shows anisotropy — physical properties (refractive index, conductivity, etc.) depend on direction.
An amorphous solid (e.g. glass, rubber, plastics) has only short-range order. It softens over a temperature range rather than melting sharply, and is isotropic — properties are the same in every direction. Amorphous solids are sometimes called "supercooled liquids".
Properties of crystalline solids
- Regular geometric external shape with definite plane faces, edges and angles.
- Sharp, fixed melting point.
- Anisotropy.
- Cleavage along definite planes.
- Definite heat of fusion.
Crystal Lattice
A crystal lattice (space lattice) is a three-dimensional array of points each of which represents the position of a constituent particle in the crystal. The smallest repeating unit that, when stacked in three dimensions, generates the entire crystal is the unit cell.
Unit cells are classified by their edge lengths (a, b, c) and angles into the seven crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral). The MCAT does not require you to memorize all seven — the testable idea is that a small repeating unit cell tiles space to build the whole lattice, and the cubic cells below are the ones you should be able to reason about quantitatively.
Cubic unit cells — packing efficiency & coordination number
- Simple Cubic (SC): atoms at the 8 corners only. CN = 6. Packing efficiency ≈ 52 %. Effective atoms per cell = 1 (8 × ⅛).
- Body-Centered Cubic (BCC): 8 corners + 1 in body center. CN = 8. Packing efficiency ≈ 68 %. Effective atoms = 2. Examples: Na, K, Fe (α), Cr.
- Face-Centered Cubic (FCC) / Cubic Close-Packed: 8 corners + 6 face centers. CN = 12. Packing efficiency ≈ 74 % (the densest possible packing of equal spheres). Effective atoms = 4. Examples: Cu, Ag, Au, Al, Pb, NaCl (anion sub-lattice).
Ionic Crystal Geometry
The arrangement of ions in a crystal is set mainly by relative ion sizes and by the requirement of overall charge neutrality. As a rule of thumb, the larger the cation-to-anion radius ratio, the more anions can pack around each cation (higher coordination number):
- Small cation → CN 4 in ZnS (tetrahedral, 4:4).
- Intermediate → CN 6 in NaCl (octahedral, 6:6).
- Large cation → CN 8 in CsCl (cubic, 8:8).
Small, highly charged cations and large, easily polarized anions add covalent character to an otherwise ionic bond (the qualitative idea behind Fajans' rules).
The Four Crystal Types
| Property | Ionic | Molecular | Covalent (network) | Metallic |
|---|---|---|---|---|
| Lattice particles | Cations + anions | Neutral molecules | Atoms (whole network) | Cations in sea of e− |
| Bonding force | Strong electrostatic | Weak van der Waals / dipole / H-bond | Strong covalent | Metallic bond |
| Hardness | Hard but brittle | Soft | Very hard (diamond hardest) | Variable; malleable & ductile |
| Melting point | High | Low | Very high | Moderate to high |
| Electrical conduction | Solid: no · molten/aq: yes | No | No (except graphite) | Excellent in all states |
| Solubility | Polar solvents (water) | Non-polar (mostly); H-bonded ones dissolve in water | Insoluble | Insoluble (react with acids) |
| Examples | NaCl, KBr, CsCl, MgO | I2, dry ice CO2, naphthalene, sucrose, ice | Diamond, graphite, SiO2, SiC | Cu, Fe, Ag, Au, Na |
| Type | Atoms / unit cell | Coordination number | Packing efficiency | Example |
|---|---|---|---|---|
| Simple cubic (SC) | 1 | 6 | 52.4% | Po (only example) |
| Body-centered cubic (BCC) | 2 | 8 | 68% | Na, K, Fe, W, Cr |
| Face-centered cubic (FCC) | 4 | 12 | 74% (closest packed) | Cu, Ag, Au, Al, Pb, NaCl |
| Hexagonal close-packed (HCP) | 6 | 12 | 74% | Mg, Zn, Cd, Ti |
Lattice Energy
Lattice energy (ΔHL) is the energy released when one mole of an ionic crystal is formed from its constituent gaseous ions:
M+(g) + X−(g) → MX(s); ΔHL = −ve
Equivalently, it is the energy required to dissociate one mole of the solid into widely separated gaseous ions (taken as positive). It is a measure of the strength of ionic bonding.
Coulomb dependence
Lattice energy is approximately proportional to:
ΔHL ∝ (q1 × q2) / r
where q1, q2 are the ionic charges and r is the inter-ionic distance (sum of ionic radii).
- Higher charges (Mg2+O2− vs Na+F−) → much larger lattice energy. MgO has ΔHL ~ 3800 kJ mol−1, NaCl ~ 787 kJ mol−1.
- Smaller ions → smaller r → larger lattice energy. NaF > NaCl > NaBr > NaI.
Significance of lattice energy
- Determines melting point and hardness of ionic solids.
- Determines solubility in water (compared with hydration energy).
- Cannot be measured directly — calculated using the Born–Haber cycle, which applies Hess's law to the formation of an ionic compound from its elements via a series of measurable steps (sublimation, ionization, dissociation, electron affinity, lattice formation).
Phase Diagrams
A phase diagram plots pressure against temperature and shows which phase (solid, liquid or gas) is stable under each set of conditions. The lines are the boundaries where two phases coexist in equilibrium:
- Fusion (melting) curve — solid–liquid boundary.
- Vaporization curve — liquid–gas boundary; it ends at the critical point.
- Sublimation curve — solid–gas boundary.
The triple point is the single P–T condition where solid, liquid and gas coexist. Beyond the critical point (critical T and P) the liquid and gas become indistinguishable — a supercritical fluid.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. Which of the following is an amorphous solid?
Glass has only short-range order, no sharp melting point (it softens over a range), and is isotropic — the defining features of an amorphous solid. NaCl, diamond and quartz are all crystalline.
Q2. The packing efficiency of a face-centered cubic (FCC) unit cell is approximately:
FCC (cubic close-packed) is the densest possible packing of equal spheres at ~74 %, with coordination number 12. BCC is ~68 % (CN 8), simple cubic ~52 % (CN 6).
Q3. Which compound has the highest lattice energy?
Lattice energy ∝ q1q2/r. MgO has doubly charged ions (Mg2+, O2−) and small inter-ionic distance, giving an enormous lattice energy (~3800 kJ mol−1). All the others have singly charged ions.
Q4. On a phase diagram, the point at which solid, liquid and gas coexist in equilibrium is the:
The triple point is the unique pressure and temperature where all three phases coexist. The critical point instead marks the end of the liquid–gas boundary, beyond which a supercritical fluid exists and liquid and gas are no longer distinct.
Q5. Which property is characteristic of an ionic crystal but not a molecular crystal?
Ionic solids have very strong electrostatic lattices (high m.p.) and contain mobile ions when molten or dissolved (good conductors). Molecular crystals have weak intermolecular forces, low m.p., and do not conduct.
Quick Recap
- Crystalline = long-range order, sharp m.p., anisotropic; amorphous = short-range order, softens, isotropic.
- Cubic unit cells: SC (CN 6, 52 %), BCC (CN 8, 68 %), FCC (CN 12, 74 %, closest packed).
- Four crystal types: ionic, covalent (network), molecular, metallic — bonding sets m.p., hardness and conductivity.
- Coordination rises with cation:anion size ratio (ZnS 4:4, NaCl 6:6, CsCl 8:8).
- Lattice energy ∝ q1q2/r; calculated via the Born–Haber cycle (Hess's law).
- Phase diagram: fusion, vaporization and sublimation curves meet at the triple point; liquid–gas line ends at the critical point; water's solid–liquid line has a negative slope.