States of Aggregation of Matter

Solids are classified into crystalline (ordered periodic arrangement) and amorphous (disordered).

Crystalline solids by bond type:

• Ionic (NaCl): high melting point, brittle, conductors when molten
• Covalent network (diamond, SiO₂): very hard, high $T_m$
• Metallic (Cu, Fe): ductile, malleable, conductive
• Molecular (ice, I₂): low $T_m$, soft, held by intermolecular forces

The unit cell is the smallest repeating unit. The Bragg equation describes X-ray diffraction.

Liquids have a fixed volume but take the shape of the container. Key properties:

• Surface tension ($\gamma$): energy per unit area to increase the surface. Water has high surface tension due to hydrogen bonds.
• Viscosity ($\eta$): resistance to flow. Increases with intermolecular force strength and molecular size.
• Capillary action: rise of a liquid in a narrow tube due to adhesion and cohesion.

The ideal gas law combines Boyle, Charles, and Avogadro: $$PV = nRT$$ where $R = 0.0821\,\mathrm{L\cdot atm\cdot mol^{-1}\cdot K^{-1}}$.

Dalton's law of partial pressures: the total pressure of a mixture of ideal gases equals the sum of the partial pressures of each component: $$P_{tot} = \sum_i P_i = \sum_i \chi_i P_{tot} \quad \text{where } \chi_i = \dfrac{n_i}{n_{tot}}$$

Real gases deviate from ideality at high pressure and low temperature because molecules have:

• Finite volume → corrected by $b$ (volume excluded per mole)
• Intermolecular attractions → corrected by $a$ (cohesion parameter)

The Van der Waals equation: $$\left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT$$