Gases, Liquids, and Solids

The behavior of gases, liquids, and solids is fundamental to fluid mechanics, hydraulics, and materials science.

The Ideal Gas Law

Gases are often described by the Ideal Gas Law under standard conditions (STP).

Ideal Gas Equation

$PV = nRT$

P: Pressure (Pa or atm)
V: Volume (L or m $^3$ )
n: Moles of gas (mol)
R: Universal Gas Constant ( $0.0821 \, L \cdot atm / (mol \cdot K)$ or $8.314 \, J / (mol \cdot K)$ )
T: Temperature (Kelvin)

Dalton's Law of Partial Pressures

The total pressure of a gas mixture is the sum of the partial pressures of each component. $P_{total} = P_1 + P_2 + ... + P_n$ $P_i = X_i P_{total}$ where $X_i$ is the mole fraction.

Intermolecular Forces (IMFs)

The attractive forces between molecules determine physical properties like boiling point, melting point, and viscosity.

Ion-Dipole: Strongest (e.g., Salt in Water).
Hydrogen Bonding: Special dipole-dipole involving H bonded to N, O, F (e.g., Water, Ammonia).
Dipole-Dipole: Between polar molecules (e.g., HCl).
London Dispersion Forces: Weakest, present in all molecules (e.g., $N_2$ , Noble Gases). Increases with molar mass.

Phase Changes

Matter changes state when energy is added or removed, overcoming or forming IMFs.

Phase Transitions

Melting/Freezing: Solid $\leftrightarrow$ Liquid (Heat of Fusion $\Delta H_{fus}$ )
Vaporization/Condensation: Liquid $\leftrightarrow$ Gas (Heat of Vaporization $\Delta H_{vap}$ )
Sublimation/Deposition: Solid $\leftrightarrow$ Gas (e.g., Dry Ice)

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