States of matter and phase behaviour

The three classical phases — solid, liquid, gas — are distinguished by the balance between thermal energy $k_BT$ and intermolecular potential energy.

Phase diagrams plot pressure $P$ vs temperature $T$ and show:

• Phase boundaries: Curves where two phases coexist.
• Triple point: All three phases coexist simultaneously.
• Critical point: Above this $(T_c, P_c)$, liquid and gas become indistinguishable (supercritical fluid).

Clausius–Clapeyron equation

$$\ln\frac{P_2}{P_1} = -\frac{\Delta H_{\text{vap}}}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$$

This relates vapour pressure to temperature along the liquid-gas boundary.

Solutions and Raoult's law

P_i = x_i\,P_i^{*}

where $x_i$ is the mole fraction and $P_i^*$ is the pure-component vapour pressure.

Colligative properties depend only on the number of dissolved particles:

• Boiling-point elevation: $\Delta T_b = i\,K_b\,m$.
• Freezing-point depression: $\Delta T_f = i\,K_f\,m$.

Key insight: Adding a non-volatile solute always lowers vapour pressure and raises the boiling point — this is why salted water boils at a higher temperature.

Common pitfall: During a phase change, added heat does not raise the temperature — it pays the latent-heat cost of rearranging molecules. A boiling pot stays at 100 °C no matter how high the flame.

States of Matter

Matter exists in three main phases, distinguished by particle arrangement and energy:

• Solid: particles in a fixed lattice, vibrating about equilibrium positions.
• Liquid: particles close together but free to slide past one another.
• Gas: particles far apart, moving rapidly with high kinetic energy.

Phase transitions occur when thermal energy overcomes intermolecular forces. The latent heat $L$ is the energy per unit mass required for the transition: $Q = mL$.

Temperature stays constant during a phase change — all added energy goes into breaking bonds.