States of matter and phase behaviour

States of Matter & Phase Maps

Matter shifts between phases depending on the balance between thermal energy $k_BT$ and intermolecular potential energy.

Transitions occur when thermal energy overcomes intermolecular forces. The latent heat $L$ governs this via $Q = mL$.

Phase diagrams map $P$ vs $T$, showing phase boundaries where two phases coexist, the unique triple point where all three meet, and the critical point $(T_c, P_c)$ beyond which liquid and gas merge into a supercritical fluid.

Common pitfall: During a phase change, added heat never raises the temperature. It pays the latent-heat cost to rearrange molecules, which is why a boiling pot stays at 100 degrees Celsius regardless of flame size.

Vapour Pressure & Colligative Properties

The Clausius–Clapeyron equation connects vapour pressure to temperature along the liquid-gas boundary:

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

Here, $\Delta H_{\text{vap}}$ is enthalpy of vaporization and $R$ is the gas constant.

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 purely on dissolved particle count, not identity:

• 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 drops vapour pressure and raises the boiling point. This exact mechanism explains why salted water requires a higher temperature to boil.