# States of matter and phase behaviour

Physics I · Chemistry · https://tryals.app/learn/physics-i/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**.

| Phase | Particle Arrangement | Energy State |
| --- | --- | --- |
| **Solid** | Fixed lattice, vibrating | Low |
| **Liquid** | Close, sliding past each other | Moderate |
| **Gas** | Far apart, moving rapidly | High |

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.

## Practice questions

4 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. Ice absorbs heat while melting at a constant 0 °C. If 100 g of ice at 0 °C sits in a drink, roughly how much energy does it soak up just by melting, in **kilojoules**? (Latent heat of fusion ≈ 334 J/g.)

**Answer:** 33.4 (within ±4)

**Why:** About 33 kJ, enough to cool 100 g of water by a huge 80 °C. Latent heat is energy spent dismantling the crystal, not raising temperature, which is why ice cools drinks so much better than cold water of the same mass.

Page: https://tryals.app/practice/physics-i/states-of-matter-and-phase-behaviour/ice-absorbs-heat-while-melting-at-a-constant-0-c-if-100-g-of-ice-at

### 2. Sweat cools you even on a hot day. At the molecular level, why does **evaporation** lower the temperature of the liquid left behind?

A. Evaporating molecules absorb cold from the air and bring it back
B. The liquid shrinks, concentrating its heat into less volume
C. Only the fastest molecules escape, lowering the average
D. Escaping molecules push heat away as they leave

**Answer:** C. Only the fastest molecules escape, lowering the average

**Why:** Evaporation is selective emigration: only molecules in the high-energy tail can pay the escape cost, so the remaining population’s average, the temperature, drops. Humidity blocks the escape route, which is why muggy heat feels unbearable.

Page: https://tryals.app/practice/physics-i/states-of-matter-and-phase-behaviour/sweat-cools-you-even-on-a-hot-day-at-the-molecular-level-why-does

### 3. At the triple point all three phases coexist, and it occurs at one specific temperature AND pressure. Why is there no freedom in either?

A. Because at that point the substance stops obeying the gas laws
B. Because three phases impose two conditions on two variables
C. Because pressure and temperature are not independent in any substance
D. Because the triple point is defined by international convention

**Answer:** B. Because three phases impose two conditions on two variables

**Why:** Gibbs’ phase rule in miniature. Two phases give one constraint and hence a line; three give two constraints and hence a point, which is why water’s triple point is stable enough to define a temperature scale.

Page: https://tryals.app/practice/physics-i/states-of-matter-and-phase-behaviour/at-the-triple-point-all-three-phases-coexist-and-it-occurs-at-one

### 4. Order the heating of a pure substance from solid to gas at constant pressure.

**Answer:**

1. Solid is heated; temperature rises until melting point
2. Melting: temperature constant while solid converts to liquid ($\Delta H$_fus absorbed)
3. Liquid is heated; temperature rises until boiling point
4. Vaporisation: temperature constant while liquid converts to gas ($\Delta H$_vap absorbed)

**Why:** The flat sections in a heating curve correspond to phase transitions at constant T; energy goes into breaking intermolecular forces.

Page: https://tryals.app/practice/physics-i/states-of-matter-and-phase-behaviour/order-the-heating-of-a-pure-substance-from-solid-to-gas-at-constant