# Physical Equilibria and Phase Diagrams

Chemistry I · Energy, Equilibrium and Electrochemistry · https://tryals.app/learn/chemistry-i/physical-equilibria-and-phase-diagrams

## Two Phases in Balance

A **physical equilibrium** is a phase change running equally fast in both directions. At the melting point solid and liquid coexist; at the boiling point liquid and vapour do. At any such point $\Delta G = 0$, which gives a useful relation immediately:

$$\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{fus}}$$

**Vapour pressure** is the pressure exerted by a vapour in equilibrium with its liquid. It depends only on temperature, never on the amount of liquid present, and it rises steeply as temperature climbs. A liquid **boils** when its vapour pressure equals the external pressure, which is why water boils below 100 °C on a mountain, and why a pressure cooker gets hotter than 100 °C.

The **Clausius-Clapeyron equation** describes that rise:

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

A plot of $\ln P$ against $1/T$ is therefore a straight line of slope $-\Delta H_{vap}/R$, which is the standard way of measuring an enthalpy of vaporisation.

A **phase diagram** maps pressure against temperature, dividing the plane into solid, liquid and gas regions separated by coexistence curves. Two points matter especially. The **triple point** is the single condition where all three phases coexist. The **critical point** ends the liquid-vapour curve: above it liquid and gas become indistinguishable and the substance is a supercritical fluid.

Water's diagram is famously anomalous. Its solid-liquid boundary slopes *backwards*, because ice is less dense than liquid water, so raising the pressure on ice melts it. Almost every other substance has a forward-sloping boundary.

> **Common pitfall:** thinking a bigger puddle has a higher vapour pressure. Vapour pressure is an intensive property fixed by temperature and the strength of the intermolecular forces. More liquid gives more vapour in total, at exactly the same pressure.

## Practice questions

7 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Match each feature of a phase diagram to what it marks.

**Answer:**

- Triple point → The one condition where all three phases coexist
- Critical point → Where liquid and gas cease to be distinguishable
- Solid-liquid boundary → Conditions at which melting and freezing balance
- Liquid-gas boundary → The vapour pressure curve of the liquid

**Why:** The triple point is a unique intersection, the critical point terminates the vaporisation curve, and the two boundaries are the loci of conditions where the neighbouring phases are in equilibrium.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/match-each-feature-of-a-phase-diagram-to-what-it-marks

### 2. A solid melts at 250 K with an enthalpy of fusion of 5.0 kJ/mol. Compute its entropy of fusion in J/mol/K.

**Answer:** 20 (within ±0.5)

**Why:** At equilibrium $\Delta G = 0$, so $\Delta S_{fus} = \Delta H_{fus}/T_{fus} = 5000/250 = 20$ J/mol/K. The positive value reflects the extra freedom a liquid has over a lattice.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/a-solid-melts-at-250-k-with-an-enthalpy-of-fusion-of-5-0-kj-mol

### 3. Vapour pressure depends purely on temperature, yet doubling the surface area of a liquid doubles the rate of evaporation. Why does an open dish of water evaporate faster without exhibiting a higher vapour pressure?

A. Wider liquid surfaces decrease the enthalpy barrier to vaporisation
B. Surface molecules escape more easily without altering vapour density
C. The vapour pressure increases locally right above the wider surface
D. The rate of condensation matches evaporation only in a closed system

**Answer:** D. The rate of condensation matches evaporation only in a closed system

**Why:** Equilibrium vapour pressure reflects a dynamic balance where forward and reverse rates balance in a closed vessel. In open air, evaporation rate scales with area, but equilibrium is never attained; vapour pressure itself remains an intensive thermodynamic property governed by temperature.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/vapour-pressure-depends-purely-on-temperature-yet-doubling-the

### 4. Arrange these phases and states in order of increasing molar entropy for the same substance.

**Answer:**

1. Perfect crystalline solid at 0 K
2. Solid just below its melting point
3. Liquid just above its melting point
4. Gas at its boiling point

**Why:** A perfect crystal at 0 K has $S = 0$ exactly. Warming adds vibrational freedom, melting adds translational freedom, and vaporising adds a very large amount more, which is why entropies of vaporisation dwarf entropies of fusion.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/arrange-these-phases-and-states-in-order-of-increasing-molar-entropy

### 5. Why does water boil at a lower temperature at high altitude?

A. The enthalpy of vaporisation decreases markedly at higher altitudes
B. Decreased surrounding air density accelerates the rate of evaporation
C. Lower ambient temperatures weaken the intermolecular hydrogen bonds
D. The external pressure is lower, so a lower vapour pressure suffices

**Answer:** D. The external pressure is lower, so a lower vapour pressure suffices

**Why:** Boiling happens when vapour pressure equals the surrounding pressure. Lower atmospheric pressure means that condition is met at a lower temperature, which is why cooking takes longer on a mountain and why a pressure cooker works.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/why-does-water-boil-at-a-lower-temperature-at-high-altitude

### 6. Which statements about vapour pressure are correct?

A. It rises as temperature rises
B. It increases if you pour more liquid into the container
C. It is higher for liquids with weaker intermolecular forces
D. It equals the external pressure at the boiling point

**Answer:** A. It rises as temperature rises; C. It is higher for liquids with weaker intermolecular forces; D. It equals the external pressure at the boiling point

**Why:** Vapour pressure is fixed by temperature and the strength of the intermolecular forces alone. Pouring in more liquid produces more vapour in total but leaves the pressure unchanged, the mark of an intensive property.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/which-statements-about-vapour-pressure-are-correct

### 7. A liquid boils at 350 K with an enthalpy of vaporisation of 35 kJ/mol. Compute its entropy of vaporisation in J/mol/K.

**Answer:** 100 (within ±1)

**Why:** $\Delta S_{vap} = \Delta H_{vap}/T_b = 35{,}000/350 = 100$ J/mol/K. Most liquids cluster near 88 J/mol/K (Trouton’s rule); a markedly higher value signals strong hydrogen bonding in the liquid.

Page: https://tryals.app/practice/chemistry-i/physical-equilibria-and-phase-diagrams/a-liquid-boils-at-350-k-with-an-enthalpy-of-vaporisation-of-35