## CHM 001 – General Chemistry
### QUESTION 1
**(a)** Define the term *phase* as used in chemistry.
**Answer:**
A phase is a physically and chemically uniform, homogeneous, and mechanically separable part of a system that has distinct and uniform properties throughout.
---
**(b)** With the aid of a labelled diagram, describe the three physical states of matter and state two distinguishing properties of each.
**Answer:**
```
SOLID LIQUID GAS
[■■■■■] [■ ■ ■] [ ■ ■ ]
[■■■■■] [ ■ ■ ■] [ ■ ]
[■■■■■] [■ ■ ■ ] [ ■ ■ ]
Particles tightly Particles close Particles far
packed in fixed but mobile apart, random
arrangement motion
```
**Solid:**
1. Has a definite shape and definite volume.
2. Particles are closely and regularly packed, vibrating about fixed positions.
**Liquid:**
1. Has a definite volume but no definite shape — it takes the shape of its container.
2. Particles are close together but can slide past one another freely.
**Gas:**
1. Has no definite shape and no definite volume — it fills any container completely.
2. Particles are far apart, moving rapidly and randomly with negligible intermolecular forces.
---
**(c)** Explain why solids are generally incompressible while gases are highly compressible.
**Answer:**
Solids are incompressible because their constituent particles are tightly and regularly packed with virtually no empty space between them, leaving no room for further compression. Gases, by contrast, are highly compressible because their particles are widely separated by large intermolecular spaces; applying pressure simply reduces these spaces without significantly affecting the particles themselves.
---
### QUESTION 2
**(a)** Define vapour pressure.
**Answer:**
Vapour pressure is the pressure exerted by the vapour of a liquid when it is in dynamic equilibrium with its liquid phase at a given temperature in a closed system.
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**(b)** State two factors that affect the vapour pressure of a liquid.
**Answer:**
1. **Temperature** — vapour pressure increases with increasing temperature.
2. **Nature of the liquid** — liquids with weaker intermolecular forces have higher vapour pressures at the same temperature.
---
**(c)** Explain the effect of pressure on the boiling point of a liquid, using water as an example.
**Answer:**
A liquid boils when its vapour pressure equals the external (atmospheric) pressure. Increasing the external pressure therefore raises the boiling point, because the liquid requires more thermal energy for its vapour pressure to reach the higher external pressure. For example, water boils at 100°C at standard atmospheric pressure (101.3 kPa), but boils above 100°C under elevated pressure — a principle exploited in pressure cookers. Conversely, at high altitudes where atmospheric pressure is lower, water boils below 100°C.
---
## CHM 002 – Physical Chemistry (Thermodynamics)
### QUESTION 3
**(a)** Explain the concept of phase equilibrium.
**Answer:**
Phase equilibrium is the condition in which two or more phases of a substance coexist simultaneously, with the rate of transition from one phase to another being equal in both directions, so there is no net change in the amount of any phase over time.
---
**(b)** Using a pressure–temperature phase diagram, explain:
**(i) Triple point**
The triple point is the unique combination of temperature and pressure at which the solid, liquid, and vapour phases of a substance coexist simultaneously in thermodynamic equilibrium. On a P–T phase diagram, it is represented by a single point at the intersection of all three phase boundary curves. For water, the triple point occurs at 0.01°C and 611.7 Pa.
**(ii) Critical point**
The critical point is the temperature and pressure beyond which the distinction between the liquid and gas phases disappears — the two phases become indistinguishable, forming a single supercritical fluid phase. On a P–T diagram, it marks the upper terminus of the liquid–vapour boundary curve. For water, the critical point is at approximately 374°C and 22.1 MPa.
---
**(c)** State the significance of the critical point of a substance.
**Answer:**
The critical point defines the highest temperature (critical temperature) at which a substance can be liquefied by pressure alone. Above the critical temperature, no amount of applied pressure can condense the substance into a distinct liquid phase. It also marks the onset of supercritical fluid behaviour, which has important industrial applications such as supercritical CO₂ extraction.
---
### QUESTION 4
**(a)** State the Clausius–Clapeyron equation and explain the meaning of each term.
**Answer:**
The Clausius–Clapeyron equation is:
ln(P₂/P₁) = (ΔH_vap / R)(1/T₁ − 1/T₂)
Where:
- **P₁, P₂** = vapour pressures at temperatures T₁ and T₂ respectively
- **ΔH_vap** = molar enthalpy of vaporisation (J/mol), assumed constant over the temperature range
- **R** = universal gas constant (8.314 J/mol·K)
- **T₁, T₂** = absolute temperatures in Kelvin
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**(b)** Describe how the equation explains the relationship between temperature and vapour pressure.
**Answer:**
The equation shows that vapour pressure increases exponentially with increasing temperature. As T increases, the term (1/T₁ − 1/T₂) becomes more positive, causing ln(P₂/P₁) to increase, meaning P₂ > P₁. This occurs because higher temperatures give more molecules sufficient energy to escape the liquid surface, increasing the equilibrium vapour pressure.
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**(c)** State one limitation of the Clausius–Clapeyron equation.
**Answer:**
The equation assumes that the enthalpy of vaporisation (ΔH_vap) remains constant over the temperature range considered and that the vapour behaves as an ideal gas. In reality, ΔH_vap varies with temperature and real gases deviate from ideal behaviour, particularly at high pressures and low temperatures, reducing the accuracy of the equation under such conditions.
---
## CHM 003 – States of Matter
### QUESTION 5
**(a)** Distinguish between the following phase changes:
**(i) Melting and sublimation**
**Melting** is the phase transition from solid to liquid upon the absorption of heat at the melting point. The substance passes through an intermediate liquid state.
**Sublimation** is the direct phase transition from solid to vapour without passing through the liquid phase, occurring when the vapour pressure of the solid exceeds the external pressure at the given temperature. Example: dry ice (solid CO₂) sublimes at atmospheric pressure.
**(ii) Condensation and deposition**
**Condensation** is the phase transition from vapour (gas) to liquid upon the release of heat. It is the reverse of vaporisation.
**Deposition** is the direct phase transition from vapour to solid without passing through the liquid phase. It is the reverse of sublimation. Example: frost forming directly on cold surfaces.
---
**(b)** Explain how temperature and pressure influence phase transitions.
**Answer:**
**Temperature:** Increasing temperature supplies kinetic energy to particles, favouring transitions to higher-energy, less ordered phases (solid → liquid → gas). Decreasing temperature has the reverse effect.
**Pressure:** Increasing pressure favours the denser, more compact phase. For most substances this stabilises the solid phase over liquid, and liquid over gas. Decreasing pressure favours the gaseous phase and lowers the boiling point of liquids.
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**(c)** Give two practical examples of phase transitions in everyday life.
**Answer:**
1. **Ice melting into water** — a solid-to-liquid transition (melting) that occurs as heat is absorbed from the surroundings.
2. **Dew forming on grass** — a vapour-to-liquid transition (condensation) that occurs when warm, moist air contacts a cool surface and the water vapour condenses into liquid droplets.
---
### QUESTION 6
**(a)** Using a phase diagram, describe the conditions under which:
**(i) Solid, liquid, and vapour coexist**
All three phases coexist exclusively at the **triple point** — a single, unique combination of temperature and pressure on the phase diagram. For water this is 0.01°C and 611.7 Pa. No other combination of temperature and pressure permits the simultaneous stable coexistence of all three phases.
**(ii) Liquid and vapour phases become indistinguishable**
The liquid and vapour phases become indistinguishable at the **critical point**. Beyond this point (i.e., above the critical temperature and critical pressure), the substance exists as a supercritical fluid that has properties intermediate between those of a liquid and a gas, and no phase boundary separates the two.
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**(b)** Explain why carbon dioxide does not exist as a liquid at atmospheric pressure.
**Answer:**
Carbon dioxide's triple point lies at −56.6°C and 518 kPa — a pressure considerably higher than standard atmospheric pressure (101.3 kPa). Since atmospheric pressure falls below the triple point pressure, there is no temperature at which liquid CO₂ is the stable phase at this pressure. Instead, solid CO₂ (dry ice) converts directly to vapour by sublimation when heated at atmospheric pressure, bypassing the liquid phase entirely.
---
## CHM 004 – Chemical Thermodynamics
### QUESTION 7
**(a)** Define enthalpy of fusion and enthalpy of vaporisation.
**Enthalpy of fusion (ΔH_fus):** The quantity of heat energy absorbed when one mole of a solid substance melts completely to form a liquid at constant temperature and pressure (at its melting point).
**Enthalpy of vaporisation (ΔH_vap):** The quantity of heat energy absorbed when one mole of a liquid substance vaporises completely to form a gas at constant temperature and pressure (at its boiling point).
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**(b)** Explain why the enthalpy of vaporisation is usually greater than the enthalpy of fusion.
**Answer:**
During melting, only partial disruption of intermolecular forces occurs — particles gain enough energy to move freely past one another but remain in close proximity. During vaporisation, however, intermolecular forces must be almost entirely overcome to separate particles into the widely spaced gas phase. This complete separation requires substantially more energy than the partial disruption involved in melting, so ΔH_vap > ΔH_fus for virtually all substances.
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**(c)** State two applications of enthalpy changes in industry.
**Answer:**
1. **Refrigeration and air conditioning** — refrigerants absorb large quantities of heat from their surroundings during vaporisation (using high ΔH_vap), providing a cooling effect, and release heat during condensation.
2. **Industrial distillation** — the separation of liquid mixtures (e.g., crude oil refining, production of industrial alcohol) exploits differences in enthalpy of vaporisation and boiling points of components to achieve selective evaporation and condensation.
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### QUESTION 8
**(a)** Explain the concept of phase stability in thermodynamics.
**Answer:**
Phase stability refers to the tendency of a particular phase of a substance to remain in existence under a given set of temperature and pressure conditions. A phase is thermodynamically stable when it has the lowest Gibbs free energy (G) relative to other possible phases at those conditions. The stable phase is the one that minimises G; any transition to another phase would require an input of free energy. Changes in temperature or pressure alter the relative Gibbs energies of the phases, causing phase transitions when one phase becomes more stable than another.
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**(b)** Discuss the effect of pressure on the stability of solid, liquid, and gaseous phases.
**Answer:**
Pressure strongly influences which phase is thermodynamically stable:
- **Solid phase:** High pressure generally stabilises the solid phase because it is the most dense and compact. For most substances, increasing pressure raises the melting point (shifts the solid–liquid boundary to higher temperatures). Ice is a notable exception — its melting point decreases slightly with pressure because liquid water is denser than ice.
- **Liquid phase:** The liquid phase is stable at intermediate pressures and temperatures, between the melting and boiling curves on a phase diagram. Increasing pressure raises the boiling point of a liquid, stabilising the liquid phase over the gas phase at higher temperatures.
- **Gaseous phase:** Low pressure stabilises the gas phase, since gases occupy large volumes. Reducing pressure lowers the boiling point and can cause liquids to vaporise at lower temperatures, as seen at high altitudes or in vacuum distillation.
---
**(c)** Differentiate between ideal gas behaviour and real gas behaviour, stating one condition under which deviations occur.
**Answer:**
| Property | Ideal Gas | Real Gas |
|---|---|---|
| Intermolecular forces | Assumed zero | Present (attractive and repulsive) |
| Particle volume | Assumed negligible | Finite, non-zero volume |
| Obedience to gas laws | Perfect at all conditions | Only approximate, especially at extremes |
| Compressibility factor Z | Always = 1 | May be > 1 or < 1 |
**Ideal gases** obey the ideal gas law (PV = nRT) exactly under all conditions, with no intermolecular attractions and negligible particle volume.
**Real gases** deviate from this behaviour because their molecules do interact with one another and do occupy a finite volume. These deviations are described by equations such as the van der Waals equation:
(P + a/V²)(V − b) = RT
**Condition under which significant deviations occur:**
Real gases deviate most markedly from ideal behaviour at **high pressures and low temperatures**, where intermolecular forces become significant relative to kinetic energy and the finite volume of molecules is no longer negligible compared to the total gas volume.