Phase Equilibrium and Colligative Properties: Study Notes for Introductory Chemistry

Phase Equilibrium

Basic Definitions and Concepts

Phase equilibrium refers to the balance between different physical states (phases) of matter—solid, liquid, and gas—within a system. Understanding phase equilibrium is essential for interpreting phase diagrams and predicting the behavior of substances under varying temperature and pressure conditions.

• Phase: Any homogeneous and physically distinct part of a system separated by definite boundaries from other parts. Examples include ice, water, and water vapor.

• Homogeneous Equilibrium: All species are in the same state of matter (e.g., all gases).

• Heterogeneous Equilibrium: At least two states of matter are present (e.g., solid and liquid).

• Component: The minimum number of independent chemical species required to define the composition of all phases in the system. For example, the H2O system (ice, water, vapor) has one component; a salt-water mixture has two components.

Example: A mixture of gases is a single phase because it is homogeneous and lacks boundaries between different gases.

Properties of Phases

State of Matter	Volume/Shape	Density	Compressibility	Motion of Molecules
Gas	Assumes volume and shape of container	Low	Very compressible	Very free motion
Liquid	Definite volume, assumes shape of container	High	Only slightly compressible	Slide past one another freely
Solid	Definite volume and shape	High	Virtually incompressible	Vibrate about fixed positions

Phase Diagrams

Understanding Phase Diagrams

A phase diagram is a graphical representation showing the stability regions of different phases of a substance as a function of temperature and pressure. Each region corresponds to a phase, and the lines (boundaries) indicate equilibrium between phases.

• The diagram is divided into three main areas: solid, liquid, and gas.

• The triple point is where all three phases coexist in equilibrium.

• The critical point marks the end of the liquid-gas boundary; above this temperature and pressure, the liquid and gas phases are indistinguishable.

Example: The phase diagram of water shows the regions where ice, liquid water, and water vapor are stable, as well as the triple and critical points.

Key Features of Phase Diagrams

• Melting Point Line (Solid-Liquid Boundary): For water, this line has a negative slope, meaning the melting point decreases with increasing pressure (unusual for solids).

• Boiling Point: The temperature at which the vapor pressure equals atmospheric pressure (1 atm for water is 100°C).

• Critical Temperature ($T_c$): The highest temperature at which a substance can exist as a liquid, regardless of pressure.

• Critical Pressure ($P_c$): The minimum pressure required to liquefy a substance at its critical temperature.

Table: Critical Temperatures and Pressures of Selected Substances

Substance	$T_c$ (°C)	$P_c$ (atm)
Ammonia (NH3)	132.4	111.5
Argon (Ar)	-122.4	48.0
Carbon dioxide (CO2)	31.1	73.0
Water (H2O)	374.4	218.5

Comparing Phase Diagrams: H2O vs. CO2

• Water (H2O): The solid-liquid line has a negative slope; ice melts at lower temperatures as pressure increases.

• Carbon Dioxide (CO2): The solid-liquid line has a positive slope; solid CO2 (dry ice) sublimes at 1 atm and does not melt.

Application: Dry ice is used as a refrigerant because it sublimes rather than melts at atmospheric pressure.

Phase Changes

Types of Phase Changes

Phase changes are transitions between solid, liquid, and gas states. They are classified as endothermic (require heat) or exothermic (release heat).

• Endothermic (require heat): Melting, vaporization, sublimation

• Exothermic (release heat): Freezing, condensation, deposition

Example: Melting ice (solid to liquid) is endothermic; freezing water (liquid to solid) is exothermic.

Colligative Properties

Definition and Types

Colligative properties are solution properties that depend only on the number of solute particles, not their identity. These properties include:

• Vapor Pressure Lowering (Raoult's Law)

• Boiling Point Elevation

• Freezing Point Depression

• Osmotic Pressure

Vapor Pressure Lowering

Adding a nonvolatile solute to a solvent reduces the solvent's vapor pressure. This is described by Raoult's Law:

$P_A = X_A P_A^0$

• $P_A$ = partial pressure of solvent vapor above the solution

• $X_A$ = mole fraction of the solvent

• $P_A^0$ = vapor pressure of the pure solvent

Example: Adding glucose to water lowers the vapor pressure compared to pure water.

Sample Calculation

• Given: $P_{H_2O}^0 = 17.5$ torr at 20°C, 36.0 g glucose in 14.4 g water

• Find: $P_{H_2O}$

• Solution: Use Raoult's Law; answer is 14.0 torr.

Boiling Point Elevation

The addition of a nonvolatile solute raises the boiling point of a solvent. The change in boiling point is proportional to the molality of the solution:

$\Delta T_b = i K_b m$

• $\Delta T_b$ = boiling point elevation

• $K_b$ = molal boiling point elevation constant (depends on solvent)

• $m$ = molality of solution (mol solute/kg solvent)

• $i$ = van't Hoff factor (number of particles the solute produces)

Example: A 1.0 m NaCl solution has a higher boiling point than a 1.0 m glucose solution because NaCl dissociates into more particles.

Freezing Point Depression

The presence of a nonvolatile solute lowers the freezing point of a solvent. The change is proportional to the molality:

$\Delta T_f = i K_f m$

• $\Delta T_f$ = freezing point depression

• $K_f$ = molal freezing point depression constant

• $m$ = molality of solution

• $i$ = van't Hoff factor

Example: Adding salt to ice lowers the freezing point, which is why salt is used to melt ice on roads.

Osmotic Pressure

Osmosis is the movement of solvent through a semipermeable membrane from a region of lower solute concentration to higher solute concentration. Osmotic pressure is the pressure required to stop this flow.

• In biological systems, osmosis regulates water flow in and out of cells.

• Placing cells in hypertonic solutions causes water to leave the cell (crenation); in hypotonic solutions, water enters the cell (hemolysis).

Everyday Examples: Cucumbers in brine lose water and become pickles; carrots in water become firm due to water uptake by osmosis.

Summary Table: Colligative Properties

Property	Effect of Solute	Key Equation
Vapor Pressure Lowering	Decreases vapor pressure	$P_A = X_A P_A^0$
Boiling Point Elevation	Increases boiling point	$\Delta T_b = i K_b m$
Freezing Point Depression	Lowers freezing point	$\Delta T_f = i K_f m$
Osmotic Pressure	Causes solvent flow through membrane	$\Pi = i M R T$ (where $\Pi$ = osmotic pressure, $M$ = molarity, $R$ = gas constant, $T$ = temperature in K)

Practice Questions

1. What is the critical temperature of compound X?

2. If you were to have a bottle containing compound X in your closet, what phase would it most likely be in?

3. At what temperature and pressure will all three phases coexist? Give the value for each of the temperature and pressure.

4. If you have a bottle of compound X at a pressure of 45 atm and temperature of 100°C, what will happen if you raise the temperature to 400°C?

5. Why can't compound X be boiled at a temperature of 200°C?

6. If you wanted to, could you drink compound X?

Additional info: Students should be able to interpret phase diagrams, calculate colligative property changes, and apply these concepts to real-world and biological systems.