Intermolecular Forces, Phase Changes, and Phase Diagrams

Intermolecular Forces and Phase Changes

Learning Objectives

• Analyze a heat transfer plot (heating or cooling curve) and explain the significance of the slopes and lengths of each segment in terms of physical constants.

• Use molecular representations to describe phase changes of a pure substance.

• Calculate the heat transfer along a heating/cooling curve.

Key Terminology

• Sublimation: The direct transition from solid to gas without passing through the liquid phase.

• Deposition: The direct transition from gas to solid.

• Fusion: The process of melting, or transition from solid to liquid.

• Freezing: The transition from liquid to solid.

• ΔHfus: Enthalpy (heat) of fusion, the energy required to melt one mole of a substance.

• ΔHsub: Enthalpy (heat) of sublimation, the energy required to sublime one mole of a substance.

• Specific heat capacity (Cs): The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

Enthalpies of Phase Changes

Comparing Enthalpies

• Typically, ΔHvap (enthalpy of vaporization) is larger than ΔHfus (enthalpy of fusion) because more energy is required to overcome intermolecular forces to convert a liquid to a gas than to convert a solid to a liquid.

• The enthalpy of sublimation can be calculated as:

$ΔH_{sub} = ΔH_{fus} + ΔH_{vap}$

• This relationship reflects that sublimation is a two-step process: solid to liquid (fusion), then liquid to gas (vaporization).

Example Table: Enthalpies of Fusion and Vaporization

Substance	ΔHfus (kJ/mol)	ΔHvap (kJ/mol)
Water	~6	~41
Rubbing alcohol	~8	~45
Acetone	~7	~30
Diethyl ether	~7	~27

Additional info: Values are approximate and for illustrative purposes.

Heating and Cooling Curves

Understanding the Curve

• A heating curve shows the temperature change of a substance as heat is added.

• Plateaus (flat segments) represent phase changes where temperature remains constant as energy is used to change phase.

• Sloped segments represent temperature changes within a single phase (solid, liquid, or gas).

Boiling and Melting

• During boiling, the highest-energy molecules escape into the gas phase, decreasing the average kinetic energy of the remaining liquid molecules.

• During melting, energy is absorbed to overcome forces holding the solid together, but temperature remains constant until all solid is melted.

$\text{H}_2\text{O}_{(l)} + E \rightarrow \text{H}_2\text{O}_{(g)}$

Heating Curve for H2O: Segment Analysis

• Segment 1: Heating ice from -25.0°C to 0.0°C (solid phase, temperature increases)

• Segment 2: Melting ice at 0.0°C (phase change, temperature constant)

• Segment 3: Heating liquid water from 0.0°C to 100.0°C (liquid phase, temperature increases)

• Segment 4: Boiling water at 100.0°C (phase change, temperature constant)

• Segment 5: Heating steam from 100.0°C to 125.0°C (gas phase, temperature increases)

Calculations for Each Segment

• Temperature Change (within a phase):

$q = m \times C_s \times \Delta T$

• Phase Change (melting or boiling):

$q = n \times \Delta H$

• Where q is heat (in kJ), m is mass (in g), n is moles, Cs is specific heat capacity, and ΔH is enthalpy of fusion or vaporization.

Example Calculations

• Segment 1 (Heating ice):

$q = (1.00\,\text{mol H}_2\text{O}) \times \frac{18.0\,\text{g}}{1\,\text{mol H}_2\text{O}} \times 2.09\,\frac{\text{J}}{\text{g} \cdot ^\circ\text{C}} \times (0.0 - (-25.0))^\circ\text{C}$ $q = 941\,\text{J} = 0.941\,\text{kJ}$

• Segment 2 (Melting ice):

$q = n \times \Delta H_{fus}$ $q = (1.00\,\text{mol}) \times (6.02\,\frac{\text{kJ}}{\text{mol}}) = 6.02\,\text{kJ}$

• Segment 3 (Heating liquid water):

$q = (1.00\,\text{mol H}_2\text{O}) \times \frac{18.0\,\text{g}}{1\,\text{mol H}_2\text{O}} \times 4.18\,\frac{\text{J}}{\text{g} \cdot ^\circ\text{C}} \times (100.0 - 0.0)^\circ\text{C}$ $q = 7.52 \times 10^3\,\text{J} = 7.52\,\text{kJ}$

• Segment 4 (Boiling water):

$q = n \times \Delta H_{vap}$ $q = (1.00\,\text{mol}) \times (40.7\,\frac{\text{kJ}}{\text{mol}}) = 40.7\,\text{kJ}$

• Segment 5 (Heating steam):

$q = (1.00\,\text{mol H}_2\text{O}) \times \frac{18.0\,\text{g}}{1\,\text{mol H}_2\text{O}} \times 2.01\,\frac{\text{J}}{\text{g} \cdot ^\circ\text{C}} \times (125.0 - 100.0)^\circ\text{C}$ $q = 904\,\text{J} = 0.904\,\text{kJ}$

Phase Diagrams

Key Terminology

• Phase diagram: A graphical representation of the physical states of a substance under different conditions of temperature and pressure.

• Triple point: The unique set of conditions at which all three phases (solid, liquid, gas) coexist in equilibrium.

• Critical point: The end point of the phase equilibrium curve, beyond which the liquid and gas phases become indistinguishable (supercritical fluid).

Phase Diagram for H2O

• The phase diagram plots pressure (y-axis) versus temperature (x-axis).

• Key features include the fusion curve (solid-liquid boundary), vaporization curve (liquid-gas boundary), and sublimation curve (solid-gas boundary).

• The triple point is where all three curves meet.

• The critical point marks the end of the liquid-gas boundary.

Interpreting Phase Diagrams

• Increasing temperature at constant pressure can cause a substance to move from solid to liquid to gas.

• Increasing pressure at constant temperature can cause a gas to condense to a liquid or solid.

• Phase diagrams help predict the state of a substance under various conditions and are essential for understanding phase transitions.

Summary Table: Key Phase Change Terms

Term	Definition
Sublimation	Solid to gas
Deposition	Gas to solid
Fusion (Melting)	Solid to liquid
Freezing	Liquid to solid
Vaporization	Liquid to gas
Condensation	Gas to liquid

Homework and Further Study

• Read textbook sections 12.6–12.9 for deeper understanding.

• Practice interpreting and sketching phase diagrams.

• Complete assigned activities and problems to reinforce concepts.