Phase Transitions and Thermodynamics

Instructor: Khashayar Ghandi
Contact: kghandi@uoguelph.ca
Chapters Referenced: 6, 9.1, 9.11, 18
Topics Covered:
- Phase transitions
- Applications of the first law of thermodynamics and thermochemistry
- Ionic compounds and bond enthalpy
- Second law of thermodynamics

Thermodynamic properties are applicable to:
- Chemical reactions
- Phase transitions

Definition: A phase transition is a change of a substance from one state (solid, liquid, gas) to another.
Types of Phase Transitions:
- Solid to liquid: Melting
- Liquid to gas: Vaporization
- Gas to liquid: Condensation
- Liquid to solid: Freezing
- Solid to gas: Sublimation
- Gas to solid: Deposition
The enthalpy changes associated with these transitions (e.g., heat of fusion, heat of vaporization) are discussed in detail in class. (See Chapter 11.2)

Relationship:
- Increasing pressure on a liquid raises the boiling point (illustrated by a pressure cooker).
- Decreasing pressure lowers the boiling point (e.g., at high altitudes).
Reasoning:
- Relates to vapor pressure, defined as the partial pressure of the vapor over the liquid at equilibrium.

Definition: The vapor pressure of a liquid at a certain temperature is its partial pressure over the liquid at equilibrium.
Dynamic Equilibrium:
- When a liquid is placed in an evacuated vessel, vapor pressure rises until equilibrium is established, where evaporation and condensation rates are equal.
Dependence:
- Vapor pressure increases exponentially with temperature (T).
Formula:
- The relationship is expressed mathematically as:
 $ext{ln } rac{K2}{K1} = -\frac{\Delta rH°}{R} \left( \frac{1}{T2} - \frac{1}{T1} \right)$

Any change of state requires energy to be added or removed from the system.
Important Temperatures:
- During phase changes, temperature remains constant despite heat being added.
Specific Enthalpy Values for Water:
- Heat of fusion:
- $\Delta H_{fus} = 6.01 \text{ kJ/mol}$
- Heat of vaporization:
- $\Delta H_{vap} = 40.7 \text{ kJ/mol}$
Specific Heat Capacities:
- For ice:
- C_p = 38 \text{ J/(mol·K)}
- For liquid water:
- C_p = 75 \text{ J/(mol·K)}

Example 1: Doubling a reaction's equation results in doubling its enthalpy.
- Conclusion: Enthalpy is an extensive state function.
Example 2: The sign of $\Delta H$ for melting is opposite that for freezing.
- Conclusion: Sign is reversed as it is a state function.

Definition: Elements can exist in different physical states and distinct forms in the same state; these forms are known as allotropes.
Examples:
- Carbon as graphite or diamond
- Oxygen as O2 or O3 (ozone)
Reference Form: The most stable form of the element, considering both physical state and allotrope.

Characteristics:
- Molten salts, ionic liquids, and salt solutions are electrically conductive due to the presence and movement of ions.
Bonding Types:
- Ionic Bond: Formed by electrostatic attraction between + and - ions.
- Covalent Bond: Formed by sharing a pair of electrons between atoms (e.g., H2).
- Definition of Bond Energy: Bond energy (or bond enthalpy) is the average enthalpy change for breaking an A—B bond in a gas-phase molecule.
Bond strength increases with larger bond enthalpy values.

Example of Ionic Bond Formation:
- Sodium and chlorine example:
- Sodium: Na ([Ne]3s1) + Chlorine: Cl ([Ne]3s23p5)
- Forms Na+ ([Ne]) and Cl− ([Ne]3s23p6) upon electron transfer.
Notation:
- The Lewis electron-dot symbol denotes valence electrons as dots around the element symbol.
- Dots are filled one side at a time, until all four sides are filled.

Formation of Calcium Oxide (CaO):
- Sodium transfers electrons to form Ca2+ and O2−.
Ionization Energy:
- Energy required to remove an electron.
Electron Affinity:
- Energy released when an electron is added.
The process is overall exothermic once ionic bonding occurs despite initially requiring energy (endothermic).

Definition: Lattice energy (enthalpy) is the energy change that occurs when an ionic solid is separated into gas-phase ions.
Measurement: Direct measurement is challenging; it can be calculated using the enthalpy changes from different steps that yield the same result.

Method to Calculate Lattice Energy:
- Involves evaluating a series of steps leading to the formation of ionic compounds from their constituent elements.

Two Key Factors:
- Ionic charge: Higher charges lead to stronger forces and energy of interaction.
- Ion size: Smaller ions result in stronger forces due to shorter distances.
Coulomb's Law:
- The lattice energy can be quantified by:
 $UL = k \frac{Q1Q_2}{r}$

Elementary Charge (e): The charge carried by protons.
- SI Unit: Coulomb (C), equal to approximately $6.25 \times 10^{18}$ elementary charges.
- Elementary charge value: $e \approx 1.6 \times 10^{-19} ext{ C}$

Definition: The average enthalpy change associated with breaking an A—B bond in gas phase.

Formula:
- $\Delta H = \text{sum of bond enthalpies of bonds broken} - \text{sum of bond enthalpies of bonds formed}$
Significance:
- If $\Delta H$ is negative, heat is released at constant pressure; if positive, heat is absorbed.
- Reference to Table 9.5 for bond energies.

Enthalpy Change for a given reaction:
- Bonds Broken:
- 1 x C=C: 602 kJ
- 1 x Cl—Cl: 240 kJ
- Total absorbed: 842 kJ
- Bonds Formed:
- 1 x C—C: 346 kJ
- 2 x C—Cl: 654 kJ
- Total released: 1000 kJ
- Final Calculation:
  $\Delta H = 842 \text{ kJ} - 1000 \text{ kJ} = -158 \text{ kJ}$

First Law: Conservation of energy does not explain the spontaneity of processes.
Second Law: Needed to understand why certain processes occur spontaneously until equilibrium is reached.
- Definition: A spontaneous process is one that occurs by itself without external influence.