Foundations of Physical Chemistry: Thermodynamics and Temperature (with Statistical Context)

Physical Chemistry: Principles and Scope

Definition and Areas of Physical Chemistry

Physical chemistry is the study of physical principles governing chemical systems. It is divided into four major areas:

• Thermodynamics

• Quantum Mechanics

• Statistical Mechanics

• Kinetics

These areas are interconnected, as illustrated below:

Thermodynamics	Statistical Mechanics	Quantum Mechanics
Kinetics

Additional info: Statistical mechanics bridges quantum mechanics and thermodynamics, translating molecular motion to bulk behavior.

Viewpoints in Physical Chemistry

• Microscopic view: Focuses on small particles (atoms, molecules).

• Macroscopic view: Studies bulk matter, based on large collections of molecules.

Physical chemistry often uses the macroscopic viewpoint, while quantum chemistry and statistical mechanics connect microscopic and macroscopic perspectives.

Historical Context and Applications

• Physical chemistry began as a discipline in 1887 (Wilhelm Ostwald).

• Founders include Ostwald, van't Hoff, Gibbs, Arrhenius.

• Journal of Chemical Physics established after quantum mechanics discovery.

• Physical chemistry underpins many fields: medicine, engineering, biology, etc.

Example: Organic Chemistry

• Kinetics determines reaction mechanisms.

• Quantum calculations find molecular structures and intermediates.

• Thermodynamics predicts yields and mixture compositions.

• Instruments: NMR, FTIR, UV-Vis for measurements.

System Size and Properties

• Properties change with system size.

• Diameter of small atom ≈ 0.1 nm ($1\text{ nm} = 1 \times 10^{-9}\text{ m}$).

• Nanoscale: 1–100 nm; systems contain thousands of atoms.

• Mesoscopic: Region between nanoscopic and macroscopic.

Example: Gold Nanoparticles

• Bulk gold: yellow, conducts electricity, melts at 1336 K, unreactive.

• 25 nm radius: reactive, melts at 903 K.

• 20 nm: red; 1 nm: orange; <1 nm: electrical insulator.

Chapter 1.2: Thermodynamics

Introduction to Thermodynamics

Thermodynamics (from Greek for "heat" and "power") studies macroscopic properties such as heat, work, and energy. The focus is on equilibrium thermodynamics, which considers systems with many particles and is independent of atomic theory.

Systems and Surroundings

• System: Part of the universe under study.

• Surroundings: Everything else.

• Example: Vapor pressure apparatus—system is liquid water and vapor, surroundings are water bath and mercury in manometer.

Types of Systems

• Open system: Matter and energy can transfer between system and surroundings.

• Closed system: Only energy can transfer; matter cannot.

• Isolated system: No transfer of matter or energy.

Question: Is an isolated system a closed system? Yes. Question: Is a closed system an isolated system? Depends.

Walls and Boundaries

• Rigid wall: Not movable.

• Nonrigid wall: Movable.

• Permeable wall: Allows matter to pass.

• Impermeable wall: Does not allow matter to pass.

• Adiabatic wall: Does not conduct heat.

• Nonadiabatic wall: Conducts heat.

Adiabatic and Nonadiabatic Walls

• Adiabatic wall: Idealization; prevents heat flow.

• Nonadiabatic wall: Allows heat flow; system properties change.

• Thermos bottle: Approximate adiabatic wall (double walls, near vacuum).

Equilibrium Concepts

• Equilibrium: System properties remain constant with time.

• Removal from contact with surroundings does not change system properties.

• Example: Metal rod between two temperature baths—eventually reaches steady state, then equilibrium at 40°C.

Types of Thermodynamic Equilibrium

• Mechanical equilibrium: No unbalanced forces; no acceleration.

• Material equilibrium: No net chemical reactions; no net matter transfer.

• Thermal equilibrium: No change in temperature when separated by nonadiabatic boundary.

Thermodynamic Properties

• Volume (V)

• Pressure (P): $P = F/A$

• Composition: Mass of each chemical species in each phase.

Extensive vs. Intensive Properties

• Extensive: Value equals sum for all parts (e.g., mass).

• Intensive: Value independent of system size (e.g., pressure).

Question: Is density intensive or extensive? Intensive.

Homogeneous and Heterogeneous Systems

• Homogeneous: Each intensive property is constant throughout.

• Heterogeneous: System with two or more phases.

Example: Solid AgBr in equilibrium with aqueous AgBr—two phases, heterogeneous. Immiscible liquids H2O and CCl4—two phases, heterogeneous.

Thermodynamic State and State Functions

• State defined by values of thermodynamic properties.

• Density: $\rho = m/V$

• State function: Property depends only on present state, not history.

Example: 8.66 g pure H2O at 1 atm and 24°C—same state regardless of history.

True/False Examples

• Closed system cannot interact with surroundings: False

• Density is intensive: True

• Atlantic Ocean is open: True

• Homogeneous system must be pure: False

• System with one substance must be homogeneous: False (e.g., solid + liquid water)

Units and Conversions

Unit	Conversion
1 m3	100 cm × 100 cm × 100 cm
1 pound	453.59 g
1 ounce	480 grains
1 grain	1/7000 pound

Example: Gold density = 19.3 g/cm3; price calculation for 1 m3 at $800/oz.

Chapter 1.3: Temperature

Mechanical and Thermal Equilibrium

• Systems of equal pressure separated by movable wall: mechanical equilibrium.

• Systems in thermal equilibrium have same temperature.

Zeroth Law of Thermodynamics

• If systems B and C are in thermal equilibrium, and A is in equilibrium with B, then A is in equilibrium with C.

• Mathematically: If $\theta_B = \theta_C$ and $\theta_A = \theta_B$, then $\theta_A = \theta_C$.

Temperature as a State Function

• Applies only to systems with many particles.

• Does not apply to single atoms or nanoscopic systems.

Measuring Temperature

• Temperature is abstract; cannot be measured directly.

• Measure another property (e.g., volume, electrical resistance) and relate to temperature.

Building a Thermometer

• Use a reference system (e.g., mercury).

• Assign unique value of temperature $\theta$ to each unique measured property $V_r$.

• Example: Linear function $\theta = aV_r + b$ where $a > 0$.

Mercury Thermometer Example

• Assume constant pressure.

• Volume of mercury: $V = A l$ (A = cross-sectional area, l = length).

• Linear relation: $\theta = aV_r + b$ or $\theta = c l + d$ (c, d constants).

Centigrade Scale (°C)

• Fix $c$ and $d$ using reference points:

• $\theta = 0$: Equilibrium between pure ice and liquid water ("ice point").

• $\theta = 100$: Equilibrium between pure liquid water and water vapor at 1 atm ("steam point").

Alternative Thermometer Fluids

• Water contracts below 4°C, expands above 4°C.

• Volume at 3°C and 5°C is the same.

Statistical Mechanics Context

Role in Physical Chemistry

• Statistical mechanics bridges microscopic and macroscopic viewpoints.

• Thermodynamics is a consequence of quantum mechanics.

• Translates molecular motion to bulk behavior.

Summary Table: Types of Systems and Walls

System Type	Matter Transfer	Energy Transfer
Open	Yes	Yes
Closed	No	Yes
Isolated	No	No

Wall Type	Property
Rigid	Not movable
Nonrigid	Movable
Permeable	Allows matter transfer
Impermeable	No matter transfer
Adiabatic	No heat transfer
Nonadiabatic	Heat transfer allowed

Additional info: These foundational concepts are essential for understanding statistical analysis of physical systems, especially in thermodynamics and equilibrium studies.