Foundations of Physical Chemistry: Thermodynamics and Temperature

Physical Chemistry: Overview

Main 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 shown in the diagram below:

Thermodynamics	Statistical Mechanics	Quantum Mechanics	Kinetics
Macroscopic properties	Bridges micro and macro views	Atomic/molecular theory	Rate processes

Additional info: The diagram in Figure 1.1 illustrates the relationships among these four areas.

Viewpoints in Physical Chemistry

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

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

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

Foundations and Applications

• Physical chemistry "started" as a discipline in 1887 (Wilhelm Ostwald)

• Originally focused on bulk matter and large collections of molecules

• Founders: Wilhelm Ostwald, Jacobus Henricus van't Hoff Jr., Josiah Willard Gibbs, Svante Arrhenius

• Applications: Medicine, pharmacy, engineering, electronics, environment, biology, etc.

Key Terms and Examples

• Kinetics: Study of rate processes (diffusion, flow of charge, speed of reactions)

• Quantum calculations: Used to find molecular structures, reaction intermediates, and symmetry

• Thermodynamics: Used to find yield and composition of mixtures

System Size and Properties

• Properties of a system may change based on system size

• Diameter of small atom: ~0.1 nm (nanometer), $1\text{ nm} = 1 \times 10^{-9}\text{ m}$

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

• Mesoscopic: Size region between nanoscopic and macroscopic

Example: Gold (Au) Particles

• Bulk gold: yellowish, conducts electricity, melts at 1336 K, chemically unreactive

• 25 nm radius: chemically reactive

• 20 nm radius: red

• 10 nm radius: orange

• 1 nm radius: electrical insulator

Chapter 1.2: Thermodynamics

Introduction to Thermodynamics

Thermodynamics comes from Greek words for "heat" and "power." It studies macroscopic properties such as heat, work, and energy, focusing on systems containing many particles and independent of atomic theory.

Types of Thermodynamic Systems

• System: Part of the universe under study

• Surroundings: Everything else

Example: Measuring vapor pressure of water. The system is liquid water and vapor within a container; the surroundings are the water bath and mercury in the manometer.

Classification of Systems

• Open system: Transfer of matter and energy with surroundings can occur

• Closed system: Only energy transfer with surroundings can occur; matter cannot

• Isolated system: No interaction with surroundings; neither matter nor energy transfer

Walls Separating System and Surroundings

• Rigid wall: Not movable

• Nonrigid wall: Movable

• Permeable wall: Allows some matter to pass through

• Impermeable wall: Does not allow matter to pass through

• 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 in Thermodynamics

• Equilibrium: System's macroscopic properties remain constant with time

• Removal of system from contact with surroundings results in no change in system properties

• Steady state: System not at equilibrium but properties remain constant over time

Types of Equilibrium

• Mechanical equilibrium: No unbalanced forces; no acceleration or turbulence

• Material equilibrium: No chemical reactions; no net transfer of matter or chemical species

• Thermal equilibrium: No change in system properties when separated by a 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 property: Value equals sum for all parts of system (e.g., mass)

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

Homogeneous and Heterogeneous Systems

• Homogeneous system: Each intensive property is constant throughout

• Heterogeneous system: System with two or more homogeneous parts (phases)

Density and Thermodynamic State

• Density: $\rho = m/V$

• Thermodynamic state: Defined by specification of values of thermodynamic properties

State Function

• Property of thermodynamic system in equilibrium state

• Depends only on present system state, not on history

Example: System of 8.66 g Pure H2O at 1 atm and 24°C

• Mass, composition, pressure, and temperature specified

• All other properties are fixed

• State function: 8.66 g H2O at 1 atm and 24°C weighs 8.66 g regardless of history

Sample Questions and Answers

• (a) A closed system cannot interact with its surroundings. False

• (b) Density is an intensive property. True

• (c) The Atlantic Ocean is an open system. True

• (d) A homogeneous system must be a pure substance. False

• (e) A system containing only one substance must be homogeneous. False (e.g., solid + liquid water)

Chapter 1.3: Temperature

Thermal Equilibrium and Zeroth Law

• Two systems of equal pressure separated by movable wall: no unbalanced forces, mechanical equilibrium

• Two systems in thermal equilibrium have the same temperature

• Zeroth law of thermodynamics: If systems A and B are each in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other.

Mathematically:

• If $\theta_A = \theta_C$ and $\theta_B = \theta_C$, then $\theta_A = \theta_B$

Temperature as a State Function

• Thermodynamics uses macroscopic viewpoint

• Temperature applies only to collections of many particles

• Does not apply to a single atom or nanoscopic systems

Measuring Temperature

• Temperature is an abstract property; cannot be measured directly

• Another system property is measured (e.g., volume, electrical resistance)

• Measured property is related to temperature via a function (calibration)

Building a Thermometer

• Reference system: homogeneous fluid with fixed pressure and composition (e.g., mercury)

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

• Example linear function: $\theta = aV_r + b$, where $a > 0$

Example: Mercury-in-Glass Thermometer

• Assume constant pressure for all measurements

• $A$ = cross-sectional area of tube

• $l$ = height/length of mercury in tube

• Mercury volume = bulb volume + tube volume

• $\theta = aV_r + b = a(V_{bulb} + Al) + b$

• $\theta = d l + d$, where $c$ and $d$ are constants

Centigrade Scale (°C)

• Define $\theta = 0$: temperature of equilibrium between pure ice and liquid water saturated with dissolved air at 1 atm ("ice point")

• Define $\theta = 100$: temperature of equilibrium between pure liquid water and water vapor at 1 atm ("steam point")

Linear function: $\theta = aV_r + b$

Alternative Thermometer Fluids

• Liquid water does not work: contracts below 4°C, expands above 4°C

• Example: Volume of water at 3°C and 5°C is the same

Unit Conversions and Density Example

• Density of Au (gold): $19.3\text{ g/cm}^3$ at room temperature and 1 atm

• 1 troy ounce = 480 grains

• 1 grain = 1/7000 pound

• 1 pound = 453.59 g

Unit	Conversion
1 m	100 cm
1 cm	1/100 m
1 pound	453.59 g
1 ounce	480 grains
1 troy ounce	480 grains
1 grain	1/7000 pound

Additional info: These conversions are useful for solving density and mass-related problems in physical chemistry.