Fundamentals of Physical Chemistry

What Is Physical Chemistry About?

Physical chemistry is the part of chemistry that connects what we see and measure (like temperature, pressure, color, reaction speed) with what happens on the atomic and molecular level (particles, energies, collisions, structures).

Within this course, “Fundamentals of Physical Chemistry” provides the basis for understanding:

• Why and how energy changes in chemical processes (chemical thermodynamics)
• How electricity and chemistry are related (electrochemical processes)
• How fast reactions proceed and what affects their speed (chemical kinetics)

Each of these blocks has its own set of chapters later. Here, the goal is to frame the common ideas behind them and prepare you for those detailed topics.

The Role of Physical Quantities and Units

Physical chemistry relies on measurable quantities. Some especially important ones are:

• Temperature $T$ (kelvin, K)
• Pressure $p$ (pascal, Pa; often bar in practice)
• Volume $V$ (liter L or cubic meter $\text{m}^3$)
• Amount of substance $n$ (mole, mol)
• Energy $E$ (joule, J)
• Charge $Q$ (coulomb, C)
• Time $t$ (second, s)

Several future chapters will make heavy use of these, but here the focus is that:

• You must always keep units with numbers.
• Many relationships in physical chemistry are written as equations; to use them meaningfully, units must be consistent (for example, not mixing L and $\text{m}^3$ without converting).

A simple and central equation that appears throughout physical chemistry is the ideal gas equation:
$$
pV = nRT
$$
with:

• $p$ = pressure
• $V$ = volume
• $n$ = amount of substance
• $R$ = gas constant
• $T$ = absolute temperature

This equation will reappear in thermodynamics, equilibrium, kinetics, and electrochemistry.

States of Matter and State Variables

Physical chemistry often describes matter not in terms of individual particles, but as a macroscopic system characterized by a few key measurable variables, such as $p$, $V$, $T$, and $n$.

A state of a system is defined by the set of such variables. For example:

• A gas sample at $T = 298\ \text{K}$, $p = 1.0\ \text{bar}$, and $V = 2.0\ \text{L}$
• A solution of a certain concentration at a given temperature and pressure

These quantities are:

• State variables (state functions): They specify the condition (state) of the system and do not depend on how that state was reached. Examples: $p$, $V$, $T$, internal energy $U$, enthalpy $H$, entropy $S$, Gibbs free energy $G$.
• Path variables: They do depend on the way a process happens (the “path”). Examples: heat $q$ and work $w$. These will be important in thermodynamics.

In later chapters on thermodynamics, these ideas are applied to describe energy changes. In electrochemistry, they are related to electrical work, and in kinetics, to energy barriers and activation energies.

Systems, Surroundings, and Types of Systems

Physical chemistry always considers a system and its surroundings:

• The system is the part of the universe you are studying (for example, the contents of a beaker).
• The surroundings are everything else (the rest of the lab, the air around the beaker, etc.).

Depending on how the system exchanges energy and matter with its surroundings, we distinguish:

• Open system: Exchanges both energy and matter with its surroundings.
• Example: An open beaker where solvent can evaporate and heat can flow in and out.
• Closed system: Exchanges energy but not matter with its surroundings.
• Example: A sealed but heat-conducting container.
• Isolated system: Exchanges neither matter nor energy with its surroundings (an idealization; real systems only approximate this).
• Example: A well-insulated container that greatly reduces heat exchange and matter exchange.

These distinctions are fundamental in thermodynamics (for formulating the laws) and also matter when considering real experimental setups.

Equilibrium and Spontaneous Change

A recurring theme in physical chemistry is the competition between:

• The tendency to change (spontaneous processes)
• The drive toward equilibrium

An equilibrium state is one in which no macroscopic changes occur over time, even though particles are still in motion on the microscopic level.

Different types of equilibrium, all described with the same general physical-chemical ideas, include:

• Thermal equilibrium: No net heat flow between system and surroundings; the temperatures are equal.
• Mechanical equilibrium: No net forces causing changes in volume or pressure.
• Chemical equilibrium: Forward and reverse reactions occur at equal rates; concentrations are constant over time.
• Phase equilibrium: Rates of processes like evaporation and condensation are equal (for example, liquid–vapor equilibrium).

Later, separate chapters on chemical equilibrium, the law of mass action, and Gibbs free energy will deepen these ideas. Here, the key point is that physical chemistry provides the quantitative tools to decide:

• Whether a process is spontaneous under given conditions
• What the final equilibrium state will be
• How fast equilibrium is approached (kinetics)

Energy Forms in Chemical Systems

Chemistry involves several forms of energy that physical chemistry helps quantify and relate:

• Thermal energy: Associated with temperature and random motion of particles.
• Chemical energy: Stored in chemical bonds and arrangements of atoms.
• Electrical energy: Associated with electric charges and electric potentials; central in electrochemistry.
• Mechanical energy: For example, work done by expanding gases.

The different specialized topics (thermodynamics, electrochemistry, kinetics) focus on different aspects of energy:

• Thermodynamics: overall energy changes and limits of what is possible
• Electrochemistry: conversion between chemical and electrical energy
• Kinetics: how energy barriers control reaction rates

In later chapters, formal definitions (for example, of internal energy $U$, enthalpy $H$, entropy $S$, Gibbs free energy $G$) will be introduced. Here, it is enough to recognize that they are all different ways of describing how energy is stored and transferred in chemical systems.

The Molecular Basis of Macroscopic Properties

Physical chemistry constantly links molecular-level behavior with macroscopic observables:

• Temperature is related to the average kinetic energy of particles.
• Pressure of a gas arises from collisions of gas molecules with container walls.
• Reaction rates depend on how often and how effectively particles collide (and how they are oriented).
• Electrical conductivity depends on the motion of ions or electrons in materials or solutions.

Later chapters on kinetics and electrochemistry will use more detailed models (such as collision theory, transition state theory, and ion transport) but are all built on the central idea: macroscopic behavior can be understood in terms of particle motion, interactions, and energy distributions.

Idealized Models and Approximations

Physical chemistry frequently uses idealized models to simplify complex reality. These models:

• Capture the main features of a system
• Are expressed in comparatively simple mathematical forms
• Have clearly known limits of applicability

Examples include:

• Ideal gas model: Assumes point-like, non-interacting particles; works well at low pressure and high temperature.
• Ideal solution: Assumes that mixing does not change interactions between particles; approximates some real solutions at low concentrations.
• Ideal electrode or reversible cell: Useful as a conceptual tool for understanding electrochemical cells.

Many later equations and concepts (for gases, solutions, electrochemical cells, etc.) start with ideal models and then add corrections for real systems. Understanding that models are approximations, not exact depictions of nature, is a core element of thinking in physical chemistry.

Mathematics as a Language in Physical Chemistry

Physical chemistry uses mathematics as a language to express relationships between quantities. You do not need advanced mathematics to begin, but you do need to be comfortable with:

• Rearranging simple equations (solving for an unknown)
• Handling proportionalities (for example, “the rate is proportional to the concentration”)
• Recognizing linear vs. exponential relations
• Using logarithms, especially in contexts like pH or Nernst equations

Later sections (for example, the equation for cell potential in electrochemistry or the Arrhenius equation in kinetics) rely on these basic mathematical tools to turn measurements into quantitative conclusions about chemical processes.

How Fundamentals Tie Together the Later Topics

The later sections of “Fundamentals of Physical Chemistry” (thermodynamics, electrochemical processes, and kinetics) each zoom in on a different perspective, but they rely on the same core ideas introduced here:

• Systems and states: Used to define and track energy changes and equilibria.
• State functions vs. path functions: Crucial in understanding energy balances.
• Equilibrium and spontaneity: Central in both thermodynamics and electrochemistry, and indirectly in kinetics (which deals with the path to equilibrium).
• Molecular interpretation of macroscopic behavior: Underlies kinetics and transport properties, and gives meaning to the thermodynamic quantities.
• Ideal models and corrections: Recur in gas laws, solution chemistry, electrochemical cells, and rate laws.

As you move into the specific subsections:

• Chemical thermodynamics will formalize energy conservation, spontaneity, and equilibrium.
• Electrochemical processes will apply energy and equilibrium concepts to systems involving charge transfer.
• Chemical kinetics will focus on the time dimension—how quickly change happens and what controls reaction speeds.

Together, these build a coherent physical picture of how and why chemical transformations occur, how far they go, and how fast they get there.