Chemical Thermodynamics

Role of Thermodynamics in Chemistry

Chemical thermodynamics studies how energy and matter are interrelated in chemical systems. It answers questions such as:

• Will a reaction proceed in a given direction (is it possible at all)?
• How far will a reaction proceed before it stops changing measurably?
• How do temperature, pressure, and composition influence chemical processes?
• In which form is energy stored and exchanged in chemical systems?

While chemical kinetics deals with how fast reactions occur, thermodynamics deals with whether a process is possible and with the initial and final states of a system, not the path in between.

In this overview chapter you will meet the basic language and central ideas of thermodynamics that chemistry uses; the following subchapters will develop them in detail.

Systems, Surroundings, and State

System and Surroundings

To describe energy changes, we first define what we are looking at:

• System: the part of the universe we focus on (e.g. the contents of a beaker where a reaction takes place).
• Surroundings: everything else that can exchange energy or matter with the system (e.g. the beaker walls, the lab air, you, the rest of the universe).

Depending on how the system interacts with its surroundings:

• Open system: exchanges both matter and energy with the surroundings
  (e.g. an uncovered beaker where solvent can evaporate and heat can flow).
• Closed system: exchanges energy but not matter
  (e.g. a sealed, but not thermally insulated, reaction flask).
• Isolated system: exchanges neither matter nor energy
  (an ideal thermos bottle is an approximation).

Most real chemical systems are best approximated as closed with respect to matter during the experimental time scale, but usually can exchange heat with their environment.

State and State Variables

A state of a system is specified by a set of macroscopic properties, called state variables (or state functions), that fully characterize it at a given moment, for example:

• temperature $T$
• pressure $p$
• volume $V$
• amount of substance $n$ (in moles)
• composition (which substances and in what proportions)
• energy-related quantities (e.g. internal energy $U$, enthalpy $H$, entropy $S$, Gibbs free energy $G$)

A system is in thermodynamic equilibrium when all its macroscopic state variables are constant in time and uniform (or appropriately balanced) throughout the system, and no net flows of matter or energy occur within or across its boundaries.

Chemical thermodynamics usually concerns transitions between an initial equilibrium state and a final equilibrium state of a system.

State Functions vs. Path Functions

Many quantities used in thermodynamics are state functions:

• They depend only on the state of the system, not on how the system reached that state.
• Differences in a state function between two states are independent of the process path.

Examples: $U$, $H$, $S$, $G$, $T$, $p$, $V$, $n$.

In contrast, heat ($q$) and work ($w$) are path functions:

• They depend on the specific way a process is carried out.
• You cannot assign a unique value of “heat contained in the system”; only the heat transferred during a particular process is meaningful.

In thermodynamics, we often express changes in state functions ($\Delta U$, $\Delta H$, etc.) in terms of heat and work involved in moving from one state to another.

Types of Thermodynamic Processes

For chemical reactions and physical changes (e.g. expansion, phase transitions), several special types of processes are important. They are often defined by which variable is held constant:

• Isothermal process: constant temperature ($T = \text{const.}$)
• Isobaric process: constant pressure ($p = \text{const.}$)
• Isochoric (isovolumetric) process: constant volume ($V = \text{const.}$)
• Adiabatic process: no heat exchange between system and surroundings ($q = 0$)

In chemical experiments:

• Reactions open to the atmosphere are typically approximated as isobaric at $p \approx 1\ \text{bar}$.
• Reactions carried out in sealed, rigid containers can often be approximated as isochoric.
• Carefully insulated systems can approximate adiabatic conditions for short times.

A reversible process is an idealized process that proceeds through a continuous sequence of equilibrium states and can be reversed by an infinitesimal change in conditions. Real processes are irreversible, but reversible processes serve as useful reference models.

Energy in Chemical Thermodynamics

Chemical thermodynamics is built on how energy is stored and transformed in matter. Several energy-related quantities are central:

• Internal energy $U$: the total energy stored in the system due to the motion and interactions of its particles.
• Enthalpy $H$: a state function particularly convenient at constant pressure.
• Entropy $S$: a measure related to the number of ways a system’s energy and particles can be arranged (linked with “disorder” and dispersal of energy).
• Gibbs free energy $G$: the key quantity for predicting spontaneity of reactions at constant temperature and pressure.

Each of these will be treated in its own section; here we only sketch their roles.

Internal Energy and the Conservation of Energy

The First Law of Thermodynamics expresses energy conservation for thermodynamic systems by relating changes in internal energy $\Delta U$ to energy exchanged as heat and work. In chemical contexts:

• Heat exchange often occurs when a reaction absorbs or releases energy.
• Work is often associated with volume changes (expansion or compression work).

The first law does not tell us whether a process will occur spontaneously; it only expresses an energy balance.

Enthalpy and Heat Effects of Reactions

Many chemical reactions are studied at constant pressure (open beakers, test tubes in air). For such conditions, enthalpy $H$ is especially useful:

• The heat exchanged at constant pressure for processes that do only expansion/compression work is equal to the change in enthalpy $\Delta H$.
• Reactions with $\Delta H < 0$ are called exothermic (heat is released).
• Reactions with $\Delta H > 0$ are called endothermic (heat is absorbed).

Enthalpy changes are tabulated for many reactions and processes (e.g. standard enthalpies of formation) and can be combined using Hess’s law to find enthalpy changes for complex reactions.

Entropy and the Direction of Change

The Second Law of Thermodynamics introduces entropy $S$ and provides a criterion for the direction of spontaneous change:

• For an isolated system, the total entropy never decreases.
• Spontaneous processes are those that lead to an increase in the total entropy of system plus surroundings.

Many chemical phenomena (e.g. dissolving, mixing, phase changes) are favored by an increase in entropy, even when they absorb heat from the surroundings.

Entropy connects to molecular-scale behavior: there are generally more possible arrangements (microstates) for “spread-out” energy and matter than for “concentrated” ones.

Gibbs Free Energy and Chemical Spontaneity

For chemical reactions at constant temperature and pressure (the most relevant conditions in laboratories and biological systems), the central quantity is Gibbs free energy $G$:

• A change in Gibbs free energy, $\Delta G$, determines whether a reaction is thermodynamically spontaneous under given conditions.
• Roughly:
• $\Delta G < 0$: reaction is thermodynamically favored (can proceed spontaneously in the forward direction).
• $\Delta G > 0$: reaction is not favored in the forward direction.
• $\Delta G = 0$: the system is at equilibrium.

Gibbs free energy summarizes the competition between enthalpy (energy release or uptake) and entropy (spreading out of energy and matter). It thus links the First and Second Laws in a form particularly convenient for chemistry.

Standard States and Reference Conditions

To tabulate thermodynamic quantities and make them comparable, chemistry uses standard states and standard conditions.

• The standard state of a pure substance (gas, liquid, or solid) is usually defined as the state of that substance at:
• pressure $p^\circ = 1\ \text{bar}$ (or historically $1\ \text{atm}$),
• and a specified temperature (commonly $298.15\ \text{K}$, which is $25^\circ\text{C}$, for tabulated values).
• For solutes in solution, the standard state is often defined for a hypothetical ideal solution at a specified reference concentration (often $1\ \text{mol L}^{-1}$).

Thermodynamic quantities under these conditions are denoted with a superscript $\circ$, for example:

• standard enthalpy change $\Delta H^\circ$
• standard entropy $S^\circ$
• standard Gibbs free energy change $\Delta G^\circ$

These standard quantities allow one to calculate thermodynamic behavior under non-standard conditions, including how free energy relates to equilibrium constants and to cell voltages in electrochemistry.

Thermodynamics of Chemical Reactions and Phase Changes

Chemical thermodynamics is applied both to:

• Chemical reactions: changes in composition (atoms rearranged; new substances formed).
• Physical (phase) changes: changes in physical state or aggregation (e.g. melting, vaporization, dissolution) without changing chemical identity.

For both types of processes, the key questions are:

1. Energy balance:
   How much heat is exchanged? How does enthalpy change?
2. Direction and extent:
   Will the process occur spontaneously under given conditions?
   To what extent (e.g. what equilibrium composition or vapour pressure) will it proceed?
3. Effect of conditions:
   How do temperature, pressure, and composition affect $\Delta H$, $\Delta S$, and $\Delta G$?
   How do they shift equilibria between reactants and products or between phases?

In later chapters, these thermodynamic ideas are connected directly to:

• Chemical equilibrium and the law of mass action
• Electrochemical cells and redox processes
• Phase diagrams and solubility
• Biological energy conversion (e.g. metabolism, photosynthesis)

Here, the focus is on the general framework and fundamental quantities; subsequent subchapters on energy and conservation of energy, the First and Second Laws, and Gibbs free energy will provide the mathematical expressions and concrete examples needed to apply chemical thermodynamics quantitatively.