Thermodynamics is the study of energy transformations, particularly the exchange of heat and work between a system and its surroundings. In chemistry, thermodynamics answers a fundamental question: will a given reaction proceed spontaneously, and how much energy will it release or absorb? It tells us whether a reaction is energetically favourable, even though it cannot tell us how fast the reaction proceeds.
The subject is built on a few carefully defined concepts: the system and its surroundings, state functions, internal energy, enthalpy and entropy. The first law of thermodynamics is essentially the law of conservation of energy extended to heat and work, while the second law introduces entropy and the direction of spontaneous change. The free energy function combines enthalpy and entropy to predict spontaneity at constant temperature and pressure.
For a chemist, thermochemistry is the practical application of thermodynamics to chemical reactions. The enthalpy changes of reactions, whether exothermic or endothermic, are calculated using Hess's law and standard enthalpy data. This chapter builds the conceptual and quantitative tools used across physical chemistry, from equilibrium to electrochemistry.
A thermodynamic system is the part of the universe under study, and the surroundings are everything else. The boundary separates the two. Systems are classified by how they exchange matter and energy with their surroundings. An open system exchanges both matter and energy, like an open beaker. A closed system exchanges energy but not matter, like a sealed flask. An isolated system exchanges neither, like a thermos flask.
A state function depends only on the state of the system and not on the path taken to reach it. Temperature, pressure, volume, internal energy and enthalpy are state functions. Heat and work are path functions because their values depend on how a process is carried out. Internal energy (U) is the total energy stored in a system, including the kinetic and potential energy of its molecules.
For a chemical process at constant volume, the heat change equals the change in internal energy (qv = delta U). At constant pressure, which is the common condition in the laboratory, the heat change equals the change in enthalpy (qp = delta H). The enthalpy is defined as:
$$H = U + PV$$
The first law of thermodynamics states that energy can be neither created nor destroyed, only converted from one form to another. For a system that undergoes a change, the change in internal energy equals the heat absorbed minus the work done by the system:
$$\Delta U = q + w$$
By convention, q is positive when heat is absorbed by the system and w is positive when work is done on the system. For pressure-volume work at constant pressure:
$$w = -P\Delta V$$
If a gas expands, delta V is positive and the work done by the gas is negative (energy leaves the system). This sign convention must be applied consistently in numerical problems.
For an ideal gas, the internal energy depends only on temperature. Therefore, during an isothermal expansion of an ideal gas, delta U = 0 and q = -w. During an adiabatic process, q = 0 and delta U = w. These special cases help in solving thermodynamic problems elegantly.
Enthalpy is the heat content of a system at constant pressure. The change in enthalpy equals the heat absorbed or released by a reaction at constant pressure:
$$\Delta H = q_p = \Delta U + P\Delta V$$
For reactions involving gases, the relation between delta H and delta U is:
$$\Delta H = \Delta U + \Delta n_g RT$$
where delta n_g is the change in the number of moles of gaseous species. If the number of gas moles is unchanged, delta H equals delta U.
An exothermic reaction releases heat to the surroundings and has a negative delta H, while an endothermic reaction absorbs heat and has a positive delta H. The enthalpy of a reaction can be measured using a calorimeter, and for solutions the heat absorbed or released can be calculated from the temperature change using q = m x c x delta T.
The standard enthalpy of reaction (delta H degree) is the enthalpy change when reactants in their standard states react to form products in their standard states, with all substances at 1 bar pressure and the specified temperature, usually 298 K.
The standard enthalpy of formation (delta_f H degree) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. By convention, the standard enthalpy of formation of an element in its standard state is zero. For example, delta_f H degree of water is the heat released when 1 mole of water forms from hydrogen and oxygen gases.
The standard enthalpy of combustion (delta_c H degree) is the enthalpy change when one mole of a substance is completely burnt in oxygen. Combustion of fuels is always exothermic. These standard enthalpies are used to calculate the enthalpy change of any reaction using Hess's law.
The enthalpy change of a reaction can be computed from standard enthalpies of formation:
$$\Delta_r H^\circ = \sum \Delta_f H^\circ (\text{products}) - \sum \Delta_f H^\circ (\text{reactants})$$
Hess's law states that the enthalpy change of a reaction depends only on the initial and final states and is independent of the path or the number of steps. Enthalpy is a state function, so the same total delta H is obtained whether a reaction proceeds directly or through intermediate steps.
Hess's law allows the calculation of enthalpy changes that are difficult to measure directly, such as the enthalpy of formation of carbon monoxide. The enthalpy of reaction can also be computed from bond enthalpies:
$$\Delta_r H^\circ = \sum \text{bond enthalpy of reactants} - \sum \text{bond enthalpy of products}$$
The bond enthalpy is the energy required to break one mole of a particular bond in the gaseous state. Bond breaking absorbs energy, while bond formation releases energy.
A spontaneous process is one that occurs without external intervention. Spontaneity does not mean speed; many spontaneous reactions are very slow. The direction of spontaneous change is governed by the second law of thermodynamics, which introduces entropy.
Entropy (S) is a measure of the disorder or randomness of a system. Gases have high entropy, liquids lower, and solids lowest. The change in entropy for a reversible process at constant temperature is:
$$\Delta S = \frac{q_{\text{rev}}}{T}$$
The second law states that the total entropy of the universe always increases for a spontaneous process. A reaction is spontaneous if the entropy of the universe increases. Since the surroundings gain or lose entropy when heat is exchanged, the criterion for spontaneity is conveniently expressed using free energy.
The Gibbs free energy is defined as:
$$G = H - TS$$
For a process at constant temperature and pressure:
$$\Delta G = \Delta H - T\Delta S$$
The sign of delta G determines the direction of a process: if delta G is negative, the process is spontaneous; if delta G is positive, it is non-spontaneous; and if delta G is zero, the system is at equilibrium.
The spontaneity of a reaction depends on the balance between enthalpy and entropy. A reaction is always spontaneous when delta H is negative and delta S is positive. When both are positive, the reaction is spontaneous at high temperature; when both are negative, spontaneous at low temperature. When delta H is positive and delta S is negative, the reaction is never spontaneous.
The standard free energy change is related to the equilibrium constant by:
$$\Delta G^\circ = -RT \ln K$$
| Function | Definition | State or path function |
|---|---|---|
| Internal energy U | Total energy of the system | State function |
| Enthalpy H | H = U + PV | State function |
| Entropy S | Measure of disorder | State function |
| Free energy G | G = H - TS | State function |
| Heat q | Energy transferred | Path function |
| Work w | Energy transferred by motion | Path function |
| Delta H | Delta S | Delta G = Delta H - T Delta S | Spontaneity |
|---|---|---|---|
| Negative | Positive | Always negative | Spontaneous at all T |
| Positive | Negative | Always positive | Never spontaneous |
| Negative | Negative | Negative at low T | Spontaneous at low T |
| Positive | Positive | Negative at high T | Spontaneous at high T |
| Type | Definition |
|---|---|
| Formation | One mole of compound from elements in standard states |
| Combustion | One mole of substance burnt completely in oxygen |
| Neutralisation | Acid and base react to form one mole of water |
| Fusion | One mole of solid melts to liquid |
| Vapourisation | One mole of liquid vapourises |
| Bond enthalpy | One mole of bonds broken in gaseous state |
Thermodynamics provides the energy framework within which all chemical change is understood. The first law quantifies the conservation of energy through internal energy and enthalpy, and thermochemistry supplies the standard enthalpies and Hess's law needed to calculate reaction energetics. The second law introduces entropy as the measure of disorder, and the Gibbs free energy combines enthalpy and entropy into a single criterion for spontaneity. Whether a reaction releases heat, requires energy, or proceeds spontaneously at a given temperature can now be predicted with confidence. These principles underpin the study of equilibrium, electrochemistry and reaction mechanisms, making thermodynamics one of the most powerful unifying theories in chemistry.