Chapter 5: Thermodynamics | Summary

Internal energy (U) represents the total energy of a system, encompassing chemical, electrical, mechanical, and all other forms. It is a state function, meaning its value depends only on the state of the system and not on the path taken to reach that state. Joule's experiments demonstrated that the same change in internal energy occurs regardless of whether work is done mechanically or electrically, confirming U as a state function.

Work (w) is positive when done on the system (compression) and negative when done by the system (expansion). For pressure-volume work, w = -pex ΔV. Heat (q) is the energy exchanged due to a temperature difference; it is positive when absorbed by the system and negative when released. For an adiabatic process, q = 0 and ΔU = wad. The IUPAC convention assigns positive sign to work done on the system and to heat absorbed by the system.

The first law of thermodynamics states that the energy of an isolated system is constant, also expressed as the law of conservation of energy: energy can neither be created nor destroyed. Mathematically, it is expressed as ΔU = q + w, where ΔU is the change in internal energy, q is the heat absorbed by the system, and w is the work done on the system. For a constant volume process, ΔU = qV, and for a constant pressure process, the heat exchanged equals the enthalpy change.

For isothermal free expansion of an ideal gas (pex = 0), both q = 0 and w = 0, so ΔU = 0. For reversible isothermal expansion, w = -nRT ln(Vf/Vi) = -2.303 nRT log(Vf/Vi). Irreversible processes differ from reversible ones, and ΔU cannot distinguish between them, but entropy (ΔS) can. At constant volume, ΔV = 0, so w = 0 and ΔU = qV.

Enthalpy (H) is defined as H = U + pV. It is a state function and its change at constant pressure equals the heat absorbed: ΔH = qp. The relationship between ΔH and ΔU for reactions involving gases is given by ΔH = ΔU + ΔngRT, where Δng is the change in the number of moles of gaseous species. For reactions involving only solids and liquids, ΔH ≈ ΔU since volume changes are negligible.

Enthalpy is negative for exothermic reactions (heat evolved) and positive for endothermic reactions (heat absorbed). The relationship Cp - CV = R for an ideal gas arises from the difference between heat capacities at constant pressure and constant volume. Heat capacity C is defined by q = CΔT; molar heat capacity Cm = C/n gives the heat needed to raise one mole by one kelvin. Specific heat capacity is the heat needed to raise one unit mass by one degree.

Calorimetry is the experimental technique used to measure energy changes in chemical or physical processes. A bomb calorimeter is used to measure ΔU at constant volume; the substance is burned in pure oxygen inside a sealed steel vessel immersed in a water bath. Since the volume is constant, no work is done, and all the energy change appears as heat. Temperature change multiplied by the heat capacity of the calorimeter gives qV.

For measuring ΔH at constant pressure, a simpler calorimeter open to the atmosphere is used. The heat absorbed or evolved at constant pressure equals the enthalpy of reaction ΔrH. In exothermic reactions, qp is negative and ΔrH is negative; in endothermic reactions, qp is positive and ΔrH is positive. The equation q = cmΔT = CΔT is used to convert temperature changes to heat values.

Standard enthalpy of reaction (ΔrH°) is the enthalpy change when all participating substances are in their standard states (pure form at 1 bar, usually 298 K). Enthalpy changes during phase transformations include: enthalpy of fusion (ΔfusH°, always positive for melting), enthalpy of vaporization (ΔvapH°, always positive), and enthalpy of sublimation (ΔsubH°). These depend on the strength of intermolecular interactions in the substance.

Standard enthalpy of formation (ΔfH°) is the enthalpy change for forming one mole of a compound from its elements in their most stable reference states. By convention, ΔfH° of an element in its reference state is zero. Standard enthalpy of combustion (ΔcH°) is the enthalpy change per mole when a substance undergoes complete combustion. Bond enthalpy (ΔbondH°) is used to estimate reaction enthalpies in the gas phase: ΔrH° = Σ bond enthalpies of reactants - Σ bond enthalpies of products. Lattice enthalpy and enthalpy of solution are relevant for ionic compounds.

Hess's law states that if a reaction takes place in several steps, the standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions at the same temperature. This follows directly from enthalpy being a state function—the total enthalpy change is independent of the path taken. The law allows calculation of enthalpy changes for reactions that cannot be measured directly.

A practical application involves the Born-Haber cycle for ionic compounds, which constructs an enthalpy diagram using sublimation, ionization, dissociation, electron gain, and lattice formation steps to calculate the lattice enthalpy indirectly. The algebraic manipulation of thermochemical equations—reversing equations changes the sign of ΔH, and multiplying equations multiplies ΔH—forms the basis of Hess's law calculations.

Spontaneous processes proceed on their own without external assistance and are irreversible. Decrease in enthalpy alone cannot be the criterion for spontaneity, as several endothermic reactions are spontaneous. Entropy (S) is introduced as a measure of randomness or disorder in a system. For a spontaneous process in an isolated system, the total entropy change (ΔStotal = ΔSsystem + ΔSsurroundings) is always positive. At equilibrium, ΔStotal = 0.

The second law of thermodynamics states that the entropy of an isolated system always increases for a spontaneous change. The third law states that the entropy of a pure crystalline substance approaches zero as temperature approaches absolute zero (0 K). This enables calculation of absolute entropy values from thermal data. Entropy change is quantified as ΔS = qrev/T for a reversible process, and it is a state function independent of path.

Gibbs energy (G) is defined as G = H - TS and combines enthalpy and entropy into a single spontaneity criterion at constant temperature and pressure. The change in Gibbs energy is ΔG = ΔH - TΔS. A process is spontaneous if ΔG < 0, non-spontaneous if ΔG > 0, and at equilibrium if ΔG = 0. This single criterion replaces the need to evaluate both enthalpy and entropy changes separately.

The standard Gibbs energy change is related to the equilibrium constant by ΔrG° = -RT ln K = -2.303 RT log K, and also by ΔrG° = ΔrH° - TΔrS°. A large negative ΔrG° implies K >> 1 (reaction favors products), while a large positive ΔrG° implies K << 1. Temperature affects spontaneity: reactions with positive ΔS can become spontaneous at sufficiently high temperatures even if ΔH is positive.

Thermodynamics provides a rigorous framework for understanding energy changes in chemical reactions and physical processes. The three laws of thermodynamics — conservation of energy, increasing entropy for spontaneous processes, and zero entropy at absolute zero — together allow prediction of whether a reaction will occur, how much useful work can be extracted, and how equilibrium position varies with temperature. The Gibbs energy function elegantly combines enthalpy and entropy to provide a single, unified criterion for spontaneity.

For CBSE board examinations, mastery of thermodynamics requires understanding state functions versus path functions, ability to apply the first law in various processes, skill in enthalpy calculations using Hess's law and bond enthalpies, interpretation of entropy changes, and the relationship ΔrG° = -RT ln K. Numerical problems from calorimetry, ΔH-ΔU interconversion, and Gibbs energy calculations are consistently tested. This chapter also builds the conceptual foundation for chemical equilibrium studied in the next unit.