Thermodynamics is the accounting system of chemistry: it tells you how much heat a reaction releases, and — more importantly — whether the reaction will happen at all. NEET reliably draws 2–3 questions from this chapter, usually numerical ones on enthalpy changes, Hess's law, or the sign of ΔG, so the payoff for mastering a handful of equations is unusually high.
Systems, Surroundings and the Language of States
Any thermodynamic discussion begins by drawing an imaginary boundary. Whatever lies inside the boundary and is under study is the system; everything outside that can exchange energy or matter with it is the surroundings. Systems are classified by what the boundary permits:
- Open system — both matter and energy cross the boundary (an uncapped beaker of hot water).
- Closed system — energy passes, matter does not (a sealed glass ampoule being heated).
- Isolated system — neither passes (an ideal thermos flask; a reaction in a perfectly insulated sealed bomb).
The condition of a system is fixed by measurable properties such as pressure, volume, temperature and composition. When these have definite values the system is in a state, and any property whose value depends only on the present state — not on the route taken to reach it — is a state function. Pressure, volume, temperature, internal energy, enthalpy, entropy and Gibbs energy are all state functions. Heat (q) and work (w) are not: they are path functions, quantities that describe the process of change rather than the condition of the system.
A second useful distinction is between extensive properties, which scale with the amount of substance (mass, volume, internal energy, enthalpy, entropy, heat capacity), and intensive properties, which do not (temperature, pressure, density, molar volume, viscosity, specific heat). Note the pattern: dividing any extensive property by moles or mass converts it into an intensive one.
Processes are named after what is held constant: isothermal (constant T), isobaric (constant p), isochoric (constant V), adiabatic (no heat exchange, q = 0), and cyclic (the system returns to its initial state, so every state function change is zero). A reversible process proceeds through an unbroken series of equilibrium states, driven by an infinitesimal imbalance; all real, finite-rate processes are irreversible.
The First Law: Internal Energy, Heat and Work
The total energy stored in a system — kinetic energy of molecules, vibrations, rotations, bond energies, intermolecular attractions — is its internal energy, U. Its absolute value cannot be measured, but changes in it can. Energy enters or leaves only as heat or work, giving the first law:
ΔU = q + w
The sign convention used throughout NCERT and NEET: heat absorbed by the system and work done on the system are positive; heat released and work done by the system are negative.
For a gas expanding against an external pressure, the pressure–volume work is w = −p_ext ΔV
Three consequences worth memorising:
- Free expansion (expansion into vacuum, p_ext = 0) does no work: w = 0. If it is also adiabatic, ΔU = 0 and, for an ideal gas, the temperature does not change.
- Isochoric process: ΔV = 0, so w = 0 and ΔU = q_V. This is why bomb calorimeters measure ΔU directly.
- Isothermal reversible expansion of an ideal gas: w = −2.303 nRT log(V₂/V₁) = −2.303 nRT log(p₁/p₂). Since ΔU = 0 for an isothermal ideal-gas change, q = −w.
For an adiabatic change, q = 0, so ΔU = w = nC_v,mΔT. Compressing a gas adiabatically (w positive) therefore raises its temperature; adiabatic expansion cools it.
Enthalpy, Heat Capacities and Calorimetry
Most laboratory reactions happen in open vessels at constant atmospheric pressure, where the system may expand and lose some energy as work. To handle this conveniently we define enthalpy:
H = U + pV, so at constant pressure ΔH = ΔU + pΔV = q_p
Enthalpy change is thus the heat exchanged at constant pressure. For reactions involving gases, pΔV = Δn_g RT, giving the crucially examinable relation:
ΔH = ΔU + Δn_g RT
where Δn_g = (moles of gaseous products) − (moles of gaseous reactants). If no gases are involved, or if Δn_g = 0, then ΔH = ΔU. A reaction with ΔH negative is exothermic; positive ΔH means endothermic.
Heat capacity is the heat needed to raise the temperature by one degree: q = CΔT. Molar heat capacity C_m is per mole, specific heat c is per gram. Because a gas heated at constant pressure must also do expansion work, C_p exceeds C_v, and for one mole of an ideal gas:
C_p − C_v = R
Measurements are made in a calorimeter. A bomb calorimeter operates at constant volume and yields ΔU (used for combustion of foods and fuels); a simple coffee-cup style calorimeter at constant pressure yields ΔH. In either case, q_reaction = −q_calorimeter = −C_cal ΔT.
Enthalpies of Specific Processes and Hess's Law
To make enthalpy data comparable, values are tabulated for standard states — the pure substance in its most stable form at 1 bar and the specified temperature (usually 298 K), symbolised ΔH°.
Important named enthalpy changes:
- Standard enthalpy of formation (Δ_fH°): for forming 1 mol of a compound from its elements in their standard states. By definition Δ_fH° of any element in its reference form (O₂ gas, C as graphite, Br₂ liquid) is zero.
- Enthalpy of combustion: complete burning of 1 mol of a substance in excess oxygen — always negative.
- Enthalpy of fusion, vaporisation, sublimation: phase changes at constant T and p; all endothermic. ΔH_sub = ΔH_fus + ΔH_vap.
- Bond dissociation enthalpy: energy to break one mole of a particular bond in the gas phase; endothermic. For polyatomic molecules we quote mean bond enthalpies.
- Enthalpy of atomisation: converting one mole of a substance completely into gaseous atoms.
- Lattice enthalpy: the enthalpy of converting one mole of an ionic solid into widely separated gaseous ions; obtained indirectly via a Born–Haber cycle.
- Enthalpy of solution and of hydration: dissolving one mole in a large excess of solvent; the sign depends on the balance of lattice and hydration enthalpies.
- Enthalpy of neutralisation: for a strong acid–strong base pair it is a near-constant −57.1 kJ mol⁻¹, because the actual reaction is always H⁺(aq) + OH⁻(aq) → H₂O(l). With weak acids or bases the magnitude is smaller, since some energy is consumed in ionisation.
Because H is a state function, Hess's law of constant heat summation holds: the total enthalpy change of a reaction is the same whether it occurs in one step or in several. Practically, you may add, reverse and multiply thermochemical equations like algebraic equations — reversing a step flips the sign of ΔH, multiplying by n multiplies ΔH by n. Two derived shortcuts:
Δ_rH° = ΣΔ_fH°(products) − ΣΔ_fH°(reactants) (each multiplied by its stoichiometric coefficient)
Δ_rH° = Σ(bond enthalpies of bonds broken) − Σ(bond enthalpies of bonds formed) (gas-phase reactions only)
Spontaneity: Entropy and the Second Law
The first law says energy is conserved but is silent about direction. Heat never flows spontaneously from cold to hot; a gas never gathers itself into one corner of a room. Nor is exothermicity a reliable criterion — ice melts above 0 °C, and NH₄Cl dissolves in water, both endothermically and spontaneously.
The missing quantity is entropy, S, a state function measuring the number of ways the energy and particles of a system can be arranged — loosely, its molecular randomness or dispersal. For a reversible transfer of heat at temperature T:
ΔS = q_rev / T
Entropy generally increases when a solid melts, a liquid vaporises, a solid dissolves, a gas is allowed to expand, temperature rises, or a reaction produces more moles of gas than it consumes. Entropy of a substance ranks: gas ≫ liquid > solid.
The second law states that in any spontaneous process the total entropy of system plus surroundings increases:
ΔS_total = ΔS_system + ΔS_surroundings > 0
At equilibrium ΔS_total = 0. Note that ΔS_system alone may be negative (as in freezing) provided the surroundings gain more entropy than the system loses. The third law completes the picture: the entropy of a perfectly crystalline pure substance is zero at 0 K, which allows absolute entropies to be tabulated.
Gibbs Energy: The Working Criterion of Spontaneity
Tracking the surroundings is inconvenient, so we combine the two drives — energy lowering and entropy raising — into one system-only function. Gibbs energy is defined as G = H − TS, and at constant temperature and pressure:
ΔG = ΔH − TΔS
The criterion for a process at constant T and p:
- ΔG < 0 → spontaneous (exergonic)
- ΔG = 0 → system at equilibrium
- ΔG > 0 → non-spontaneous in the forward direction
−ΔG also equals the maximum useful (non-expansion) work obtainable from the process. The interplay of the two terms gives four cases:
- ΔH negative, ΔS positive → spontaneous at all temperatures.
- ΔH positive, ΔS negative → never spontaneous.
- ΔH negative, ΔS negative → spontaneous only at low T (below T = ΔH/ΔS).
- ΔH positive, ΔS positive → spontaneous only at high T (above T = ΔH/ΔS).
At a phase-transition temperature (melting point, boiling point) the two phases are in equilibrium, so ΔG = 0 and T = ΔH/ΔS — a standard numerical question.
Gibbs energy links thermodynamics to equilibrium through:
ΔG° = −RT ln K = −2.303 RT log K
So a negative ΔG° corresponds to K > 1 (products favoured), ΔG° = 0 to K = 1, and positive ΔG° to K < 1. Do not confuse ΔG (the instantaneous value, which reaches zero at equilibrium for any reaction) with ΔG° (a fixed number for a given reaction at a given temperature, generally not zero).
Common Mistakes and Exam Traps
- Sign convention slips. Work done by the system is negative. In w = −p_extΔV, an expansion (ΔV > 0) gives negative w. Students who memorise w = +pΔV get every gas-expansion question backwards.
- Using ΔH = ΔU carelessly when gases are involved. ΔH = ΔU only when Δn_g = 0; whenever the moles of gaseous reactants and products differ, the correction term Δn_gRT must be added — skipping this term is one of the most common numerical slips in this chapter.
- Assuming an exothermic reaction is automatically spontaneous. Spontaneity is decided by ΔG = ΔH − TΔS, not by the sign of ΔH alone — many exothermic reactions are non-spontaneous at high T if ΔS is sufficiently negative, and many endothermic processes (ice melting above 0°C, dissolution of NH₄Cl) are spontaneous because the entropy term dominates.
- Confusing ΔG and ΔG°. ΔG (no superscript) is the actual free-energy change at the prevailing concentrations/pressures and becomes zero at equilibrium for any reaction; ΔG° is a fixed reference value for standard-state conditions at a given temperature and is generally not zero even at equilibrium — treating the two as interchangeable leads to wrong conclusions about K.