Introduction

Chemical thermodynamics is the branch of chemistry that studies energy changes in chemical reactions and physical transformations. It provides the fundamental criteria for predicting whether a reaction will occur spontaneously, how much work can be extracted, and where equilibrium lies. For NEET, thermodynamics contributes 2–3 questions annually and tests the application of the Gibbs equation, Hess's law, and heat capacity relationships.

The First Law of Thermodynamics

The first law states that energy cannot be created or destroyed — only converted between forms. Mathematically, $\Delta U = q + w$, where $\Delta U$ is the change in internal energy, $q$ is heat absorbed by the system, and $w$ is work done on the system (IUPAC sign convention). This convention is crucial: in NCERT and NEET, work done ON the system is positive (compression), and work done BY the system is negative (expansion).

Three types of work arise in NEET problems. Free expansion ($P_{ext} = 0$) gives $w = 0$ — gas expands into vacuum doing no work. Irreversible expansion against constant external pressure gives $w = -P_{ext}\Delta V$. Reversible isothermal expansion gives $w = -nRT\ln(V_2/V_1) = -2.303\,nRT\log(V_2/V_1)$, which represents the maximum work obtainable from an expansion. The dimensional check (mol × J/(mol·K) × K = J) confirms these expressions.

Enthalpy and $\Delta n_g$

Enthalpy is defined as $H = U + PV$. For processes at constant pressure, $\Delta H = q_p$ (heat at constant pressure). The central relationship linking $\Delta H$ and $\Delta U$ for chemical reactions is $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in the number of moles of gas ($\Delta n_g =$ moles of gaseous products $-$ moles of gaseous reactants). Critically, only gaseous species are counted — solids and liquids have negligible PV compared to gases and are excluded.

For example, in $CaCO_{3}$(s) → CaO(s) + $CO_{2}$(g): $\Delta n_g = 1 - 0 = +1$ (only $CO_{2}$ is gaseous). For $N_{2}$(g) + $3H_{2}$(g) → $2NH_{3}$(g): $\Delta n_g = 2 - 4 = -2$. When $\Delta n_g > 0$, $\Delta H > \Delta U$; when $\Delta n_g < 0$, $\Delta H < \Delta U$; when $\Delta n_g = 0$, $\Delta H = \Delta U$ exactly.

Hess's Law and Enthalpy Types

Hess's law states that enthalpy change is path-independent because $H$ is a state function: $\Delta H_{rxn}^\circ = \Sigma\Delta H_f^\circ(\text{products}) - \Sigma\Delta H_f^\circ(\text{reactants})$. The standard enthalpy of formation of any element in its standard state is zero by definition (e.g., $\Delta H_f^\circ(H_2, g) = 0$, $\Delta H_f^\circ(C, \text{graphite}) = 0$).

Using bond enthalpies: $\Delta H = \Sigma(BE_{\text{broken}}) - \Sigma(BE_{\text{formed}})$. Breaking bonds is always endothermic (positive); forming bonds is always exothermic (negative). Key sign conventions for enthalpy types: combustion ($\Delta H_c^\circ$) is always negative; atomization and ionization enthalpies are always positive; lattice and hydration enthalpies are always negative.

Heat Capacities

The relationship $C_p - C_v = R$ holds for all ideal gases, arising because at constant pressure, extra energy goes into PV expansion work ($R$ per mole per kelvin). For monoatomic gases (He, Ne, Ar): $C_v = 3R/2$, $C_p = 5R/2$, $\gamma = 5/3 \approx 1.67$. For diatomic gases ($H_{2}$, $N_{2}$, $O_{2}$): $C_v = 5R/2$, $C_p = 7R/2$, $\gamma = 7/5 = 1.40$. These values arise from the equipartition theorem — each degree of freedom contributes $R/2$ to $C_v$.

Entropy and the Second Law

Entropy ($S$) quantifies disorder: $\Delta S = q_{rev}/T$ for reversible processes. The second law states $\Delta S_{universe} > 0$ for all spontaneous processes. Entropy increases when: (1) phase changes from solid → liquid → gas; (2) number of gas moles increases in a reaction; (3) mixing occurs; (4) temperature increases.

Gibbs Free Energy and Spontaneity

The Gibbs free energy $G = H - TS$ unifies enthalpy and entropy into a single criterion at constant $T$ and $P$: $\Delta G = \Delta H - T\Delta S$. Spontaneous when $\Delta G < 0$; at equilibrium when $\Delta G = 0$; non-spontaneous when $\Delta G > 0$.

Four cases arise based on signs of $\Delta H$ and $\Delta S$: (1) $\Delta H < 0$, $\Delta S > 0$ → always spontaneous; (2) $\Delta H > 0$, $\Delta S < 0$ → never spontaneous; (3) $\Delta H < 0$, $\Delta S < 0$ → spontaneous below the crossover temperature $T = \Delta H/\Delta S$; (4) $\Delta H > 0$, $\Delta S > 0$ → spontaneous above $T = \Delta H/\Delta S$.

The relationship $\Delta G^\circ = -RT\ln K = -2.303RT\log K$ connects thermodynamics to equilibrium. At equilibrium, $\Delta G = 0$ (not $\Delta G^\circ$). $\Delta G^\circ = 0$ only when $K = 1$. This distinction is the most frequently tested trap in NEET thermodynamics.

Key NEET Takeaways

Thermodynamics is conceptually rich but formula-dependent. Master the four-case spontaneity table, the $\Delta n_g$ rule (gaseous moles only), and the distinction between $\Delta G$ and $\Delta G^\circ$. Practice numerical problems involving reversible work calculations, bond enthalpy applications, and crossover temperature calculations.