Physical ChemistryTop Priority (3-4 Qs in JEE)

Chemical Thermodynamics & Energetics Formulas

Enthalpy, entropy, Gibbs free energy, Hess law, Kirchhoff equation, and equilibrium constant temperature dependence.

8 Formulas•703+ Questions in Bank•

Concept Diagram

Carnot Engine P-V Cycle

Reversible thermodynamic cycle: 1→2 Isothermal expansion, 2→3 Adiabatic expansion, 3→4 Isothermal compression, 4→1 Adiabatic compression.

Core Formulas & Mathematical Identities

First Law & Enthalpy Relation

\Delta U = q + w = q - P_{\text{ext}}\Delta V, \quad \Delta H = \Delta U + \Delta n_g R T

First law formulation with enthalpy-internal energy gaseous conversion.

Examiner Tip: Δn_g = (moles of gaseous products) - (moles of gaseous reactants).

Gibbs Free Energy & Spontaneity

\Delta G = \Delta H - T\Delta S, \quad \Delta G^\circ = -RT \ln K = -2.303 RT \log_{10} K

Universal thermodynamic criterion for spontaneity and chemical equilibrium.

Examiner Tip: Spontaneous if ΔG < 0; at equilibrium ΔG = 0; non-spontaneous if ΔG > 0.

Kirchhoff's Thermochemical Equation

\Delta H_{T_2} = \Delta H_{T_1} + \Delta C_p(T_2 - T_1), \quad \Delta U_{T_2} = \Delta U_{T_1} + \Delta C_v(T_2 - T_1)

Temperature dependence of standard reaction enthalpy and internal energy.

Examiner Tip: ΔC_p = ∑ C_p(products) - ∑ C_p(reactants).

Entropy Changes in Physical Processes

\Delta S = \frac{q_{\text{rev}}}{T}, \quad \Delta S_{\text{gas}} = n C_v \ln\frac{T_2}{T_1} + n R \ln\frac{V_2}{V_1} = n C_p \ln\frac{T_2}{T_1} - n R \ln\frac{P_2}{P_1}

Entropy change for state transitions of ideal gas.

Examiner Tip: In isothermal process, ΔS = n R ln(V₂/V₁) = -n R ln(P₂/P₁).

Van 't Hoff Isochore Equation

\ln\frac{K_2}{K_1} = \frac{\Delta H^\circ}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Temperature variation of equilibrium constant K.

Examiner Tip: For endothermic reactions (ΔH° > 0), K increases as T increases; for exothermic, K decreases.

Work Done: Reversible vs Irreversible (Isothermal & Adiabatic)

w_{\text{iso, rev}} = -2.303 n R T \log_{10}\left(\frac{V_2}{V_1}\right), \quad w_{\text{adiab, rev}} = \frac{n R(T_2 - T_1)}{\gamma - 1} = \frac{P_2 V_2 - P_1 V_1}{\gamma - 1}

Pressure-volume work for fundamental paths. In expansion, reversible work output is strictly greater than irreversible work.

Examiner Tip: Free expansion against vacuum (P_ext = 0) has w = 0, q = 0, ΔT = 0 for ideal gas (both isothermal and adiabatic).

Standard Enthalpy via Bond Energies & Hess's Law

\Delta_r H^\circ = \sum \text{B.E.}_{\text{reactants}} - \sum \text{B.E.}_{\text{products}} = \sum \Delta_f H^\circ_{\text{products}} - \sum \Delta_f H^\circ_{\text{reactants}}

Enthalpy calculation from chemical bond dissociation energies or standard enthalpies of formation.

Examiner Tip: Standard enthalpy of formation Δ_f H° of elements in their reference standard states (e.g. C_graphite, O₂ gas, Br₂ liquid) is zero by convention.

Molar Heat Capacities & Degrees of Freedom

C_p - C_v = R, \quad \gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f} \implies \begin{cases} \text{Monoatomic } (f=3): \gamma = 5/3 \approx 1.67 \\ \text{Diatomic } (f=5): \gamma = 7/5 = 1.40 \end{cases}

Mayer's relation and adiabatic exponent γ connection to molecular translational and rotational degrees of freedom.

Examiner Tip: At high temperatures, vibrational modes become active, contributing an additional R to C_v.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Chemical Thermodynamics & Energetics

•Sign convention: in chemistry, work done ON system is positive: ΔU = q + w, where w = -P_ext ΔV.
•Spontaneity requires ΔG < 0 at CONSTANT temperature and pressure (not just ΔH < 0).

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