Chemical Thermodynamics formulas for JEE Main & Advanced

19 formula entries for Chemical Thermodynamics, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

First Law of Thermodynamics

Δ U = q + w

When to use. Calculate energy changes in any thermodynamic process.

Trap. Sign convention: w positive if work done on system, negative if by system; q positive if heat added.

Work Done in Reversible Processes

w = - \int_{V_{1}}^{V_{2}} P d V

; for isothermal reversible:

w = - n R T \ln (\frac{V_{2}}{V_{1}})

When to use. Calculate work for reversible expansion/compression of ideal gas.

Trap. Using the isothermal formula for adiabatic processes—different formula applies.

Enthalpy and Enthalpy Change

H = U + P V

;

Δ H = Δ U + Δ (P V)

; for ideal gas:

Δ H = n C_{p} Δ T

When to use. Calculate heat absorbed/released at constant pressure (most reactions).

Trap. Assuming ΔH = q always; true only at constant pressure.

Hess's Law

Δ H_{reaction} = \sum Δ H_{f}^{\circ} (products) - \sum Δ H_{f}^{\circ} (reactants)

When to use. Calculate ΔH for reactions where direct measurement is difficult.

Trap. Forgetting to multiply by stoichiometric coefficients.

Standard Enthalpy of Formation

Δ H_{f}^{\circ}

When to use. Calculate reaction enthalpies using standard formation data.

Trap. Assuming ΔH_f° of O2(g) is not zero; it is zero.

Spontaneity and Second Law

Δ S_{univ} = Δ S_{sys} + Δ S_{surr} \geq 0

When to use. Predict spontaneity of a process.

Trap. Thinking ΔS_sys > 0 always means spontaneity; need ΔS_univ > 0.

Entropy Change for Ideal Gas

Δ S = n C_{v} \ln (\frac{T_{2}}{T_{1}}) + n R \ln (\frac{V_{2}}{V_{1}})

; also

Δ S = n C_{p} \ln (\frac{T_{2}}{T_{1}}) - n R \ln (\frac{P_{2}}{P_{1}})

When to use. Calculate entropy change for ideal gas undergoing any process.

Trap. The formula gives ΔS_sys for any process between the given states (S is a state function); for irreversible processes ΔS_surr ≠ -ΔS_sys, so ΔS_univ > 0.

Gibbs Free Energy

G = H - T S

;

Δ G = Δ H - T Δ S

When to use. Predict spontaneity at constant T and P.

Trap. Assuming ΔG < 0 always means fast reaction; it only indicates spontaneity, not kinetics.

Gibbs Free Energy and Equilibrium

Δ G^{\circ} = - R T \ln K

;

Δ G = Δ G^{\circ} + R T \ln Q

When to use. Calculate equilibrium constant from thermodynamic data or vice versa.

Trap. Using ΔG° directly for non-standard conditions; must use ΔG = ΔG° + RT ln Q.

Temperature Dependence of ΔG and K

\ln (\frac{K_{2}}{K_{1}}) = - \frac{Δ H^{\circ}}{R} (\frac{1}{T_{2}} - \frac{1}{T_{1}})

When to use. Calculate K at different temperatures or find ΔH° from K vs T data.

Trap. Assuming ΔH° is constant over temperature range (often valid for small ranges).

Third Law of Thermodynamics

S (0 K) = 0

for perfect crystal

When to use. Calculate absolute entropies of substances at given temperatures.

Trap. Assuming entropy is zero at 0 K for all substances; only perfect crystals.

Standard Entropy Change of Reaction

Δ S_{rxn}^{\circ} = \sum S^{\circ} (products) - \sum S^{\circ} (reactants)

When to use. Calculate entropy change for a reaction from standard entropy data.

Trap. Forgetting to multiply by stoichiometric coefficients.

Adiabatic Process for Ideal Gas

P V^{γ} = constant

;

γ = \frac{C_{p}}{C_{v}}

;

w = Δ U = n C_{v} (T_{2} - T_{1}) = \frac{n R (T_{2} - T_{1})}{γ - 1}

(work done by the gas

= \frac{n R (T_{1} - T_{2})}{γ - 1}

)

When to use. Calculate work, temperature, or volume changes in adiabatic processes.

Trap. Using isothermal formulas for adiabatic; they are different.

Carnot Cycle and Efficiency

η = 1 - \frac{T_{c}}{T_{h}}

When to use. Calculate maximum possible efficiency of a heat engine.

Trap. Assuming efficiency can be 100%; requires T_c = 0 K, impossible.

Bond Enthalpy and Reaction Enthalpy

Δ H_{rxn} = \sum Δ H_{bond break} - \sum Δ H_{bond form}

When to use. Estimate reaction enthalpy when formation data is unavailable.

Trap. Forgetting that bond breaking is endothermic (positive), bond forming is exothermic (negative).

Kirchhoff's Law

Δ H (T_{2}) = Δ H (T_{1}) + Δ C_{p} (T_{2} - T_{1})

;

Δ C_{p} = \sum C_{p} (products) - \sum C_{p} (reactants)

When to use. Calculate ΔH at a different temperature from known ΔH at another temperature.

Trap. Assuming Cp is constant over temperature range; often valid for small ranges.

Spontaneity and Temperature: ΔG = ΔH - TΔS

Δ G = Δ H - T Δ S

When to use. Determine temperature range for spontaneity.

Trap. Thinking ΔH negative always means spontaneous; need to consider ΔS.

Trouton's Rule

Δ S_{vap} = \frac{Δ H_{vap}}{T_{b}} \approx 85 {J mol}^{- 1} K^{- 1}

When to use. Estimate ΔH_vap from boiling point or vice versa.

Trap. Applying to liquids with strong hydrogen bonding (water, ethanol) where ΔS_vap is higher (~109 for water).

Clausius-Clapeyron Equation

\ln (\frac{P_{2}}{P_{1}}) = - \frac{Δ H_{vap}}{R} (\frac{1}{T_{2}} - \frac{1}{T_{1}})

When to use. Calculate vapor pressure at different temperatures or find ΔH_vap.

Trap. Assuming ΔH_vap is constant; valid over small T ranges.

Values to remember

$R = 8.314 {J mol}^{- 1} K^{- 1}$ Work Done in Reversible Processes
$R = 0.0821 {L atm mol}^{- 1} K^{- 1}$ Work Done in Reversible Processes
$C_{p} - C_{v} = R$ Enthalpy and Enthalpy Change
$Δ H_{f}^{\circ} (elements) = 0$ Standard Enthalpy of Formation
$γ_{monatomic} = 5 / 3$ Adiabatic Process for Ideal Gas
$γ_{diatomic} = 7 / 5$ Adiabatic Process for Ideal Gas
Bond enthalpy of C-H ~ 413 kJ/mol Bond Enthalpy and Reaction Enthalpy
O=O ~ 498 kJ/mol Bond Enthalpy and Reaction Enthalpy
$Δ H_{neut} \approx - 57 kJ/mol$ for strong acid-strong base Enthalpy of Combustion, Neutralization, and Solution
$Δ S_{vap} \approx 85 {J mol}^{- 1} K^{- 1}$ Trouton's Rule

Read the full chapter: Chemical Thermodynamics for JEE, with what JEE asks and the common traps.