Chemical Thermodynamics: Enthalpy, Entropy & Gibbs

Chemical thermodynamics determines whether a reaction is spontaneous, how much heat it releases or absorbs, and the direction of natural change. JEE focuses on enthalpy, entropy, Gibbs free energy, and Hess's law calculations.

System and Surroundings: The system is the part under study; surroundings are everything else. Open system: exchanges both matter and energy. Closed system: exchanges energy only. Isolated system: no exchange. State functions depend only on current state (P, V, T, U, H, S, G). Path functions depend on the process (q, w).

First Law of Thermodynamics: $\delta_{U}$ = q + w (IUPAC convention: w done ON the system is positive).
For expansion against constant external pressure: w = -$P_{ext}$ * $\delta_{V}$.
For reversible isothermal expansion of ideal gas: w = -nRT ln(V₂/V₁).
At constant volume: $\delta_{U}$ = qv.
At constant pressure: $\delta_{H}$ = qp.

Enthalpy (H): H = U + PV.
$\delta_{H}$ = $\delta_{U}$ + $\delta$(ngas)RT (for reactions involving gases). $\delta_{H}$ < 0: exothermic. $\delta_{H}$ > 0: endothermic.

Standard Enthalpy Changes:

• Formation ($\delta_{Hf_standard}$): enthalpy change when 1 mole of compound is formed from elements in standard states. By convention, $\delta_{Hf}$(elements) = 0.
• Combustion ($\delta_{Hc}$): enthalpy change when 1 mole burns completely in O₂.

Common combustion enthalpy examples:

Methane (CH₄) — $\delta_{Hc}$ = -890 kJ/mol

Ethanol (C₂H₅OH) — $\delta_{Hc}$ = -1367 kJ/mol

Cyclohexane — $\delta_{Hc}$ = -3920 kJ/mol (used in Hess's law to find strain energy)

• Bond dissociation: energy to break 1 mole of bonds in gaseous state.
• Atomisation: enthalpy to convert 1 mole of substance to gaseous atoms.
• Lattice energy: energy to separate 1 mole of ionic solid into gaseous ions.
• Hydration: enthalpy when gaseous ions dissolve in water.
• Solution: $\delta_{H_solution}$ = $\delta_{H_lattice}$ + $\delta_{H_hydration}$.

Hess's Law: The total enthalpy change is independent of the path — it depends only on initial and final states.
$\delta_{H_rxn}$ = sum($\delta_{Hf_products}$) - sum($\delta_{Hf_reactants}$).
Also: $\delta_{H_rxn}$ = sum(bond energies of reactants) - sum(bond energies of products). Note the sign reversal for bond energies vs formation enthalpies.

Kirchhoff's Equation: $\delta_{H}$(T₂) = $\delta_{H}$(T₁) + $\delta_{Cp}$ * (T₂ - T₁), where $\delta_{Cp}$ = sum(Cp_products) - sum(Cp_reactants).

Entropy (S): A measure of disorder/randomness.
$\delta_{S}$ = $q_{rev}$/T. Second Law: for a spontaneous process, $\delta_{S_universe}$ > 0 ($\delta_{S_system}$ + $\delta_{S_surroundings}$ > 0). Third Law: entropy of a perfect crystalline substance at 0 K is zero.

Entropy increases: solid → liquid → gas, dissolution, increase in moles of gas, mixing, heating. Standard molar entropy $S_{standard}$ > 0 for all substances at T > 0 K.

Gibbs Free Energy: G = H - TS.
$\delta_{G}$ = $\delta_{H}$ - T*$\delta_{S}$.
For spontaneity: $\delta_{G}$ < 0 (spontaneous), $\delta_{G}$ = 0 (equilibrium), $\delta_{G}$ > 0 (non-spontaneous).

Four cases based on signs of $\delta_{H}$ and $\delta_{S}$:

1. $\delta_{H}$ < 0, $\delta_{S}$ > 0: Always spontaneous ($\delta_{G}$ < 0 at all T)
2. $\delta_{H}$ > 0, $\delta_{S}$ < 0: Never spontaneous ($\delta_{G}$ > 0 at all T)
3. $\delta_{H}$ < 0, $\delta_{S}$ < 0: Spontaneous at low T (below T = $\frac{\delta_{H}}{\delta_{S}}$)
4. $\delta_{H}$ > 0, $\delta_{S}$ > 0: Spontaneous at high T (above T = $\frac{\delta_{H}}{\delta_{S}}$)

Relationship to Equilibrium: $\delta_{G_standard}$ = -RTln(K). If K > 1, $\delta_{G_standard}$ < 0.