Thermochemistry and Spontaneity: Energy, Enthalpy, Entropy, and Free Energy

Thermochemistry and Spontaneity

Energy, Work, and Heat

Thermochemistry studies the energy changes that occur during chemical reactions and physical processes. Energy can be transferred as heat (q) or work (w), and the system's energy change is the sum of these transfers.

• Energy: The capacity to do work or produce heat. It exists as potential energy (stored) and kinetic energy (motion).

• Work (w): Energy transfer resulting from a force acting over a distance. $w = -P \Delta V$ (for pressure-volume work at constant pressure)

• Heat (q): Energy transfer due to temperature difference between system and surroundings.

• System and Surroundings: The system is the part of the universe under study; everything else is the surroundings.

• First Law of Thermodynamics: Energy is conserved. $\Delta E = q + w$

Example: If a system loses 10 kJ of energy, the surroundings gain 10 kJ.

Endothermic and Exothermic Processes

Processes are classified by the direction of heat flow:

• Exothermic: Heat is released by the system to the surroundings ($q < 0$).

• Endothermic: Heat is absorbed by the system from the surroundings ($q > 0$).

• Example: Sublimation (solid to gas) is typically endothermic because energy is required to break intermolecular forces.

State Functions and Enthalpy

State functions depend only on the current state of the system, not the path taken to reach it.

• Examples: Internal energy ($E$), enthalpy ($H$), pressure ($P$), volume ($V$), temperature ($T$).

• Enthalpy (H): $H = E + PV$

• Change in Enthalpy: At constant pressure, $\Delta H = q_p$ (heat at constant pressure).

• Relationship: $\Delta E = q + w = q_p - P \Delta V$

Calorimetry and Heat Calculations

Calorimetry measures heat changes in physical and chemical processes.

• Specific Heat Capacity (c): Amount of heat required to raise the temperature of 1 g of a substance by 1°C (or 1 K). $q = mc\Delta T$

• Heat of Fusion (melting) and Vaporization: Energy required for phase changes at constant temperature.

• Example Calculation: For 1.00 kg of water, $c = 4.184 \ \mathrm{J/g\cdot K}$, $q = m c \Delta T$

Thermochemical Equations and Hess's Law

Thermochemical equations show the enthalpy change associated with chemical reactions.

• Hess's Law: The total enthalpy change for a reaction is the sum of enthalpy changes for individual steps.

• Manipulating Equations: Reverse reactions change the sign of $\Delta H$; multiplying coefficients multiplies $\Delta H$.

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): Enthalpy change for forming 1 mol of a compound from its elements in their standard states at 298 K.

• Bond Dissociation Enthalpy: Energy required to break a bond in a molecule (always endothermic).

Sample Table: Bond Dissociation Energies (kJ/mol)

Bond	Energy (kJ/mol)
H–H	436
C–H	413
C–C	358
C=O	463
O=O	498
N≡N	941
Additional info: Values inferred from standard tables.

Entropy (S) and the Second Law of Thermodynamics

Entropy is a measure of disorder or randomness in a system. The Second Law states that the total entropy of the universe increases in a spontaneous process.

• Change in Entropy: $\Delta S = S_{\text{final}} - S_{\text{initial}}$

• For a Reaction: $\Delta S_{\text{rxn}} = \sum S_{\text{products}} - \sum S_{\text{reactants}}$

• Entropy of the Universe: $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$

• Spontaneity: A process is spontaneous if $\Delta S_{\text{univ}} > 0$.

• Entropy Trends:

  • Increases with more particles, higher temperature, and phase changes (solid → liquid → gas).

  • More complex molecules and more degrees of freedom increase entropy.

Gibbs Free Energy (G) and Spontaneity

Gibbs free energy combines enthalpy and entropy to predict spontaneity at constant temperature and pressure.

• Definition: $G = H - TS$

• Change in Free Energy: $\Delta G = \Delta H - T \Delta S$

• Spontaneity Criteria:

  • $\Delta G < 0$: Spontaneous process

  • $\Delta G > 0$: Nonspontaneous process

  • $\Delta G = 0$: Equilibrium

• Temperature Dependence: Spontaneity can depend on temperature, especially when $\Delta H$ and $\Delta S$ have the same sign.

Standard Free Energy and Equilibrium

At equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant.

• Relationship to Equilibrium Constant: $\Delta G = \Delta G^\circ + RT \ln Q$

• At Equilibrium: $\Delta G = 0$, $Q = K$, so $\Delta G^\circ = -RT \ln K$

• Interpretation:

  • If $K > 1$, $\Delta G^\circ < 0$ (product-favored)

  • If $K < 1$, $\Delta G^\circ > 0$ (reactant-favored)

Enthalpy, Entropy, and Solution Formation

The formation of solutions involves changes in enthalpy and entropy, which together determine spontaneity.

• Solution Formation Steps:

  • Breaking solute-solute interactions (endothermic)

  • Breaking solvent-solvent interactions (endothermic)

  • Forming solute-solvent interactions (exothermic or endothermic)

• Overall Enthalpy Change: $\Delta H_{\text{solution}} = \Delta H_{\text{solute}} + \Delta H_{\text{solvent}} + \Delta H_{\text{mix}}$

• Entropy Change: Usually positive due to increased disorder, but can be negative for highly charged ions.

• Spontaneity: Even if $\Delta H_{\text{solution}} > 0$, a large positive $\Delta S$ can make $\Delta G < 0$ at higher temperatures.

• Example: Dissolving ammonium nitrate is endothermic but spontaneous due to a large increase in entropy.

Summary Table: Spontaneity Based on $\Delta H$ and $\Delta S$

$\Delta H$	$\Delta S$	Spontaneity
–	+	Always spontaneous
–	–	Spontaneous at low T
+	+	Spontaneous at high T
+	–	Never spontaneous

Key Equations

• First Law: $\Delta E = q + w$

• Work (at constant P): $w = -P \Delta V$

• Heat (calorimetry): $q = mc\Delta T$

• Enthalpy: $H = E + PV$

• Change in Enthalpy: $\Delta H = q_p$

• Entropy: $\Delta S = \sum S_{\text{products}} - \sum S_{\text{reactants}}$

• Gibbs Free Energy: $\Delta G = \Delta H - T \Delta S$

• Free Energy and Equilibrium: $\Delta G = \Delta G^\circ + RT \ln Q$

• Standard Free Energy: $\Delta G^\circ = -RT \ln K$

Additional info:

• Standard state is typically 298 K (25°C) and 1 atm pressure.

• Most stable forms of elements at 298 K are used for standard enthalpy calculations (e.g., O2(g), H2(g), graphite for C).

• Entropy units: J/(mol·K).