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 (E): The capacity to do work or transfer heat.

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

• Heat (q): Energy transfer due to temperature difference.

• 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. Formula: $\Delta E = q + w$

Exothermic Process: Heat is released by the system to the surroundings (q < 0). Endothermic Process: Heat is absorbed by the system from the surroundings (q > 0).

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

Enthalpy (H) and Calorimetry

Enthalpy is a state function that measures heat flow at constant pressure. Calorimetry is used to measure heat changes in chemical reactions.

• Enthalpy Change (ΔH): $\Delta H = \Delta E + P\Delta V$

• State Functions: Properties that depend only on the current state, not the path (e.g., E, H, P, V, T).

• Calorimetry: Measurement of heat flow using a calorimeter.

• Heat Capacity (C): Amount of heat required to raise temperature by 1 K. Formula: $q = C \Delta T$

• Specific Heat (c): Heat required to raise 1 g of a substance by 1 K. Formula: $q = m c \Delta T$

• Phase Changes: Heat is absorbed or released during phase changes (e.g., melting, vaporization, sublimation). Example: Sublimation (solid to gas) is typically endothermic.

Thermochemical Equations and Hess's Law

Thermochemical equations show the enthalpy change associated with chemical reactions. Hess's Law allows calculation of enthalpy changes for complex reactions by combining simpler reactions.

• Thermochemical Equation: A balanced equation with enthalpy change (ΔH) indicated.

• Hess's Law: The total enthalpy change for a reaction is the sum of enthalpy changes for individual steps. Application: Reverse reactions change the sign of ΔH; multiplying a reaction multiplies ΔH by the same factor.

• Standard Enthalpy of Formation (ΔHof): 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; always endothermic.

Entropy (S) and Disorder

Entropy is a measure of the disorder or randomness of a system. Spontaneous processes tend to increase the total entropy of the universe.

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

• Second Law of Thermodynamics: For any spontaneous process, the entropy of the universe increases: $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} > 0$

• Entropy and Phase Changes: Melting and vaporization increase entropy; freezing and condensation decrease entropy.

• Factors Affecting Entropy:

  • Number of particles (more particles = higher entropy)

  • Complexity of molecules (more complex = higher entropy)

  • Physical state (gas > liquid > solid)

• Example: The entropy of steam (gas) is higher than that of liquid water due to more degrees of freedom.

Gibbs Free Energy (G) and Spontaneity

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

• Gibbs Free Energy Change (ΔG): $\Delta G = \Delta H - T\Delta S$

• Spontaneity Criteria:

  • If $\Delta G < 0$, the process is spontaneous.

  • If $\Delta G > 0$, the process is nonspontaneous.

  • If $\Delta G = 0$, the system is at equilibrium.

• Temperature Dependence: Spontaneity can depend on temperature, especially when ΔH and ΔS have the same sign.

• Relationship to Equilibrium Constant (K): $\Delta G = -RT \ln K$

• Example: If $K \gg 1$, the reaction is product-favored and $\Delta G^\circ < 0$.

Application: Calorimetry and Solution Formation

Calorimetry can be used to measure heat changes in solution formation, which may be endothermic or exothermic depending on the interactions involved.

• Heat of Solution (ΔHsoln): The enthalpy change when a solute dissolves in a solvent.

• Endothermic Solution: Solution feels cooler (e.g., ammonium nitrate in water).

• Exothermic Solution: Solution feels warmer (e.g., magnesium sulfate in water).

• Entropy and Solution Formation: Mixing increases disorder, so ΔS is usually positive.

• Spontaneity of Solution Formation: Even if ΔH is positive (endothermic), a large positive ΔS can make ΔG negative, making the process spontaneous.

Sample Table: Standard Molar Entropies (So)

The following table compares standard molar entropies for selected substances (values in J/mol·K):

Substance	So (J/mol·K)
H2O (l)	69.91
H2O (g)	188.7
CO2 (g)	213.8
O2 (g)	205.0
Graphite (C, s)	5.7
CH4 (g)	186.2
Additional info: Values inferred from standard tables for illustration.

Summary of Key Equations

• $\Delta E = q + w$

• $w = -P\Delta V$

• $q = m c \Delta T$

• $\Delta H = \Delta E + P\Delta V$

• $\Delta S = S_{\text{final}} - S_{\text{initial}}$

• $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$

• $\Delta G = \Delta H - T\Delta S$

• $\Delta G = -RT \ln K$

Additional info:

• Standard state is 1 atm pressure, 298 K temperature, and 1 M concentration for solutions.

• Most stable form of an element at 298 K is used as reference for enthalpy of formation.

• Spontaneity does not imply speed; a process can be spontaneous but slow.