Thermodynamics and Chemical Equilibrium: Predicting Chemical Change

Thermodynamics and Chemical Equilibrium

Introduction to Predicting Chemical Change

The study of chemical change involves understanding the factors that determine whether a reaction will occur and to what extent. Thermodynamics provides a quantitative framework for predicting the directionality and extent of chemical reactions, focusing on energetic and entropic factors.

Energetic and Entropic Factors in Chemical Reactions

Energetic Factors: Enthalpy (ΔH)

- Enthalpy (ΔH) is the heat content of a system. The change in enthalpy during a reaction, ΔHrxn, indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). - Exothermic reactions are generally product-favored, while endothermic reactions may require additional factors to be product-favored.

Entropic Factors: Entropy (ΔS)

- Entropy (ΔS) measures the disorder or randomness in a system. The change in entropy, ΔSrxn, reflects the increase or decrease in disorder during a reaction. - Positive ΔS means increased disorder, often favoring product formation, especially at higher temperatures.

Temperature (T)

- Temperature influences the relative importance of enthalpy and entropy in determining reaction directionality. At high temperatures, entropic effects dominate; at low temperatures, energetic effects are more significant.

Classification of Chemical Processes

Chemical processes can be classified based on the signs of ΔHrxn and ΔSrxn:

• ΔSrxn > 0, ΔHrxn < 0: Always product-favored

• ΔSrxn < 0, ΔHrxn > 0: Always reactant-favored

• ΔSrxn > 0, ΔHrxn > 0 or ΔSrxn < 0, ΔHrxn < 0: Directionality depends on temperature

Second Law of Thermodynamics and Gibbs Free Energy

Second Law of Thermodynamics

The second law states that for thermodynamically favored processes in an isolated system, the total entropy change must be positive: $\Delta S_{\text{TOTAL}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} > 0$

Gibbs Free Energy (ΔG)

Gibbs free energy combines enthalpy and entropy to predict reaction spontaneity: $\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T \Delta S_{\text{rxn}}$ - ΔG < 0: Reaction is product-favored (spontaneous) - ΔG > 0: Reaction is reactant-favored (non-spontaneous)

Example: Formation of Water

Reaction: 2 H2(g) + O2(g) → 2 H2O(g) - ΔHrxn is negative (exothermic) - ΔSrxn is negative (decrease in disorder) - ΔGrxn is negative at low temperatures, favoring product formation

Quantitative Analysis of Reaction Directionality

Calculating ΔG, ΔH, and ΔS

Standard thermodynamic data are used to calculate these values:

• ΔHrxn = Σ ΔHf,products - Σ ΔHf,reactants

• ΔSrxn = Σ Sproducts - Σ Sreactants

• ΔGrxn = Σ ΔGf,products - Σ ΔGf,reactants

Example Table: Standard Thermodynamic Data

Substance	So (J/(mol K))	ΔHof (kJ/mol)	ΔGof (kJ/mol)
CO2(g)	213.7	-393.5	-394.6
H2(g)	130.7	0	0
CH4(g)	186.3	-74.8	-50.8

Chemical Equilibrium and the Equilibrium Constant

Definition of Chemical Equilibrium

At equilibrium, the concentrations of reactants and products remain constant over time.

Equilibrium Constant (K)

The equilibrium constant quantifies the extent of a reaction: $K_c = \frac{[C]_{eq}^c [D]_{eq}^d}{[A]_{eq}^a [B]_{eq}^b}$ - K > 1: Product-favored equilibrium - K < 1: Reactant-favored equilibrium

Relationship Between ΔG and K

The equilibrium constant is related to Gibbs free energy: $\Delta G^\circ_{\text{rxn}} = -RT \ln K$ $K = e^{-\Delta G^\circ_{\text{rxn}} / RT}$

Temperature Dependence of K

The value of K changes with temperature, reflecting the balance between enthalpy and entropy: $K = e^{-(\Delta H^\circ_{\text{rxn}} / RT) + (\Delta S^\circ_{\text{rxn}} / R)}$

Summary Table: Directionality and Temperature

ΔHrxn	ΔSrxn	ΔGrxn	Directionality
< 0	> 0	< 0	Always product-favored
> 0	< 0	> 0	Always reactant-favored
< 0	< 0	T-dependent	Product-favored at low T
> 0	> 0	T-dependent	Product-favored at high T

Practice Problem Example

Calculate ΔGrxn for N2O4(g) → 2 NO2(g) at 0°C (273 K)

• ΔHrxn = 52.7 kJ

• ΔSrxn = 176.9 J/K = 0.1769 kJ/K

• ΔGrxn = 52.7 kJ - (273 K × 0.1769 kJ/K) = 52.7 kJ - 48.3 kJ = 4.4 kJ

• Since ΔG > 0, the reaction is reactant-favored at 0°C.

Conclusion

Understanding the interplay between enthalpy, entropy, and temperature allows chemists to predict the directionality and extent of chemical reactions. The equilibrium constant provides a quantitative measure of reaction extent, and its relationship with Gibbs free energy is fundamental to chemical thermodynamics. Key Equations:

• $\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T \Delta S_{\text{rxn}}$

• $\Delta G^\circ_{\text{rxn}} = -RT \ln K$

• $K = e^{-\Delta G^\circ_{\text{rxn}} / RT}$