Chemical Equilibrium and Thermodynamics: Study Notes and Key Equations

Chemical Equilibrium and Thermodynamics

Introduction

This study guide covers the fundamental concepts of chemical equilibrium and thermodynamics, including spontaneity, entropy, Gibbs free energy, equilibrium constants, and the application of thermodynamic data to chemical reactions. These topics are essential for understanding how and why chemical reactions occur, and how to predict the direction and extent of reactions under various conditions.

Spontaneity and Thermodynamic Processes

Spontaneous vs. Nonspontaneous Processes

• Spontaneous Process: A process that occurs naturally under given conditions without external intervention. Examples include a rock falling to the ground or iron rusting in moist air.

• Nonspontaneous Process: A process that does not occur naturally and requires continuous input of energy from the surroundings.

• Key Factors: Spontaneity is determined by changes in enthalpy (ΔH), entropy (ΔS), and temperature (T).

Example: A raindrop falling to the ground is spontaneous; water flowing uphill is nonspontaneous.

Entropy and the Second Law of Thermodynamics

Entropy (S)

• Definition: Entropy is a measure of the disorder or randomness of a system.

• Second Law of Thermodynamics: In any spontaneous process, the total entropy of the universe increases.

Equation:

$\Delta S = \frac{q_{rev}}{T}$

where $q_{rev}$ is the heat exchanged reversibly and $T$ is the temperature in Kelvin.

Gibbs Free Energy and Spontaneity

Gibbs Free Energy (G)

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

• Key Equation:

$\Delta G = \Delta H - T\Delta S$

• 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.

Standard Free Energy Changes

Standard State and Standard Free Energy of Formation

• Standard State: The pure substance at 1 bar pressure and a specified temperature (usually 298 K).

• Standard Free Energy of Formation ($\Delta G_f^\circ$): The change in free energy when 1 mole of a compound forms from its elements in their standard states.

Equation for a Reaction:

$\Delta G^\circ_{rxn} = \sum n \Delta G_f^\circ (\text{products}) - \sum n \Delta G_f^\circ (\text{reactants})$

Chemical Equilibrium

Equilibrium Constant (K)

• Definition: The equilibrium constant expresses the ratio of product and reactant concentrations at equilibrium, each raised to the power of their coefficients.

• Expression for a General Reaction:

$aA + bB \rightleftharpoons cC + dD$

$K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• Relationship to Free Energy:

$\Delta G^\circ = -RT \ln K$

where $R$ is the gas constant (8.314 J/mol·K) and $T$ is temperature in Kelvin.

Reaction Quotient (Q)

• Definition: The reaction quotient has the same form as the equilibrium constant but uses initial (or non-equilibrium) concentrations.

• Direction of Reaction:

  • If $Q < K$, the reaction proceeds forward (toward products).

  • If $Q > K$, the reaction proceeds in reverse (toward reactants).

  • If $Q = K$, the system is at equilibrium.

Calculating ΔG, ΔH, and ΔS for Reactions

Using Standard Thermodynamic Data

• Standard enthalpy ($\Delta H^\circ$), entropy ($\Delta S^\circ$), and free energy ($\Delta G^\circ$) values are used to calculate changes for reactions.

• General Formula:

$\Delta X^\circ_{rxn} = \sum n \Delta X^\circ (\text{products}) - \sum n \Delta X^\circ (\text{reactants})$

where $X$ can be $H$, $S$, or $G$.

Effect of Temperature and Volume on Equilibrium

• Le Châtelier’s Principle: If a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Temperature: Increasing temperature favors the endothermic direction; decreasing temperature favors the exothermic direction.

• Volume: Decreasing volume favors the side with fewer moles of gas; increasing volume favors the side with more moles of gas.

Key Equations

• $\Delta S = \frac{q_{rev}}{T}$

• $\Delta G = \Delta H - T\Delta S$

• $\Delta G^\circ_{rxn} = \sum n \Delta G_f^\circ (\text{products}) - \sum n \Delta G_f^\circ (\text{reactants})$

• $\Delta H^\circ_{rxn} = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$

• $\Delta S^\circ_{rxn} = \sum n S^\circ (\text{products}) - \sum n S^\circ (\text{reactants})$

• $\Delta G = \Delta G^\circ + RT \ln Q$

• $\Delta G^\circ = -RT \ln K$

• $K_p = K_c(RT)^{\Delta n}$

• $\ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H^\circ}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$

Thermodynamic Properties Tables

Main Purpose:

These tables provide standard enthalpy, entropy, and free energy values for various substances, which are essential for calculating reaction thermodynamics.

Substance	ΔHof (kJ/mol)	ΔGof (kJ/mol)	So (J/mol·K)
Ca(s)	0.0	0.0	41.6
Ca2+(aq)	-542.8	-553.6	-53.1
CO2(g)	-393.5	-394.4	213.6
CO(g)	-110.5	-137.2	197.7
O2(g)	0.0	0.0	205.0
H2O(l)	-285.8	-237.1	69.9
H2O(g)	-241.8	-228.6	188.8
H2(g)	0.0	0.0	130.6

Additional info: The above table is a partial reconstruction based on the provided thermodynamic data. For full calculations, refer to the complete table in your course materials.

Sample Problem Types

• Classifying processes as spontaneous or nonspontaneous

• Arranging ions by increasing entropy

• Calculating ΔG, ΔH, and ΔS for reactions using standard values

• Calculating equilibrium constants and reaction quotients

• Predicting the direction of reaction shifts based on Q and K

• Applying Le Châtelier’s Principle to temperature and volume changes

Summary

• Spontaneity is determined by Gibbs free energy ($\Delta G$).

• Entropy ($S$) and enthalpy ($H$) changes are key to predicting reaction behavior.

• Equilibrium constants ($K$) relate to free energy and reaction direction.

• Thermodynamic tables provide essential data for calculations.