Chemical reactions are the heart of many processes in nature and industry. Understanding their thermodynamics helps us predict if they'll happen on their own or need a push. We'll look at key concepts like Gibbs free energy, enthalpy, and entropy.

We'll also explore how reactions progress, from start to finish. This includes energy profiles, reaction coordinates, and what happens when reactions reach equilibrium. These ideas are crucial for grasping chemical reaction equilibria.

Thermodynamic Quantities

Gibbs Free Energy and Spontaneity

• Gibbs free energy ($G$) measures the maximum reversible work that can be performed by a system at constant temperature and pressure
• Changes in Gibbs free energy ($\Delta G$) determine the spontaneity of a process
  • If $\Delta G < 0$, the process is spontaneous and will occur naturally
  • If $\Delta G > 0$, the process is non-spontaneous and requires an input of energy to proceed
  • If $\Delta G = 0$, the system is at equilibrium, and no net change occurs
• Gibbs free energy is related to enthalpy ($H$) and entropy ($S$) by the equation: $G = H - TS$, where $T$ is the absolute temperature

Enthalpy and Heat of Reaction

• Enthalpy ($H$) is a state function that represents the total heat content of a system
• Changes in enthalpy ($\Delta H$) during a chemical reaction are known as the heat of reaction
  • For an exothermic reaction, $\Delta H < 0$, indicating heat is released by the system to the surroundings
  • For an endothermic reaction, $\Delta H > 0$, indicating heat is absorbed by the system from the surroundings
• The heat of reaction can be measured using calorimetry experiments (constant-pressure calorimetry)
• Hess's law states that the total enthalpy change for a reaction is independent of the pathway and depends only on the initial and final states

Entropy and Spontaneity

• Entropy ($S$) is a measure of the disorder or randomness of a system
• According to the second law of thermodynamics, the entropy of the universe always increases for a spontaneous process
• Changes in entropy ($\Delta S$) contribute to the spontaneity of a process
  • If $\Delta S > 0$, the process is spontaneous and will occur naturally
  • If $\Delta S < 0$, the process is non-spontaneous and requires an input of energy to proceed
• Entropy increases with increasing temperature, volume, and the number of particles in a system (ideal gas equation)

Reaction Dynamics

Reaction Coordinate and Energy Profile

• A reaction coordinate is a geometric parameter that describes the progress of a chemical reaction from reactants to products
• An energy profile is a plot of the potential energy of the system as a function of the reaction coordinate
  • The energy profile shows the activation energy barrier that must be overcome for the reaction to proceed
  • The difference in potential energy between the reactants and products represents the heat of reaction ($\Delta H$)
• Catalysts lower the activation energy barrier without being consumed in the reaction, increasing the reaction rate (enzymes in biological systems)

Spontaneity and Thermodynamic Equilibrium

• The spontaneity of a reaction is determined by the sign of $\Delta G$, which depends on both $\Delta H$ and $\Delta S$
• A reaction will proceed spontaneously in the direction that decreases Gibbs free energy until equilibrium is reached
• At thermodynamic equilibrium, $\Delta G = 0$, and the forward and reverse reaction rates are equal
  • The equilibrium constant ($K$) is related to the standard Gibbs free energy change ($\Delta G^{\circ}$) by the equation: $\Delta G^{\circ} = -RT \ln K$, where $R$ is the gas constant and $T$ is the absolute temperature
• The equilibrium position can be shifted by changing the temperature, pressure, or concentrations of reactants or products (Le Chatelier's principle)

Reference States

Standard State and Standard Thermodynamic Quantities

• The standard state of a substance is defined as the pure substance at a pressure of 1 atm (or 1 bar) and a specified temperature (usually 25°C or 298 K)
• Standard thermodynamic quantities, such as standard enthalpy of formation ($\Delta H_f^{\circ}$), standard entropy ($S^{\circ}$), and standard Gibbs free energy of formation ($\Delta G_f^{\circ}$), are defined for substances in their standard states
  • These values are used to calculate the standard enthalpy change ($\Delta H^{\circ}$), standard entropy change ($\Delta S^{\circ}$), and standard Gibbs free energy change ($\Delta G^{\circ}$) for a reaction
• Standard thermodynamic quantities can be found in reference tables (thermodynamic tables) and are essential for predicting the spontaneity and equilibrium of chemical reactions under standard conditions
• The standard heat of formation ($\Delta H_f^{\circ}$) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (Hess's law)