7.2 Free energy and spontaneity

Free energy and spontaneity are key concepts in understanding chemical reactions. They help us predict whether a reaction will happen on its own or needs a push. This topic connects enthalpy and entropy, showing how they work together to determine a reaction's direction.

Gibbs free energy is the main player here. It combines heat changes and disorder changes to give us a single number. This number tells us if a reaction will go forward, backward, or stay put. It's a powerful tool for figuring out what chemicals will do.

Gibbs Free Energy and Spontaneity

Defining Gibbs Free Energy

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• Gibbs free energy (G) combines enthalpy (H) and entropy (S) to determine the spontaneity of a process at constant temperature and pressure
• Change in Gibbs free energy (ΔG) equals the change in enthalpy (ΔH) minus the product of temperature (T) and the change in entropy (ΔS): [ΔG = ΔH - TΔS](https://www.fiveableKeyTerm:δg_=_δh_-_tδs)
• Negative ΔG indicates a spontaneous process, positive ΔG indicates a non-spontaneous process, and zero ΔG indicates equilibrium with no net change in concentrations of reactants and products

Relationship between Gibbs Free Energy and Spontaneity

• Spontaneity of a chemical reaction determined by the sign and magnitude of ΔG
• Spontaneous reactions (ΔG < 0) proceed in the forward direction without external input of energy (exothermic reactions, increase in entropy)
• Non-spontaneous reactions (ΔG > 0) require an external input of energy to proceed in the forward direction (endothermic reactions, decrease in entropy)
• Equilibrium reached when ΔG equals zero, forward and reverse reactions occur at equal rates resulting in no net change in concentrations

Interpreting Gibbs Free Energy Change

Sign of ΔG and Spontaneity

• Sign of ΔG determines spontaneity of a process at constant temperature and pressure
  • Negative ΔG (ΔG < 0) indicates a spontaneous process proceeding in the forward direction (formation of products favored)
  • Positive ΔG (ΔG > 0) indicates a non-spontaneous process not proceeding in the forward direction without external energy input (formation of reactants favored)
  • Zero ΔG (ΔG = 0) indicates equilibrium with no net change in concentrations of reactants and products
• Examples of spontaneous processes: ice melting at room temperature, gas expanding to fill a container, salt dissolving in water

Factors Influencing Spontaneity

• Enthalpy change (ΔH) and entropy change (ΔS) contribute to spontaneity
  • Exothermic reactions (negative ΔH) and reactions with an increase in entropy (positive ΔS) tend to be spontaneous
  • Endothermic reactions (positive ΔH) and reactions with a decrease in entropy (negative ΔS) tend to be non-spontaneous
• Temperature (T) affects spontaneity by influencing the magnitude of the entropy term (TΔS)
  • Higher temperatures increase the impact of entropy on spontaneity, favoring processes with a positive ΔS
  • Lower temperatures decrease the impact of entropy on spontaneity, favoring processes with a negative ΔH

Calculating Gibbs Free Energy Change

Using the Gibbs Free Energy Equation

• Change in Gibbs free energy (ΔG) calculated using the equation: $ΔG = ΔH - TΔS$
  • ΔH is the change in enthalpy, T is the absolute temperature, and ΔS is the change in entropy
  • Units for ΔG, ΔH, and TΔS are typically kJ/mol or J/mol, and temperature must be in Kelvin (K)
  • Ensure units of ΔH, T, and ΔS are consistent and temperature is in Kelvin when calculating ΔG
• Example calculation: For a reaction with ΔH = -50 kJ/mol and ΔS = 100 J/mol·K at 298 K, $ΔG = -50 kJ/mol - (298 K)(100 J/mol·K) = -79.8 kJ/mol$, indicating a spontaneous process

Obtaining Thermodynamic Data

• ΔH and ΔS values obtained from standard tables or calculated using thermodynamic principles
  • Standard enthalpy of formation (ΔH°f) used to calculate ΔH using Hess's law: $ΔH = ΣΔH°f (products) - ΣΔH°f (reactants)$
  • Standard entropy values (S°) used to calculate ΔS using the Second Law of Thermodynamics: $ΔS = ΣS° (products) - ΣS° (reactants)$
• Tabulated values for ΔH°f and S° available in thermodynamic data tables for common compounds and elements
• Hess's law and the Second Law of Thermodynamics allow for the calculation of ΔH and ΔS for reactions not found in tables

Thermodynamic Equilibrium and Gibbs Free Energy

Concept of Thermodynamic Equilibrium

• Thermodynamic equilibrium is a state with no net change in macroscopic properties over time (temperature, pressure, composition)
  • Forward and reverse reactions proceed at equal rates, resulting in no net change in concentrations of reactants and products
  • System has reached a balance between opposing processes, such as evaporation and condensation or dissolution and precipitation
• Examples of systems at thermodynamic equilibrium: saturated solution, sealed container with liquid and vapor phases, reversible chemical reaction at steady state

Relationship between Equilibrium and Gibbs Free Energy

• Condition for thermodynamic equilibrium: change in Gibbs free energy equals zero (ΔG = 0)
  • Negative ΔG: system spontaneously moves towards equilibrium by favoring formation of products
  • Positive ΔG: system spontaneously moves towards equilibrium by favoring formation of reactants
  • Zero ΔG: system has reached equilibrium, no net change in concentrations of reactants and products
• Equilibrium constant (K) related to standard Gibbs free energy change (ΔG°) by the equation: $ΔG° = -RTlnK$, where R is the gas constant and T is the absolute temperature
  • Relationship allows for calculation of equilibrium constants from thermodynamic data and vice versa
  • Larger K values indicate a greater extent of product formation at equilibrium, corresponding to a more negative ΔG°
  • Smaller K values indicate a lesser extent of product formation at equilibrium, corresponding to a less negative or positive ΔG°