7.1 Gibbs and Helmholtz free energies

Free energy concepts are crucial for understanding chemical equilibrium and spontaneity. Gibbs and Helmholtz free energies help predict how systems behave under different conditions. Gibbs free energy applies to constant temperature and pressure, while Helmholtz free energy is for constant temperature and volume.

These thermodynamic potentials measure the maximum work a system can do. By calculating changes in free energy, we can determine if reactions will happen spontaneously. This connects to broader ideas about energy, equilibrium, and the driving forces behind chemical processes.

Gibbs Free Energy vs Helmholtz Free Energy

Definitions and Key Differences

Top images from around the web for Definitions and Key Differences

• 

  Potential, Kinetic, Free, and Activation Energy · Biology View original

  Is this image relevant?

• 

  Pressure and Free Energy | Introduction to Chemistry View original

  Is this image relevant?

• 

  Free Energy | Chemistry View original

  Is this image relevant?

• 

  Potential, Kinetic, Free, and Activation Energy · Biology View original

  Is this image relevant?

• 

  Pressure and Free Energy | Introduction to Chemistry View original

  Is this image relevant?

1 of 3

Top images from around the web for Definitions and Key Differences

• 

  Potential, Kinetic, Free, and Activation Energy · Biology View original

  Is this image relevant?

• 

  Pressure and Free Energy | Introduction to Chemistry View original

  Is this image relevant?

• 

  Free Energy | Chemistry View original

  Is this image relevant?

• 

  Potential, Kinetic, Free, and Activation Energy · Biology View original

  Is this image relevant?

• 

  Pressure and Free Energy | Introduction to Chemistry View original

  Is this image relevant?

1 of 3

• Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and pressure
• Helmholtz free energy (A) is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and volume
• The key difference between Gibbs and Helmholtz free energy lies in the constraints under which the system operates
  • Gibbs free energy is used for processes occurring at constant temperature and pressure
  • Helmholtz free energy is used for processes occurring at constant temperature and volume

State Functions and Spontaneity

• Both Gibbs and Helmholtz free energies are state functions, meaning that their values depend only on the initial and final states of the system, not on the path taken between those states
• Changes in Gibbs and Helmholtz free energies can be used to determine the spontaneity of a process under the respective constant conditions
  • A negative change in Gibbs free energy (ΔG < 0) indicates a spontaneous process at constant temperature and pressure
  • A negative change in Helmholtz free energy (ΔA < 0) indicates a spontaneous process at constant temperature and volume

Gibbs Free Energy Equation

Derivation from Thermodynamic Laws

• The Gibbs free energy (G) is defined as G = H - TS, where H is the enthalpy, T is the absolute temperature, and S is the entropy of the system
• This relationship can be derived from the first and second laws of thermodynamics, considering a system at constant temperature and pressure
• The change in Gibbs free energy (ΔG) for a process is given by ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the absolute temperature, and ΔS is the change in entropy

Components of the Equation

• The enthalpy term (ΔH) represents the heat exchanged during the process
  • A negative ΔH indicates an exothermic process, which releases heat to the surroundings
  • A positive ΔH indicates an endothermic process, which absorbs heat from the surroundings
• The entropy term (TΔS) represents the energy unavailable for work due to the dispersal of energy within the system
  • A positive ΔS indicates an increase in disorder or randomness of the system
  • A negative ΔS indicates a decrease in disorder or randomness of the system
• The temperature (T) in the Gibbs free energy equation is always expressed in Kelvin (K)

Spontaneity of Chemical Processes

Determining Spontaneity using Gibbs Free Energy

• A process is considered spontaneous if it occurs without external intervention and results in a decrease in the Gibbs free energy of the system (ΔG < 0)
• To determine the spontaneity of a process, calculate the change in Gibbs free energy (ΔG) using the equation ΔG = ΔH - TΔS
  • If ΔG is negative (ΔG < 0), the process is spontaneous and will occur naturally under the given conditions
  • If ΔG is positive (ΔG > 0), the process is non-spontaneous and will not occur naturally under the given conditions. An input of energy is required to drive the process forward
  • If ΔG is equal to zero (ΔG = 0), the system is at equilibrium, and there is no net change in the concentrations of reactants and products

Factors Affecting Spontaneity

• The spontaneity of a process can be affected by changes in temperature, pressure, and concentration, as these factors influence the values of ΔH and ΔS
  • Increasing temperature favors processes with a positive entropy change (ΔS > 0) and disfavors processes with a negative entropy change (ΔS < 0)
  • Increasing pressure favors processes that result in a decrease in volume (ΔV < 0) and disfavors processes that result in an increase in volume (ΔV > 0)
  • Changes in concentration can shift the equilibrium position of a reaction, affecting the spontaneity of the process (Le Chatelier's principle)

Significance of Gibbs Free Energy Change

Relationship between ΔG and Spontaneity

• The sign of the Gibbs free energy change (ΔG) indicates the spontaneity of a process at constant temperature and pressure
  • A negative ΔG (ΔG < 0) signifies that the process is spontaneous and will occur naturally without external intervention. The system releases energy to its surroundings during a spontaneous process
  • A positive ΔG (ΔG > 0) indicates that the process is non-spontaneous and will not occur naturally under the given conditions. An input of energy is required to drive the process forward. The system absorbs energy from its surroundings during a non-spontaneous process
  • When ΔG is equal to zero (ΔG = 0), the system is at equilibrium, and there is no net change in the concentrations of reactants and products. The forward and reverse reactions occur at equal rates, and the system has no tendency to change spontaneously

Magnitude of ΔG and Driving Force

• The magnitude of ΔG provides information about the driving force of the process
  • A larger negative ΔG indicates a greater driving force for a spontaneous process, meaning the process will occur more readily and rapidly
  • A larger positive ΔG indicates a greater energy requirement for a non-spontaneous process, meaning the process will be more difficult to initiate and sustain
  • The magnitude of ΔG can be used to compare the relative spontaneity of different processes under the same conditions

Temperature and Pressure Effects on Gibbs Free Energy

Temperature Effects

• The effect of temperature on the Gibbs free energy is determined by the entropy change (ΔS) of the system
  • An increase in temperature will make the -TΔS term more negative, favoring processes with a positive entropy change (ΔS > 0)
    • Example: Melting of ice (ΔS > 0) is favored at higher temperatures
  • Conversely, a decrease in temperature will make the -TΔS term less negative, favoring processes with a negative entropy change (ΔS < 0)
    • Example: Freezing of water (ΔS < 0) is favored at lower temperatures
• The relationship between temperature and Gibbs free energy is given by the equation (∂G/∂T)P = -S, which shows that the change in Gibbs free energy with respect to temperature at constant pressure is equal to the negative of the entropy of the system

Pressure Effects

• The effect of pressure on the Gibbs free energy is determined by the volume change (ΔV) of the system
  • An increase in pressure will favor processes that result in a decrease in volume (ΔV < 0), as this reduces the overall Gibbs free energy
    • Example: Formation of a solid from a gas (ΔV < 0) is favored at higher pressures
  • A decrease in pressure will favor processes that result in an increase in volume (ΔV > 0)
    • Example: Vaporization of a liquid (ΔV > 0) is favored at lower pressures
• The relationship between pressure and Gibbs free energy is given by the equation (∂G/∂P)T = V, where V is the volume of the system. This equation shows that the change in Gibbs free energy with respect to pressure at constant temperature is equal to the volume of the system
• In general, the effect of pressure on the Gibbs free energy is less significant compared to the effect of temperature, as most chemical reactions involve relatively small volume changes