7.1 Gibbs and Helmholtz free energies
6 min read•july 30, 2024
Free energy concepts are crucial for understanding chemical equilibrium and spontaneity. Gibbs and Helmholtz free energies help predict how systems behave under different conditions. applies to and pressure, while 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
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- 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 , 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 (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
- An increase in temperature will make the -TΔS term more negative, favoring processes with a positive entropy change (ΔS > 0)
- 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 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
- An increase in pressure will favor processes that result in a decrease in volume (ΔV < 0), as this reduces the overall Gibbs free energy
- 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
Key Terms to Review (16)
A = u - ts: The equation $$a = u - ts$$ represents the Helmholtz free energy, where 'a' is the Helmholtz free energy, 'u' is the internal energy, 't' is the temperature, and 's' is the entropy of the system. This relationship connects thermodynamic properties, illustrating how energy available for work decreases when a system's entropy increases at a given temperature. Understanding this equation helps in analyzing the spontaneity of processes and phase transitions.
Chemical potential: Chemical potential is the change in free energy of a system when an additional amount of substance is introduced, reflecting the energy required to add or remove particles from a system at constant temperature and pressure. It connects to the concepts of spontaneity, equilibrium, partial molar quantities, and the various forms of free energy, playing a crucial role in predicting the direction of chemical reactions and phase changes.
Constant pressure: Constant pressure refers to a thermodynamic condition where the pressure of a system remains unchanged during a process. This concept is crucial when examining how energy changes occur in systems, especially when discussing heat transfer, work done by or on the system, and changes in enthalpy, which connects energy to pressure and volume. Understanding constant pressure helps clarify how processes unfold in real-world applications like chemical reactions and phase changes.
Constant temperature: Constant temperature refers to a condition in which the temperature of a system remains unchanged over time, even as other variables, like pressure or volume, may change. This concept is crucial for understanding processes in thermodynamics, particularly when exploring Gibbs and Helmholtz free energies, as these energies are evaluated at a constant temperature to determine the spontaneity and equilibrium of chemical reactions.
Constant volume: Constant volume refers to a thermodynamic process in which the volume of a system remains unchanged throughout the process. This concept is crucial when discussing energy changes in thermodynamic systems, particularly in the context of Gibbs and Helmholtz free energies, as it directly influences the relationships between enthalpy, temperature, and entropy.
Equilibrium condition: The equilibrium condition refers to a state in which the forward and reverse reactions occur at the same rate, resulting in no net change in the concentrations of reactants and products over time. This concept is crucial for understanding chemical reactions and thermodynamics, particularly in the context of free energies, where the system is balanced and stable.
Free energy change: Free energy change refers to the difference in free energy between the products and reactants of a chemical reaction, indicating the spontaneity and thermodynamic favorability of that reaction. It is a crucial concept in understanding chemical processes, as it helps predict whether a reaction will occur under specific conditions. The two primary forms of free energy, Gibbs free energy and Helmholtz free energy, are used in different contexts depending on the variables involved, such as temperature and pressure.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. This concept is vital for predicting the spontaneity of processes, as it combines the system's enthalpy and entropy to determine whether a reaction or process can occur naturally without external input.
Helmholtz Free Energy: Helmholtz free energy is a thermodynamic potential that measures the useful work obtainable from a system at constant temperature and volume. It connects the concepts of state functions and path functions, where state functions represent the properties that depend only on the state of the system, while path functions are dependent on the specific process taken. This potential is essential for understanding free energy changes and spontaneity in chemical processes.
Maximal work: Maximal work refers to the maximum amount of useful work that can be extracted from a system as it undergoes a thermodynamic process. This concept is crucial for understanding the efficiency and spontaneity of reactions, especially in relation to free energy changes in a system, as it indicates how much energy can be converted into work rather than lost as heat or other forms of energy.
Non-expansion work: Non-expansion work refers to the energy transfer that occurs without a change in the volume of a system. This type of work is significant in various thermodynamic processes, especially when considering changes in internal energy, enthalpy, and free energy. It includes work done in electrical, magnetic, and chemical systems where volume remains constant while energy is still exchanged.
Phase Transitions: Phase transitions are the processes where a substance changes from one state of matter to another, such as solid to liquid or liquid to gas, due to changes in temperature or pressure. These transitions are crucial in understanding the energy changes involved, specifically in how heat capacity influences these processes and how Gibbs and Helmholtz free energies determine the stability of phases under varying conditions.
Reaction kinetics: Reaction kinetics is the study of the rates of chemical reactions and the factors that affect these rates. It focuses on understanding how different conditions, such as temperature, concentration, and catalysts, influence the speed at which reactants convert to products. This field of study is crucial in various applications, including the development of new materials and optimizing reaction conditions in industrial processes.
Reaction quotient: The reaction quotient, denoted as Q, is a measure of the relative concentrations of products and reactants in a chemical reaction at any given point, used to determine the direction in which a reaction will proceed to reach equilibrium. It is calculated using the same expression as the equilibrium constant, but with the current concentrations instead of those at equilibrium. Understanding Q helps predict whether a system will shift toward products or reactants based on the comparison between Q and the equilibrium constant K.
Thermodynamic Stability: Thermodynamic stability refers to the condition in which a system is in its lowest energy state and is resistant to changes or disturbances. A thermodynamically stable system will not spontaneously change its state unless an external influence is applied, indicating that it has achieved a balance between enthalpy and entropy. Understanding thermodynamic stability is crucial for evaluating reactions and processes, as it relates to heat capacity, free energy, and electrochemical systems.
δg = δh - tδs: The equation δg = δh - tδs represents the Gibbs free energy change of a system, where δg is the change in free energy, δh is the change in enthalpy, t is the temperature in Kelvin, and δs is the change in entropy. This equation is crucial for understanding how spontaneous processes occur, as it relates thermodynamic properties to determine whether a reaction can proceed without external energy input. It highlights the balance between energy and disorder, showing that a decrease in free energy indicates a favorable reaction.