7.2 Free energy and spontaneity
4 min read•july 30, 2024
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 , showing how they work together to determine a reaction's direction.
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 and
- 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 , 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:
- 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, , 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:
- Standard entropy values (S°) used to calculate ΔS using the Second Law of Thermodynamics:
- 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
- (K) related to (ΔG°) by the equation: , 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°
Key Terms to Review (16)
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.
Endergonic reaction: An endergonic reaction is a type of chemical reaction that requires an input of energy to proceed, resulting in a change in free energy that is positive. In these reactions, the products have higher energy than the reactants, which makes them non-spontaneous under standard conditions. This means that endergonic reactions do not occur without a constant supply of energy, highlighting the relationship between energy changes and the spontaneity of chemical processes.
Entropy: Entropy is a measure of the disorder or randomness in a system and reflects the number of ways a system can be arranged. It helps predict the direction of spontaneous processes and the energy available for work. Understanding entropy is crucial for comprehending how energy disperses in different situations and how it relates to equilibrium and spontaneity.
Equilibrium Constant: The equilibrium constant, often represented as K, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction at a specific temperature. It provides insight into the extent of a reaction and helps determine whether reactants or products are favored in a chemical process. This concept connects closely to the notions of free energy, chemical potential, and reaction rates, illustrating how changes in conditions can shift equilibria.
Exergonic reaction: An exergonic reaction is a chemical reaction that releases energy, typically in the form of heat or light, as it proceeds towards the products. This type of reaction is characterized by a decrease in free energy, making it spontaneous and able to occur without the need for external energy input. The concept is crucial in understanding the relationship between free energy and spontaneity in various chemical processes.
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.
Non-spontaneous process: A non-spontaneous process is a reaction or change that does not occur naturally under a given set of conditions and requires an input of energy to proceed. These processes are characterized by an increase in free energy, meaning that they will not happen without external work or energy supply, distinguishing them from spontaneous processes, which occur without additional energy. Understanding these processes involves exploring how entropy and free energy influence the likelihood of reactions occurring.
Pressure: Pressure is the force exerted per unit area on a surface, typically measured in atmospheres or pascals. It plays a crucial role in determining the behavior of gases, affecting their volume, temperature, and how they interact with other substances. Understanding pressure is essential for predicting the spontaneity of chemical reactions, analyzing chemical potentials, and assessing how entropy changes during those reactions.
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.
Standard Gibbs Free Energy Change: Standard Gibbs free energy change ($\Delta G^{\circ}$) is the change in Gibbs free energy of a system when it transitions from reactants to products under standard conditions (1 bar pressure, 298 K temperature, and 1 M concentration for all reactants and products). It provides insight into the spontaneity of a reaction, as negative values indicate that a process is thermodynamically favorable while positive values suggest non-spontaneity.
Standard State: The standard state refers to the reference conditions used to define the properties of substances, specifically at a pressure of 1 bar and a specified temperature, typically 25°C (298 K). This concept is crucial for comparing thermodynamic values like internal energy, enthalpy, free energy, and chemical potential across different reactions and processes, ensuring consistency and accuracy in calculations.
Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance, reflecting how hot or cold that substance is. It plays a crucial role in various physical and chemical processes, influencing gas behavior, thermal interactions, and reaction dynamics.
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.
δg° = -rt ln k: The equation $$ ext{δg°} = - ext{RT} ext{ln} K$$ relates the standard Gibbs free energy change (δg°) of a chemical reaction to the equilibrium constant (K) of that reaction. This relationship shows how the spontaneity of a reaction at standard conditions is influenced by the position of equilibrium, indicating that a more favorable (negative) δg° corresponds to a larger equilibrium constant, signifying a greater tendency for products to form. Essentially, it connects thermodynamics with chemical equilibrium, emphasizing that spontaneous reactions tend to favor product formation.