Glossary

6.4 Gibbs free energy and spontaneity of reactions

4 min read•july 22, 2024

is a crucial concept in chemistry, helping us predict whether reactions will happen spontaneously. It combines and , giving us a powerful tool to understand chemical processes and their likelihood of occurring under specific conditions.

Calculating Gibbs free energy allows us to determine reaction spontaneity, constants, and the stability of compounds. This knowledge is vital for understanding real-world applications, from industrial processes to biological systems, and helps us manipulate reactions to achieve desired outcomes.

Gibbs Free Energy and Spontaneity

Gibbs free energy fundamentals

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  • Gibbs free energy (GG) thermodynamic quantity determines spontaneity of process at constant temperature and pressure
    • Process spontaneous if ΔG<0\Delta G < 0 (diamond formation from graphite)
    • Process non-spontaneous if ΔG>0\Delta G > 0 (water flowing uphill)
    • Process at equilibrium if ΔG=0\Delta G = 0 (saturated solution of sugar in water)
  • GG defined as: G=H−TSG = H - TS
    • HH enthalpy, measure of total heat content of system (energy released or absorbed during chemical reaction)
    • SS , measure of disorder or randomness of system (gas has higher entropy than solid)
    • TT absolute temperature in Kelvin () (room temperature ~298 K)
  • Change in Gibbs free energy (ΔG\Delta G) given by: ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S
    • ΔH\Delta H change in enthalpy (heat released or absorbed)
    • ΔS\Delta S change in entropy (increase or decrease in disorder)

Calculation of Gibbs free energy

  • (ΔGf∘\Delta G_f^\circ) change in Gibbs free energy when one mole of compound formed from constituent elements in standard states at 1 atm pressure and specified temperature (usually 298 K)
    • Table of standard Gibbs free energies of formation available for many compounds (CRC Handbook of Chemistry and Physics)
  • (ΔG∘\Delta G^\circ) for reaction calculated using standard Gibbs free energies of formation:
    • ΔG∘=∑νpΔGf,p∘−∑νrΔGf,r∘\Delta G^\circ = \sum \nu_p \Delta G_{f,p}^\circ - \sum \nu_r \Delta G_{f,r}^\circ
      1. Identify the chemical reaction and write a balanced equation
      2. Look up the ΔGf∘\Delta G_f^\circ values for each reactant and product
      3. Multiply each ΔGf∘\Delta G_f^\circ value by its stoichiometric coefficient (ν\nu)
      4. Sum the products and subtract the reactants to obtain ΔG∘\Delta G^\circ

Spontaneity prediction using Gibbs energy

  • Sign of ΔG\Delta G determines spontaneity of reaction:
    • ΔG<0\Delta G < 0, reaction spontaneous (product-favored) (rusting of iron)
    • ΔG>0\Delta G > 0, reaction non-spontaneous (reactant-favored) (electrolysis of water)
    • ΔG=0\Delta G = 0, reaction at equilibrium (vapor pressure of liquid)
  • Magnitude of ΔG\Delta G indicates driving force for reaction:
    • Large negative ΔG\Delta G indicates strongly spontaneous reaction (combustion of methane)
    • Small negative ΔG\Delta G indicates weakly spontaneous reaction (dissolution of salt in water)
    • Large positive ΔG\Delta G indicates strongly non-spontaneous reaction (decomposition of water into hydrogen and oxygen)
    • Small positive ΔG\Delta G indicates weakly non-spontaneous reaction (melting of ice)

Interpretation of Gibbs energy diagrams

  • Gibbs free energy diagrams plot GG as function of reaction coordinate (progress of reaction)
    • Reactants and products represented as local minima on diagram (stable states)
    • Transition state represented as local maximum between reactants and products (highest energy state)
  • (KK) determined from Gibbs free energy change:
    • ΔG∘=−RTln⁡K\Delta G^\circ = -RT \ln K
      • RR ideal gas constant (8.314 J/mol·K)
      • TT absolute temperature in Kelvin (K)
      • Larger KK values indicate equilibrium favors products (reaction spontaneous)
      • Smaller KK values indicate equilibrium favors reactants (reaction non-spontaneous)
  • Direction of spontaneous change determined from Gibbs free energy diagram:
    • System will spontaneously move from higher GG state to lower GG state (downhill on diagram)
    • At equilibrium, reactants and products have same GG value (no net change)

Applications of Gibbs free energy

  • Feasibility of chemical processes assessed using Gibbs free energy:
    • Processes with ΔG<0\Delta G < 0 feasible and occur spontaneously (synthesis of ammonia from nitrogen and hydrogen)
    • Processes with ΔG>0\Delta G > 0 not feasible and require input of energy (decomposition of water into hydrogen and oxygen)
  • Stability of compounds compared using standard Gibbs free energies of formation:
    • Compounds with lower (more negative) ΔGf∘\Delta G_f^\circ values more stable (diamond vs graphite)
    • Compounds with higher (less negative or positive) ΔGf∘\Delta G_f^\circ values less stable (ozone vs oxygen)
  • Relationship between ΔG∘\Delta G^\circ and equilibrium constant (KK) given by:
    • ΔG∘=−RTln⁡K\Delta G^\circ = -RT \ln K
      • ΔG∘<0\Delta G^\circ < 0, K>1K > 1 (products favored at equilibrium) (formation of water from hydrogen and oxygen)
      • ΔG∘>0\Delta G^\circ > 0, K<1K < 1 (reactants favored at equilibrium) (decomposition of calcium carbonate into calcium oxide and carbon dioxide)
      • ΔG∘=0\Delta G^\circ = 0, K=1K = 1 (reactants and products equally favored at equilibrium) (vaporization of water at its boiling point)
  • Equilibrium position shifted by changing conditions (temperature, pressure, or concentration) to alter value of ΔG\Delta G
    • Conditions changed to make ΔG\Delta G more negative, equilibrium shifts towards products (increasing temperature for endothermic reaction)
    • Conditions changed to make ΔG\Delta G more positive, equilibrium shifts towards reactants (decreasing pressure for reaction with fewer moles of gas)

Key Terms to Review (27)

Biochemical pathways: Biochemical pathways are sequences of chemical reactions occurring within a cell, where the product of one reaction serves as the substrate for the next. These pathways are essential for various cellular processes, including metabolism, signal transduction, and synthesis of biomolecules, and they often involve a series of enzymes that facilitate each step. Understanding these pathways is crucial for grasping how cells harness energy and maintain homeostasis.
Chemical Equilibrium: Chemical equilibrium is a state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time. This balance allows for a dynamic process where reactants are continuously converted to products and vice versa, without any net change in concentration. Understanding this concept is crucial for relating it to spontaneity and energy changes in reactions, as well as determining equilibrium concentrations in various chemical scenarios.
Chemical equilibrium: Chemical equilibrium is the state in which the concentrations of reactants and products in a chemical reaction remain constant over time, indicating that the forward and reverse reactions occur at equal rates. This balance reflects a dynamic process where the reactants are continuously converting to products and vice versa, making it essential for understanding reaction behavior and spontaneity in thermodynamics.
Endergonic: Endergonic refers to a type of chemical reaction that absorbs energy from its surroundings, resulting in a positive change in Gibbs free energy ($$\Delta G > 0$$). These reactions are non-spontaneous, meaning they require energy input to proceed. Understanding endergonic reactions is crucial for grasping how energy flows in biochemical processes and the role of Gibbs free energy in determining reaction spontaneity.
Enthalpy: Enthalpy is a thermodynamic quantity that represents the total heat content of a system at constant pressure, combining internal energy with the product of pressure and volume. It helps in understanding energy changes during chemical reactions, particularly in predicting whether reactions can occur spontaneously and how they relate to the laws of thermodynamics.
Entropy: Entropy is a measure of the disorder or randomness of a system, reflecting the number of ways in which the energy of a system can be arranged. It plays a crucial role in understanding the direction of spontaneous processes and energy dispersal, linking directly to concepts of thermodynamics and the overall behavior of chemical reactions.
Entropy: Entropy is a measure of the disorder or randomness in a system and is a key concept in understanding the direction of spontaneous processes. It relates to how energy disperses in a system, often increasing over time, which helps explain why certain reactions occur without external energy. Entropy plays a crucial role in linking thermodynamic principles, determining the spontaneity of reactions, and defining the behavior of state functions.
Equilibrium: Equilibrium refers to the state in a chemical reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time. This dynamic balance means that even though reactions are occurring, there is no net change in the concentrations of the substances involved. Understanding equilibrium is essential for grasping concepts such as Gibbs free energy and spontaneity of reactions, as it helps determine whether a reaction can occur under specific conditions.
Equilibrium Constant: The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a reversible chemical reaction. It helps predict the direction in which a reaction will proceed and is related to the Gibbs free energy change, which indicates the spontaneity of a reaction, and to the stability constants of complex ions, showing the strength of their formation.
Gibbs Free Energy: Gibbs Free Energy is a thermodynamic potential that measures the maximum reversible work obtainable from a closed system at constant temperature and pressure. It connects the concepts of enthalpy, entropy, and temperature to determine whether a process is spontaneous or non-spontaneous, making it essential for understanding chemical reactions, equilibrium, and thermodynamic stability.
K: In chemistry, 'k' typically refers to the equilibrium constant, a numerical value that expresses the ratio of concentrations of products to reactants at equilibrium for a given chemical reaction. This constant helps predict the direction in which a reaction will proceed and indicates the extent of the reaction under specific conditions. The value of 'k' is crucial in understanding not only the position of equilibrium but also its relationship with Gibbs free energy and spontaneity of reactions.
Phase Changes: Phase changes are the transformations between different states of matter, such as solid, liquid, and gas. These changes occur when energy is added or removed from a substance, impacting the arrangement and movement of its particles. Understanding phase changes is essential for grasping how Gibbs free energy and spontaneity affect chemical reactions and the stability of different phases under varying conditions.
Phase transitions: Phase transitions refer to the changes between different states of matter, such as solid, liquid, and gas, that occur when energy is added or removed from a system. These transitions are characterized by changes in temperature and pressure, which influence the arrangement and behavior of particles in the substance. The study of phase transitions is closely tied to thermodynamics, especially in understanding how Gibbs free energy can predict the spontaneity of reactions and transitions under varying conditions.
Prediction of reaction direction: The prediction of reaction direction refers to the ability to determine whether a chemical reaction will proceed in the forward or reverse direction based on Gibbs free energy changes. This concept is closely tied to spontaneity, as reactions tend to move toward lower free energy, indicating that they are more likely to occur in a certain direction under given conditions.
Pressure Effects: Pressure effects refer to the influence of pressure changes on the properties and behavior of substances, particularly in chemical reactions and phase changes. These effects are significant in determining the spontaneity of reactions as they impact the Gibbs free energy, which is a measure of the energy available to do work in a system. Changes in pressure can shift equilibrium positions and alter the reaction pathways, making it essential to consider pressure when evaluating reaction feasibility.
Reaction Feasibility: Reaction feasibility refers to the likelihood that a chemical reaction will occur under specific conditions. It is closely tied to the concept of Gibbs free energy, which helps determine whether a reaction is spontaneous or requires input of energy. Understanding reaction feasibility allows chemists to predict which reactions will proceed and how they can be harnessed for practical applications.
Reaction Quotient: The reaction quotient (Q) is a measure of the relative amounts of reactants and products present in a chemical reaction at any point in time. It is calculated using the same expression as the equilibrium constant (K), but it can be used to determine the direction in which a reaction will proceed to reach equilibrium, based on the current concentrations of reactants and products. Understanding Q helps to assess whether a reaction is spontaneous and how far it is from equilibrium.
Spontaneous process: A spontaneous process is a physical or chemical change that occurs without the need for external energy input, driven by the natural tendency of systems to increase their entropy. This concept is crucial in understanding how reactions proceed and the conditions under which they can occur, often linked to the changes in Gibbs free energy, which determines whether a reaction can happen spontaneously at constant temperature and pressure.
Standard Gibbs Free Energy Change: The standard Gibbs free energy change ($$ ext{ΔG}^ ext{°}$$) is the amount of energy available to do work during a chemical reaction under standard conditions, typically 1 atm pressure and a specified temperature, usually 25°C. This value helps predict whether a reaction is spontaneous; if $$ ext{ΔG}^ ext{°}$$ is negative, the reaction can proceed without external energy input, while a positive value indicates that the reaction is non-spontaneous under standard conditions.
Standard Gibbs Free Energy of Formation: The standard Gibbs free energy of formation is the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states. This value is crucial for predicting the spontaneity of reactions, as it helps determine whether a process will occur naturally under specified conditions.
Temperature dependence: Temperature dependence refers to the way in which the rate and direction of a chemical reaction change with varying temperatures. This concept plays a crucial role in determining the spontaneity of reactions and the activation energy needed for those reactions to occur, impacting both the equilibrium position and kinetic behavior of chemical processes.
Thermodynamic stability: Thermodynamic stability refers to the tendency of a system to remain in a state of equilibrium, where it experiences no net change in energy or composition over time. This concept is crucial for understanding the conditions under which reactions occur and whether they will proceed spontaneously or reach a state of equilibrium. Factors such as Gibbs free energy and equilibrium constants play significant roles in determining the thermodynamic stability of a system, influencing both the direction and extent of chemical reactions.
δg < 0: The expression δg < 0 indicates that the change in Gibbs free energy for a process is negative, which means the reaction is spontaneous. This negative change implies that the system can do work on its surroundings and will naturally proceed in the direction that decreases its free energy, ultimately favoring the formation of products over reactants. Understanding this concept is essential for predicting whether a reaction will occur under specific conditions.
δg = δh - tδs: The equation δg = δh - tδs describes the relationship between Gibbs free energy (δg), enthalpy (δh), and entropy (δs) at a given temperature (t). This equation helps determine the spontaneity of chemical reactions, indicating whether a process will occur naturally under specific conditions. When δg is negative, the reaction is spontaneous, while a positive δg suggests that the reaction is non-spontaneous, linking thermodynamic principles with reaction behavior.
δg > 0: The expression δg > 0 indicates that the change in Gibbs free energy for a process is positive, meaning that the process is non-spontaneous under the given conditions. This concept connects to the fundamental principles of thermodynamics, specifically the relationship between Gibbs free energy, enthalpy, and entropy. When δg is greater than zero, it implies that the forward reaction does not occur spontaneously and requires energy input to proceed.
δg_f°: The standard Gibbs free energy of formation, represented as δg_f°, is the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states at a specified temperature, usually 298 K. This term is essential for understanding the spontaneity of reactions, as it provides a criterion for predicting whether a reaction will occur spontaneously under standard conditions.
δg°: The symbol δg° represents the standard Gibbs free energy change of a reaction, which is a measure of the spontaneity of that reaction under standard conditions. It helps predict whether a reaction will proceed in the forward direction or if it is more likely to be spontaneous in the reverse direction, based on the difference in energy between reactants and products. This value is crucial for understanding the favorability of reactions and is tied to concepts like equilibrium and thermodynamic stability.
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