Glossary

2.2 Free energy and chemical potential

5 min read•august 1, 2024

Free energy and are key concepts in biological thermodynamics. They help us understand why reactions happen and how energy flows in living systems. These ideas explain everything from enzyme reactions to how cells maintain their structure.

determines if a process will happen on its own. Chemical potential drives the movement of substances in cells. Together, they're essential for predicting and explaining the complex chemical dance of life.

Gibbs free energy in biological systems

Definition and significance

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  • Gibbs free energy represents the maximum amount of work that can be extracted from a system at constant temperature and pressure
  • The change in Gibbs free energy () determines the spontaneity of a reaction or process
    • A negative ΔG indicates a
    • A positive ΔG indicates a
  • Gibbs free energy is a crucial factor in determining the direction and feasibility of biochemical reactions in biological systems
    • Examples include metabolic pathways, protein folding, and ligand binding
  • The change in Gibbs free energy is influenced by the change in enthalpy (), the change in entropy () of the system, and the temperature (T) according to the equation: ΔG=ΔH−TΔSΔG = ΔH - TΔS
  • The (ΔG°) is the change in free energy under (1 atm pressure, 1 M concentration, and 298 K temperature) and serves as a reference point for comparing the spontaneity of different reactions

Factors influencing Gibbs free energy

  • Temperature affects the change in Gibbs free energy by influencing the entropy term (TΔS) in the equation ΔG=ΔH−TΔSΔG = ΔH - TΔS
    • Higher temperatures favor reactions with positive entropy changes (ΔS > 0)
    • Lower temperatures favor reactions with negative entropy changes (ΔS < 0)
  • Pressure can impact the change in Gibbs free energy, particularly for reactions involving gases, by altering the enthalpy term (ΔH) in the equation ΔG=ΔH−TΔSΔG = ΔH - TΔS
    • Increasing pressure favors reactions that result in a decrease in volume (fewer moles of gas)
    • Decreasing pressure favors reactions that result in an increase in volume (more moles of gas)
  • Concentration of reactants and products affects the change in Gibbs free energy by influencing the (Q) in the equation ΔG=ΔG°+RTln⁡QΔG = ΔG° + RT \ln Q
    • Higher concentrations of reactants relative to products drive the reaction forward (negative ΔG)
    • Higher concentrations of products relative to reactants drive the reaction backward (positive ΔG)

Calculating Gibbs free energy changes

Calculating ΔG using the reaction quotient

  • The change in Gibbs free energy for a reaction can be calculated using the equation: ΔG=ΔG°+RTln⁡QΔG = ΔG° + RT \ln Q
    • R is the gas constant (8.314 J/mol·K)
    • T is the temperature in Kelvin
    • Q is the reaction quotient
  • The reaction quotient (Q) is the ratio of the product of the concentrations of the reaction products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients
  • At equilibrium, ΔG = 0 and Q = K, where K is the
    • The relationship between ΔG° and K is given by the equation: ΔG°=−RTln⁡KΔG° = -RT \ln K

Calculating ΔG using standard Gibbs free energy of formation

  • The change in Gibbs free energy can also be calculated using the standard Gibbs free energy of formation (ΔG°f) of the reactants and products according to the equation: ΔG°=Σ(n×ΔG°f products)−Σ(n×ΔG°f reactants)ΔG° = Σ(n × ΔG°f \text{ products}) - Σ(n × ΔG°f \text{ reactants})
    • n is the stoichiometric coefficient
  • Standard Gibbs free energy of formation values are tabulated for many compounds at standard conditions (1 atm pressure, 1 M concentration, and 298 K temperature)
  • By using these tabulated values, the ΔG° for a reaction can be calculated without the need for experimental measurements

Coupling reactions to drive spontaneity

  • Coupling reactions with favorable (negative) ΔG to reactions with unfavorable (positive) ΔG can drive the overall process in the direction of spontaneity
  • This coupling is essential for many biological processes
    • ATP synthesis is driven by the coupling of the unfavorable reaction (positive ΔG) with the favorable oxidation of glucose (negative ΔG) during cellular respiration
    • Active transport of molecules across membranes against their concentration gradient (positive ΔG) is coupled with the favorable hydrolysis of ATP (negative ΔG)

Chemical potential and free energy

Definition and relationship to Gibbs free energy

  • Chemical potential (μ) represents the change in Gibbs free energy of a system when one mole of a substance is added or removed at constant temperature, pressure, and composition of other components
  • The chemical potential of a substance depends on its concentration and other factors such as temperature, pressure, and the presence of other substances in the system
  • In a mixture of substances, the chemical potential of each component is related to its partial molar Gibbs free energy, which is the contribution of that component to the total Gibbs free energy of the system

Driving force for substance movement

  • The difference in chemical potential between two states or locations is the driving force for the net movement of a substance
    • Examples include diffusion, osmosis, and active transport across biological membranes
  • Substances tend to move from regions of higher chemical potential to regions of lower chemical potential, reducing the overall Gibbs free energy of the system
  • At equilibrium, the chemical potentials of a substance in all phases or compartments of a system are equal, resulting in no net movement of the substance

Spontaneity of biological processes

Predicting spontaneity using ΔG

  • The spontaneity of a biological process can be predicted by considering the change in Gibbs free energy (ΔG) of the system
    • Processes with a negative ΔG are spontaneous
    • Processes with a positive ΔG are non-spontaneous
  • The direction of a biochemical reaction can be determined by comparing the chemical potentials of the reactants and products
    • Reactions proceed in the direction that reduces the overall Gibbs free energy of the system

Examples of spontaneity in biological systems

  • Maintenance of concentration gradients across biological membranes
    • Requires the input of energy to overcome the natural tendency of substances to move down their concentration gradients (from high chemical potential to low chemical potential)
  • Conformational changes in proteins (, signal transduction)
    • Driven by the minimization of Gibbs free energy, resulting in the most stable and thermodynamically favorable structures
  • Binding of ligands to proteins (oxygen to hemoglobin, substrates to enzymes)
    • Governed by the change in Gibbs free energy of the system, with the most stable complexes having the lowest free energy
  • Protein folding and stability
    • Native protein structures represent the lowest Gibbs free energy state under physiological conditions
    • Denaturation of proteins occurs when the Gibbs free energy of the unfolded state becomes lower than that of the native state (e.g., due to changes in temperature, pH, or presence of denaturants)

Key Terms to Review (20)

ATP Hydrolysis: ATP hydrolysis is the chemical reaction where adenosine triphosphate (ATP) is broken down into adenosine diphosphate (ADP) and an inorganic phosphate (Pi), releasing energy that can be used for various biological processes. This reaction is crucial for understanding how energy is transferred in biological systems, particularly in the context of free energy changes and the movement of molecular motors.
Chemical Potential: Chemical potential is a measure of the change in free energy of a system when an additional amount of substance is added, keeping temperature and pressure constant. It reflects how the potential energy of a species changes as its concentration varies, linking closely to concepts like free energy and equilibrium. Understanding chemical potential is essential for grasping how systems respond to changes, both at equilibrium and during dynamic processes.
Electrochemical Potential: Electrochemical potential is the energy required to move a charged particle across a membrane, combining both the chemical potential and the electrical potential into one measure. This concept is crucial because it helps understand how ions move in biological systems, which is essential for processes like nerve impulses and muscle contractions. The electrochemical potential reflects the gradient of concentration and charge across a membrane, indicating the driving force behind the movement of ions and molecules.
Enzyme Catalysis: Enzyme catalysis refers to the process by which enzymes accelerate chemical reactions in biological systems, lowering the activation energy required for the reaction to occur. This process is essential for sustaining life, as it allows biochemical reactions to proceed at rates necessary for cellular functions. Enzyme catalysis is closely linked to concepts like free energy changes in reactions and the role of chemical potential in determining reaction direction and spontaneity.
Equilibrium Constant: The equilibrium constant, denoted as $$K$$, is a numerical value that expresses the ratio of the concentration of products to reactants at equilibrium in a reversible chemical reaction. It provides insight into the favorability of a reaction and its extent, linking directly to free energy changes and chemical potential, which describe the energy landscape of reactions. Understanding the equilibrium constant is essential for studying biomolecular interactions and for performing free energy calculations that help model molecular systems under various conditions.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another, meaning the total energy of an isolated system is constant. This principle is crucial in understanding how energy transformations occur in biological processes, as it helps explain how organisms convert food into usable energy and how this impacts their biochemical reactions.
Gibbs Free Energy: Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is crucial in determining the spontaneity of reactions, as reactions with a negative change in Gibbs Free Energy (ΔG < 0) occur spontaneously, while those with a positive change do not.
Non-spontaneous process: A non-spontaneous process is a reaction or change that does not occur naturally under specific conditions and requires external energy input to proceed. These processes are characterized by a positive change in free energy, indicating that the system needs energy from its surroundings to overcome thermodynamic barriers. Understanding non-spontaneous processes is crucial for analyzing chemical potential and the behavior of systems at equilibrium versus those out of equilibrium.
Non-standard conditions: Non-standard conditions refer to the specific state of a system that differs from the standard state, typically involving variations in temperature, pressure, and concentrations of reactants and products. These conditions can significantly influence the thermodynamic properties, including free energy and chemical potential, which are essential for understanding reaction spontaneity and equilibrium under real-world scenarios.
Reaction Quotient: The reaction quotient, denoted as Q, is a measure that describes the ratio of the concentrations of products to the concentrations of reactants at any given point in a chemical reaction that is not necessarily at equilibrium. It provides insight into the direction in which a reaction will proceed to reach equilibrium, as it compares the current state of a reaction to its equilibrium state represented by the equilibrium constant (K). Understanding Q is essential for predicting how changes in concentration, pressure, or temperature will affect the reaction.
Rt ln q: The expression 'rt ln q' relates to the concept of free energy and chemical potential in thermodynamics. Here, 'r' represents the universal gas constant, 't' is the absolute temperature in Kelvin, and 'q' denotes the reaction quotient. This term plays a critical role in determining the spontaneity of a reaction and understanding the behavior of chemical systems at equilibrium, linking thermodynamic properties to chemical concentrations.
Second Law of Thermodynamics: The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time and is often understood in the context of energy transformations. This principle is crucial in understanding how biological systems use energy, highlighting that processes occur in a direction that increases overall disorder, thus impacting metabolic pathways, free energy changes, and interactions between biomolecules.
Spontaneous Process: A spontaneous process is a physical or chemical change that occurs without the need for external energy once it has been initiated. These processes often lead to an increase in entropy and can be associated with a decrease in free energy, making them favorable under specific conditions. Understanding spontaneous processes is crucial as they relate to the principles of free energy and the dynamics of systems approaching equilibrium.
Standard Conditions: Standard conditions refer to a specific set of temperature, pressure, and concentration values used as a reference point for thermodynamic measurements. These conditions typically include a temperature of 25°C (298 K), a pressure of 1 atmosphere (atm), and a concentration of 1 molar (1 M) for all solutes. Standard conditions are crucial for comparing thermodynamic data, such as free energy and chemical potential, across different reactions and systems.
Standard Gibbs Free Energy Change: Standard Gibbs free energy change, denoted as $$\Delta G^{\circ}$$, represents the change in Gibbs free energy during a chemical reaction when reactants and products are in their standard states at a specific temperature, usually 298 K. This term is crucial because it helps predict the spontaneity of reactions; a negative value indicates that a reaction can occur spontaneously, while a positive value suggests non-spontaneity. It connects to various thermodynamic principles that describe how energy transformations influence chemical processes.
Temperature Dependence: Temperature dependence refers to how the properties of a system, such as free energy and chemical potential, change as the temperature varies. This relationship is crucial for understanding the behavior of chemical reactions and phase transitions, as many thermodynamic functions are sensitive to temperature fluctuations, impacting equilibrium conditions and reaction spontaneity.
Thermal Equilibrium: Thermal equilibrium is a state in which two or more systems have reached a point where there is no net heat transfer between them, resulting in equal temperatures. This concept is crucial in understanding how energy exchanges occur, as systems in thermal equilibrium do not experience any temperature changes or energy flow. It also plays a significant role in determining free energy and chemical potential, as these thermodynamic properties rely on the thermal states of the systems involved.
δg: δg represents the change in Gibbs free energy, a crucial concept in thermodynamics that reflects the amount of work a system can perform at constant temperature and pressure. It connects to chemical reactions and processes, guiding our understanding of spontaneity, equilibrium, and how biological systems harness energy. By analyzing δg, we can gain insights into the energetics of protein folding, stability, and the effects of different sampling techniques in computational studies.
δh: The symbol δh represents the change in enthalpy, a key thermodynamic quantity that reflects the heat content of a system at constant pressure. It is crucial for understanding energy transformations in chemical reactions and processes, including those involving protein folding. By connecting δh to free energy and chemical potential, we can assess how reactions favorably proceed under different conditions.
δs: The term δs represents the change in entropy of a system during a reversible process. Entropy is a key concept in thermodynamics that quantifies the amount of disorder or randomness in a system, and δs specifically captures how this disorder changes when a system undergoes transformation. Understanding δs is crucial because it connects to the principles of free energy and chemical potential as well as the thermodynamic aspects of processes like protein folding.
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