17.4 Potential, Free Energy, and Equilibrium
3 min read•june 25, 2024
and are closely linked through , free energy, and equilibrium constants. These concepts help us understand how energy is transformed in chemical reactions and predict their spontaneity.
Calculations in electrochemical systems involve cell potentials, free energy changes, and equilibrium constants. The relates cell potential to concentrations, allowing us to predict cell behavior under various conditions.
Electrochemistry and Thermodynamics
Cell potential and energy relationships
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- Cell potential () measures the potential difference between two half-cells in an electrochemical cell (galvanic cell or voltaic cell)
- Directly related to the change () of the redox reaction occurring in the cell
- , where represents the number of electrons transferred in the redox reaction and represents (96,485 C/mol)
- Also related to the () of the redox reaction taking place
- , where represents the (8.314 J/mol·K) and represents the temperature in Kelvin
- Directly related to the change () of the redox reaction occurring in the cell
- () represents the cell potential measured under standard conditions (1 M concentrations for all species, 1 atm pressure, and 25°C)
- Related to the () and the () for the redox reaction
- relates standard cell potential to standard Gibbs free energy change
- relates standard Gibbs free energy change to standard equilibrium constant
- Related to the () and the () for the redox reaction
- The concept of free energy in electrochemistry is closely related to entropy and , which are fundamental thermodynamic properties
Calculations for electrochemical systems
- Cell potential can be calculated using the of the half-reactions occurring at the and
- , where represents the standard reduction potential of the cathode half-reaction and represents the standard reduction potential of the anode half-reaction
- Free energy change can be calculated using the cell potential and Faraday's constant
- , where a negative value indicates a and a positive value indicates a
- Equilibrium constant can be calculated using the standard cell potential and the Nernst equation
- relates the natural logarithm of the equilibrium constant to the standard cell potential
- allows for the direct calculation of the equilibrium constant from the standard cell potential
Nernst equation in cell potentials
- The Nernst equation relates the cell potential to the standard cell potential and the concentrations of the reactants and products involved in the redox reaction
- , where represents the
- The reaction quotient () represents the ratio of the concentrations of the products to the reactants, each raised to their respective stoichiometric coefficients
- For the general redox reaction , the reaction quotient is calculated as , where the square brackets represent the molar concentrations of the respective species
- The Nernst equation can be used to calculate the cell potential at any given concentration of reactants and products, allowing for the prediction of cell behavior under non-standard conditions
- At equilibrium, and , so the Nernst equation simplifies to , relating the standard cell potential to the equilibrium constant of the redox reaction
- can be applied to predict how changes in concentration will affect the cell potential and the direction of electron flow in an electrochemical cell
Key Terms to Review (35)
$E_{cell}^°$: $E_{cell}^°$ is the standard cell potential, which is a measure of the driving force for a redox reaction to occur under standard conditions. It represents the potential difference between the reduction potentials of the cathode and anode in an electrochemical cell, and is a fundamental concept in understanding the spontaneity and feasibility of chemical reactions.
$E_{cell}$: $E_{cell}$ is the cell potential or electromotive force (EMF) of an electrochemical cell, which is the potential difference between the two half-cells that make up the cell. It represents the ability of the cell to do electrical work and is a crucial parameter in understanding the spontaneity and feasibility of redox reactions.
$E_{cell}$ is directly related to the Gibbs free energy change ($ ext{\Delta G}$) and the equilibrium constant ($K_{eq}$) of the overall cell reaction, providing a quantitative measure of the driving force behind the chemical process.
$K^°$: $K^°$ is a fundamental constant used in chemistry to describe the equilibrium state of a system. It represents the standard equilibrium constant, which quantifies the extent of a reaction at equilibrium under standard conditions of temperature and pressure. This constant is crucial in understanding the spontaneity and feasibility of chemical reactions, as well as the concept of chemical equilibrium.
$K$: $K$ is a fundamental constant that represents the equilibrium constant, which is a measure of the extent of a chemical reaction at equilibrium. It is a dimensionless quantity that reflects the balance between the concentrations of reactants and products at the point where the forward and reverse reactions occur at the same rate, indicating that the system has reached a state of dynamic equilibrium.
$Q$: $Q$ is a fundamental concept in chemistry that represents the capacity to do work or cause change. It is a central theme in the topics of 17.4 Potential, Free Energy, and Equilibrium, as it directly influences the behavior and transformations of chemical systems.
$Q$ can be thought of as a measure of the energy available to drive a process or reaction forward. It is closely related to the concepts of potential, free energy, and the state of equilibrium in a chemical system.
$ΔG^°$: $ΔG^°$ is the standard Gibbs free energy change, which is a fundamental concept in chemistry that describes the spontaneity and feasibility of a chemical reaction. It combines the effects of enthalpy (energy released or absorbed) and entropy (disorder or randomness) to determine the overall energy change and the direction a reaction will naturally proceed. $ΔG^°$ is crucial in understanding potential, free energy, and equilibrium in chemical systems.
$ΔG$: $ΔG$, or Gibbs free energy change, is a thermodynamic quantity that combines the concepts of energy, entropy, and temperature to determine the spontaneity and feasibility of a chemical process. It is a crucial factor in understanding the potential, free energy, and equilibrium of a system.
Anode: The anode is the electrode where oxidation occurs in a galvanic cell. It is typically the negative terminal in such cells.
Anode: The anode is the electrode in an electrochemical cell where oxidation occurs, and electrons are released to flow through an external circuit. It is the negatively charged electrode that attracts positively charged ions and initiates the flow of electrons in a redox reaction.
Cathode: A cathode is an electrode where reduction occurs during an electrochemical reaction. It plays a crucial role in various processes such as galvanic cells, where it attracts cations from the electrolyte, facilitating the flow of electric current. Understanding the function of the cathode is essential for grasping concepts like electrode potentials and energy transformations in electrochemical cells.
Cell Potential: Cell potential, also known as electrochemical potential or redox potential, is a measure of the driving force or tendency for a chemical reaction to occur in an electrochemical cell. It represents the potential difference between the two electrodes in a galvanic cell, which determines the spontaneity and direction of the redox reaction.
Cell potentials, Ecell: Cell potential, denoted as $E_{cell}$, is the measure of the electromotive force (emf) of an electrochemical cell. It represents the potential difference between the two electrodes.
Chemical thermodynamics: Chemical thermodynamics studies the interrelation of heat and work with chemical reactions or physical changes. It applies principles of thermodynamics to predict the direction and extent of chemical processes.
Concentration cell: A concentration cell is an electrochemical cell where both electrodes are made of the same material, but they are immersed in electrolytes of different concentrations. The potential difference between the two half-cells drives the electron flow.
Electrochemistry: Electrochemistry is the study of the relationship between electrical energy and chemical energy, and the interconversion between the two. It involves the study of chemical reactions that produce electricity and the use of electrical energy to drive chemical reactions.
Enthalpy: Enthalpy is a measure of the total energy of a thermodynamic system, including both the internal energy of the system and the work done by or on the system due to changes in pressure and volume. It is a key concept in understanding the energy changes that occur during chemical reactions and phase changes.
Enthalpy (H): Enthalpy (H) is the total heat content of a system at constant pressure. It is a thermodynamic property that includes internal energy and the product of pressure and volume.
Equilibrium Constant: The equilibrium constant is a quantitative measure of the extent of a chemical reaction at equilibrium. It represents the ratio of the concentrations of the products to the reactants, raised to their respective stoichiometric coefficients, and is a fundamental concept in understanding the behavior of chemical systems at equilibrium.
Equilibrium constant, K: The equilibrium constant, $K$, is a ratio that quantifies the concentrations of reactants and products in a chemical reaction at equilibrium. It provides insight into the position of the equilibrium and the extent to which reactants are converted into products.
Faraday's Constant: Faraday's constant is a fundamental physical constant that represents the amount of electric charge carried by one mole of electrons. It is a crucial parameter in electrochemical processes and is essential for understanding the relationship between electrical and chemical quantities.
Gas Constant: The gas constant, often represented by the symbol R, is a fundamental physical constant that relates the pressure, volume, amount of substance, and absolute temperature of a gas. It is a crucial parameter in the study of thermodynamics, particularly in understanding the behavior of gases and their role in processes involving potential, free energy, and equilibrium.
Gibbs Free Energy: Gibbs free energy is a thermodynamic property that combines the concepts of enthalpy and entropy to determine the spontaneity and feasibility of a chemical process. It is a crucial factor in understanding the driving forces behind chemical reactions and phase changes.
Gibbs free energy (G): Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. It is used to predict the direction of chemical reactions.
Le Chatelier's Principle: Le Chatelier's Principle states that when a system at equilibrium is subjected to a change in one of the conditions (concentration, temperature, or pressure) affecting that equilibrium, the system will shift to counteract the change and re-establish equilibrium.
Nernst Equation: The Nernst equation is a fundamental relationship in electrochemistry that describes the relationship between the reduction potential of an electrochemical half-reaction and the activities of the chemical species involved. It is a crucial tool for understanding and predicting the behavior of galvanic cells, electrode potentials, and the spontaneity of electrochemical processes.
Non-spontaneous Redox Reaction: A non-spontaneous redox reaction is a type of oxidation-reduction reaction that does not occur naturally and requires an external energy input to proceed. These reactions have a positive Gibbs free energy change, indicating that they are not thermodynamically favored to occur on their own.
Reaction Quotient: The reaction quotient, denoted as Q, is a measure of the relative concentrations of the products and reactants in a chemical reaction at any given time, regardless of whether the system has reached equilibrium or not. It is a useful tool for understanding the direction and extent of a reaction as it progresses towards equilibrium.
Reaction quotient (Q): The reaction quotient, Q, is a measure of the relative amounts of products and reactants present in a reaction mixture at any given point in time. It is calculated using the same expression as the equilibrium constant but with current concentrations or partial pressures.
Redox Reactions: Redox (reduction-oxidation) reactions are a fundamental type of chemical reaction where the transfer of electrons occurs between two or more reactants. In these reactions, one substance is oxidized (loses electrons) while another is reduced (gains electrons), maintaining the overall charge balance.
Spontaneous Redox Reaction: A spontaneous redox reaction is a type of oxidation-reduction reaction that occurs naturally without the input of external energy. These reactions involve the transfer of electrons between chemical species, resulting in a change in their oxidation states.
Standard Cell Potential: The standard cell potential, also known as the standard reduction potential, is a measure of the tendency of a chemical species to acquire electrons and be reduced. It is a fundamental concept in electrochemistry that is closely related to the free energy and equilibrium of a redox reaction.
Standard equilibrium constant: The standard equilibrium constant, represented as K° or K_eq°, quantifies the ratio of concentrations of products to reactants at equilibrium under standard conditions. It reflects the extent to which a reaction proceeds and indicates the balance between reactants and products when a system has reached its equilibrium state, highlighting the relationship between Gibbs free energy and chemical potential.
Standard Gibbs Free Energy Change: The standard Gibbs free energy change is a thermodynamic quantity that represents the maximum amount of non-expansion work that can be extracted from a chemical or physical process at constant temperature and pressure. It is a crucial concept in understanding the spontaneity and feasibility of chemical reactions and physical transformations.
Standard Reduction Potentials: Standard reduction potentials are a measure of the tendency of a chemical species to gain or lose electrons in an electrochemical reaction. They provide a quantitative assessment of the oxidizing or reducing power of a substance, which is crucial for understanding concepts like potential, free energy, and equilibrium in chemistry.
Thermodynamics: Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It describes the fundamental physical laws governing the transformation of energy and the flow of heat, which are essential to understanding the behavior of chemical systems and processes.