2.3 Thermodynamics and kinetics of electrochemical systems

Electrochemical systems are all about energy flow and reaction speed. Understanding how energy moves and changes in these systems helps us grasp how batteries and fuel cells work.

We'll look at the thermodynamics behind electrochemical reactions and explore what makes them tick. We'll also dive into reaction kinetics, which tell us how fast these reactions happen and what affects their speed.

Thermodynamics of Electrochemical Reactions

Gibbs Free Energy and Spontaneity

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• Gibbs free energy ($\Delta G$) determines the spontaneity and maximum work of an electrochemical reaction
  • Negative $\Delta G$ indicates a spontaneous reaction that can perform electrical work
  • Positive $\Delta G$ requires an input of electrical energy to drive the reaction (electrolysis)
• Gibbs free energy is related to the cell potential ($E_{cell}$) by $\Delta G = -nFE_{cell}$, where $n$ is the number of electrons transferred and $F$ is Faraday's constant
• Standard cell potentials ($E^{\circ}_{cell}$) are determined by the difference in standard reduction potentials of the half-reactions (e.g., in a Daniell cell: $Zn^{2+} + 2e^- \rightarrow Zn$ and $Cu^{2+} + 2e^- \rightarrow Cu$)

Enthalpy and Entropy Contributions

• Enthalpy change ($\Delta H$) represents the heat absorbed or released by the reaction at constant pressure
  • Exothermic reactions ($\Delta H < 0$) release heat, while endothermic reactions ($\Delta H > 0$) absorb heat
• Entropy change ($\Delta S$) represents the change in disorder or randomness of the system
  • Reactions with an increase in entropy ($\Delta S > 0$) are more favorable, as they lead to a more disordered state
• Gibbs free energy is related to enthalpy and entropy by $\Delta G = \Delta H - T\Delta S$, where $T$ is the absolute temperature

Temperature Dependence and Nernst Equation

• The cell potential depends on temperature and the concentrations of reactants and products, as described by the Nernst equation: $E_{cell} = E^{\circ}_{cell} - \frac{RT}{nF} \ln Q$
  • $Q$ is the reaction quotient, which depends on the concentrations of reactants and products
  • At equilibrium, $Q = K$ (equilibrium constant) and $E_{cell} = 0$
• Increasing temperature generally favors reactions with positive entropy change ($\Delta S > 0$) and decreases the cell potential

Electrochemical Reaction Kinetics

Reaction Rate and Activation Energy

• Reaction rate determines the current density in an electrochemical cell
  • Current density ($i$) is the current per unit area of the electrode ($A/cm^2$)
• Activation energy ($E_a$) is the minimum energy required for reactants to overcome the energy barrier and form products
  • A lower activation energy leads to a faster reaction rate
• The Arrhenius equation relates the reaction rate constant ($k$) to the activation energy: $k = A e^{-E_a/RT}$, where $A$ is the pre-exponential factor and $R$ is the gas constant

Butler-Volmer and Tafel Equations

• The Butler-Volmer equation describes the relationship between current density and overpotential ($\eta$) in an electrochemical reaction: $i = i_0 [\exp(\frac{\alpha_a nF\eta}{RT}) - \exp(-\frac{\alpha_c nF\eta}{RT})]$
  • $i_0$ is the exchange current density, $\alpha_a$ and $\alpha_c$ are the anodic and cathodic transfer coefficients, respectively
• The Tafel equation is a simplified form of the Butler-Volmer equation at high overpotentials: $\eta = a + b \log i$, where $a$ and $b$ are constants
  • Tafel plots (overpotential vs. log current density) are used to determine the exchange current density and transfer coefficients

Overpotential and Its Components

• Overpotential ($\eta$) is the additional potential required to drive an electrochemical reaction at a desired rate
  • It is the difference between the applied potential and the equilibrium potential: $\eta = E_{applied} - E_{eq}$
• Overpotential has three main components: activation overpotential ($\eta_{act}$), concentration overpotential ($\eta_{conc}$), and ohmic overpotential ($\eta_{ohmic}$)
  • Activation overpotential is related to the kinetics of the charge transfer process at the electrode-electrolyte interface
  • Concentration overpotential arises from mass transport limitations of reactants and products
  • Ohmic overpotential is due to the resistance of the electrolyte and other cell components

Factors Affecting Electrochemical Performance

Exchange Current Density and Electrode Materials

• Exchange current density ($i_0$) is a measure of the intrinsic kinetics of an electrochemical reaction
  • A higher exchange current density indicates faster reaction kinetics and lower activation overpotential
• Exchange current density depends on the electrode material, surface area, and electrolyte composition
  • Electrocatalysts (e.g., platinum for hydrogen oxidation) increase the exchange current density by lowering the activation energy
• Electrode materials should have high electrical conductivity, stability, and catalytic activity for the desired reaction

Mass Transport Limitations and Concentration Overpotential

• Mass transport of reactants and products to and from the electrode surface can limit the reaction rate
  • Diffusion, migration, and convection are the main mass transport mechanisms
• Concentration overpotential ($\eta_{conc}$) arises when the concentration of reactants at the electrode surface differs from the bulk concentration
  • It is related to the limiting current density ($i_L$), which is the maximum current density achievable under mass transport control
• Strategies to minimize concentration overpotential include increasing the electrolyte concentration, improving electrode porosity, and enhancing mass transport (e.g., by stirring or using flow cells)

Charge Transfer Kinetics and Electrode-Electrolyte Interface

• Charge transfer kinetics describe the rate of electron transfer between the electrode and the electrolyte
  • The rate of charge transfer depends on the electrode potential, reactant concentrations, and the nature of the electrode-electrolyte interface
• The electrical double layer (EDL) at the electrode-electrolyte interface plays a crucial role in charge transfer kinetics
  • The EDL consists of the Helmholtz layer (compact layer) and the diffuse layer
  • The capacitance of the EDL affects the charging current and the overall cell performance
• Strategies to improve charge transfer kinetics include modifying the electrode surface (e.g., roughening or coating), optimizing the electrolyte composition, and controlling the electrode potential