🔌Electrochemistry Unit 3 – Electrochemical Thermodynamics

Key Concepts and Definitions

• Electrochemistry studies the interrelation of electrical and chemical effects, focusing on the conversion between chemical and electrical energy
• Thermodynamics is the study of energy changes and the direction of spontaneous processes
• Electrochemical cells convert chemical energy into electrical energy (galvanic cells) or electrical energy into chemical energy (electrolytic cells)
• Oxidation-reduction (redox) reactions involve the transfer of electrons between species
  • Oxidation is the loss of electrons and increase in oxidation state
  • Reduction is the gain of electrons and decrease in oxidation state
• Electrodes are the sites where electrochemical reactions occur, with the anode being the site of oxidation and the cathode being the site of reduction
• Electrolytes are substances that conduct electricity when dissolved in water, allowing for the flow of ions
• Standard reduction potentials ($E^0$) measure the tendency of a species to be reduced under standard conditions (1 M concentrations, 1 atm pressure, 25°C)

Fundamentals of Thermodynamics

• First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
• Second Law of Thermodynamics indicates that the total entropy of an isolated system always increases over time, and that spontaneous processes occur in the direction of increasing entropy
• Enthalpy ($H$) is a measure of the total heat content of a system, and changes in enthalpy ($\Delta H$) can be used to determine the heat absorbed or released during a process
• Entropy ($S$) is a measure of the disorder or randomness of a system, and changes in entropy ($\Delta S$) can be used to predict the spontaneity of a process
  • Processes with positive $\Delta S$ are spontaneous, while those with negative $\Delta S$ are non-spontaneous
• Gibbs free energy ($G$) combines enthalpy and entropy to determine the spontaneity of a process at constant temperature and pressure
  • $\Delta G = \Delta H - T\Delta S$, where $T$ is the absolute temperature
  • Processes with negative $\Delta G$ are spontaneous, while those with positive $\Delta G$ are non-spontaneous
• Standard state conditions are used as a reference point for thermodynamic calculations (1 M concentrations, 1 atm pressure, 25°C)

Electrochemical Cells and Reactions

• Galvanic (voltaic) cells spontaneously convert chemical energy into electrical energy, consisting of two half-cells connected by a salt bridge or porous membrane
  • Examples include batteries (dry cells, lead-acid batteries) and fuel cells
• Electrolytic cells use an external electrical energy source to drive non-spontaneous redox reactions, often used for electrolysis and electroplating
• Half-cells are the individual compartments of an electrochemical cell, each containing an electrode and an electrolyte
  • The anode is the site of oxidation, where electrons are released
  • The cathode is the site of reduction, where electrons are consumed
• Salt bridges or porous membranes allow for the flow of ions between half-cells to maintain charge balance, while preventing the mixing of electrolytes
• Cell notation is used to represent the components of an electrochemical cell, with vertical lines (|) separating phases and double vertical lines (||) representing the salt bridge or porous membrane
  • Example: Zn(s) | Zn^2+(aq) || Cu^2+(aq) | Cu(s)
• Redox reactions in electrochemical cells involve the transfer of electrons from the anode to the cathode, with the species being oxidized at the anode and reduced at the cathode
  • The overall cell reaction can be obtained by combining the half-reactions and canceling out common terms

Nernst Equation and Cell Potentials

• The cell potential ($E_{cell}$) is the measure of the potential difference between the two electrodes in an electrochemical cell, and is a measure of the driving force for the redox reaction
• The standard cell potential ($E^0_{cell}$) is the cell potential under standard state conditions (1 M concentrations, 1 atm pressure, 25°C), and is calculated by subtracting the standard reduction potential of the anode from that of the cathode
  • $E^0_{cell} = E^0_{cathode} - E^0_{anode}$
• The Nernst equation relates the cell potential to the standard cell potential and the concentrations (or partial pressures) of the reactants and products
  • $E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln Q$, where $R$ is the gas constant, $T$ is the absolute temperature, $n$ is the number of electrons transferred, $F$ is Faraday's constant, and $Q$ is the reaction quotient
• The reaction quotient ($Q$) is the ratio of the concentrations (or partial pressures) of the products to the reactants, each raised to their stoichiometric coefficients
  • For the general reaction $aA + bB \rightleftharpoons cC + dD$, $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• The Nernst equation can be used to calculate the cell potential at non-standard conditions, predict the direction of spontaneous reaction, and determine the equilibrium constant for a redox reaction
  • At equilibrium, $E_{cell} = 0$ and $Q = K$, where $K$ is the equilibrium constant

Gibbs Free Energy in Electrochemistry

• Gibbs free energy ($G$) is a thermodynamic quantity that determines the spontaneity of a process at constant temperature and pressure
  • $\Delta G = \Delta H - T\Delta S$, where $\Delta H$ is the change in enthalpy, $T$ is the absolute temperature, and $\Delta S$ is the change in entropy
• The change in Gibbs free energy ($\Delta G$) for an electrochemical reaction is related to the cell potential ($E_{cell}$) and the number of electrons transferred ($n$)
  • $\Delta G = -nFE_{cell}$, where $F$ is Faraday's constant
• Under standard state conditions, the change in Gibbs free energy is related to the standard cell potential
  • $\Delta G^0 = -nFE^0_{cell}$
• The spontaneity of an electrochemical reaction can be determined by the sign of $\Delta G$ or $E_{cell}$
  • If $\Delta G < 0$ or $E_{cell} > 0$, the reaction is spontaneous in the forward direction
  • If $\Delta G > 0$ or $E_{cell} < 0$, the reaction is non-spontaneous in the forward direction and spontaneous in the reverse direction
• The relationship between $\Delta G$ and $E_{cell}$ can be used to calculate the equilibrium constant ($K$) for a redox reaction
  • $\Delta G^0 = -RT \ln K$, where $R$ is the gas constant and $T$ is the absolute temperature
  • Combining with $\Delta G^0 = -nFE^0_{cell}$, we get $\ln K = \frac{nFE^0_{cell}}{RT}$

Electrochemical Equilibrium

• Electrochemical equilibrium is the state in which the forward and reverse reactions of a redox process occur at equal rates, resulting in no net change in the concentrations of reactants and products
• At equilibrium, the cell potential ($E_{cell}$) is zero, and the reaction quotient ($Q$) is equal to the equilibrium constant ($K$)
  • $E_{cell} = 0$ and $Q = K$
• The Nernst equation can be used to determine the concentrations of reactants and products at equilibrium
  • For the general reaction $aA + bB \rightleftharpoons cC + dD$, $E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln \frac{[C]^c[D]^d}{[A]^a[B]^b} = 0$
• Le Chatelier's principle can be applied to predict the shift in equilibrium when changes in concentration, pressure, or temperature are applied to an electrochemical system
  • Adding a reactant or removing a product will shift the equilibrium to the right (forward reaction)
  • Adding a product or removing a reactant will shift the equilibrium to the left (reverse reaction)
• The solubility product ($K_{sp}$) is a special case of the equilibrium constant for the dissolution of a slightly soluble salt, and can be determined using the Nernst equation and the standard reduction potentials of the relevant half-reactions

Applications and Real-World Examples

• Batteries are common examples of galvanic cells, converting chemical energy into electrical energy to power devices
  • Dry cells (alkaline batteries) use a zinc anode and a manganese dioxide cathode in an alkaline electrolyte
  • Lead-acid batteries, used in vehicles, have a lead anode and a lead dioxide cathode in a sulfuric acid electrolyte
• Fuel cells are galvanic cells that convert the chemical energy from fuel (hydrogen, methanol, or other hydrocarbons) into electricity, with applications in transportation and stationary power generation
  • Proton exchange membrane (PEM) fuel cells use hydrogen as a fuel and oxygen as an oxidant, with a polymer electrolyte membrane separating the anode and cathode
• Corrosion is an electrochemical process in which a metal is oxidized by its environment, leading to degradation and material loss
  • Rusting of iron involves the oxidation of iron to iron(III) oxide in the presence of water and oxygen
  • Cathodic protection is a method to prevent corrosion by connecting the metal to be protected (e.g., underground pipelines) to a more easily oxidized "sacrificial anode" (e.g., zinc or magnesium)
• Electroplating is an electrolytic process used to deposit a thin layer of a desired metal onto a substrate, often for decorative or protective purposes
  • Examples include chrome plating of vehicle parts, gold plating of jewelry, and copper plating of printed circuit boards
• Electrolysis is the use of electrical energy to drive non-spontaneous chemical reactions, often to produce pure substances or separate compounds
  • Electrolysis of water produces hydrogen and oxygen gases, which can be used as a source of clean fuel (hydrogen) or for industrial applications (oxygen)
  • Hall-Heroult process involves the electrolysis of molten aluminum oxide (alumina) to produce pure aluminum metal

Problem-Solving Strategies

• Identify the type of electrochemical cell (galvanic or electrolytic) and the relevant half-reactions occurring at the anode and cathode
• Determine the standard reduction potentials for each half-reaction using a table of standard reduction potentials
• Calculate the standard cell potential by subtracting the standard reduction potential of the anode from that of the cathode
  • $E^0_{cell} = E^0_{cathode} - E^0_{anode}$
• Use the Nernst equation to calculate the cell potential at non-standard conditions, given the concentrations (or partial pressures) of the reactants and products
  • $E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln Q$, where $Q$ is the reaction quotient
• Determine the spontaneity of the reaction by evaluating the sign of the cell potential or the change in Gibbs free energy
  • $\Delta G = -nFE_{cell}$, where a negative value indicates a spontaneous process
• Calculate the equilibrium constant for a redox reaction using the relationship between the standard cell potential and the change in Gibbs free energy
  • $\ln K = \frac{nFE^0_{cell}}{RT}$
• Apply Le Chatelier's principle to predict the shift in equilibrium when changes in concentration, pressure, or temperature are made to an electrochemical system
• Use dimensional analysis and unit conversions to ensure that all quantities are expressed in the appropriate units (e.g., converting between volts, joules, and calories)