🔌Electrochemistry Unit 4 – Electrode Potentials & Nernst Equation

Key Concepts and Definitions

• Electrochemistry studies the interconversion of electrical and chemical energy in redox reactions
• Electrode potential quantifies the tendency of a half-reaction to occur at an electrode surface
• Reduction potential measures the ability of a species to gain electrons and be reduced
• Oxidation potential measures the ability of a species to lose electrons and be oxidized
• Standard electrode potential ($E^0$) is measured under standard conditions (1 M concentrations, 1 atm pressure, 25°C)
• Anode is the electrode where oxidation occurs and electrons are released
• Cathode is the electrode where reduction occurs and electrons are consumed

Electrochemical Cells and Half-Reactions

• Electrochemical cells convert chemical energy into electrical energy (galvanic) or vice versa (electrolytic)
• Consist of two half-cells, each with an electrode immersed in an electrolyte solution
  • Oxidation half-reaction occurs at the anode, releasing electrons
  • Reduction half-reaction occurs at the cathode, consuming electrons
• Half-reactions are separated by a salt bridge or porous membrane to allow ion flow and maintain charge balance
• Electrons flow from the anode to the cathode through an external circuit, generating current
• Examples of electrochemical cells include batteries (lithium-ion, lead-acid) and fuel cells (hydrogen, methanol)

Standard Electrode Potentials

• Standard electrode potentials ($E^0$) are measured relative to the standard hydrogen electrode (SHE) with an assigned potential of 0.00 V
• Reduction potentials are tabulated for various half-reactions under standard conditions
• More positive $E^0$ values indicate a greater tendency for the species to be reduced and a stronger oxidizing agent
  • Example: $F_2$ has an $E^0$ of +2.87 V, making it a strong oxidizing agent
• More negative $E^0$ values indicate a greater tendency for the species to be oxidized and a stronger reducing agent
  • Example: $Li$ has an $E^0$ of -3.04 V, making it a strong reducing agent
• The difference in standard electrode potentials determines the cell potential ($E_{cell}^0$) and the direction of spontaneous electron flow
  • $E_{cell}^0 = E_{cathode}^0 - E_{anode}^0$
  • Positive $E_{cell}^0$ values indicate a spontaneous redox reaction

Nernst Equation: Theory and Applications

• The Nernst equation relates the electrode potential to the standard electrode potential and the concentrations (or partial pressures) of the reactants and products
  • $E = E^0 - \frac{RT}{nF} \ln Q$, where $R$ is the gas constant, $T$ is the temperature, $n$ is the number of electrons transferred, $F$ is Faraday's constant, and $Q$ is the reaction quotient
• Allows for the calculation of electrode potentials under non-standard conditions
• Can be used to determine the concentration of an ion in solution or the equilibrium constant of a redox reaction
• Helps predict the direction of spontaneous electron flow and the feasibility of redox reactions
• Example: In a concentration cell, the Nernst equation determines the potential difference between two half-cells with different concentrations of the same redox couple

Measuring and Calculating Electrode Potentials

• Electrode potentials can be measured using a potentiometer or a high-impedance voltmeter
• Reference electrodes with known and stable potentials (e.g., SHE, silver/silver chloride, saturated calomel) are used to measure the potential of the working electrode
• The cell potential is the difference between the cathode and anode potentials
  • $E_{cell} = E_{cathode} - E_{anode}$
• Standard electrode potentials can be used to calculate the cell potential under standard conditions
• The Nernst equation is used to calculate the electrode potential under non-standard conditions
• Example: In a zinc-copper cell, the cell potential can be calculated using the standard reduction potentials of $Zn^{2+}/Zn$ (-0.76 V) and $Cu^{2+}/Cu$ (+0.34 V)
  • $E_{cell}^0 = E_{cathode}^0 - E_{anode}^0 = 0.34 V - (-0.76 V) = 1.10 V$

Factors Affecting Electrode Potentials

• Concentration (or partial pressure) of reactants and products affects the electrode potential according to the Nernst equation
  • Increasing the concentration of reactants or decreasing the concentration of products shifts the equilibrium to the right and increases the electrode potential
• Temperature changes affect the electrode potential by altering the equilibrium constant and the rate of electron transfer
  • Higher temperatures generally increase the electrode potential for endothermic reactions and decrease it for exothermic reactions
• pH of the solution can influence the electrode potential by affecting the concentration of H+ ions and the stability of the redox species
  • Example: The reduction potential of the $O_2/H_2O$ couple decreases by 0.059 V per unit increase in pH (at 25°C)
• Surface area and roughness of the electrode can affect the rate of electron transfer and the electrode potential
  • Larger surface areas and rougher surfaces generally increase the rate of electron transfer and the electrode potential
• Presence of complexing agents or precipitates can alter the concentration of free ions and affect the electrode potential
  • Example: The formation of a sparingly soluble salt (e.g., $AgCl$) can reduce the concentration of free ions and lower the electrode potential

Real-World Applications and Examples

• Batteries use redox reactions to store and deliver electrical energy
  • Example: In a lead-acid battery, $PbO_2$ is reduced to $PbSO_4$ at the cathode, while $Pb$ is oxidized to $PbSO_4$ at the anode
• Fuel cells generate electricity through the controlled oxidation of a fuel (e.g., hydrogen, methanol) at the anode and reduction of an oxidant (e.g., oxygen) at the cathode
  • Example: In a hydrogen fuel cell, $H_2$ is oxidized to $H^+$ at the anode, while $O_2$ is reduced to $H_2O$ at the cathode
• Corrosion of metals involves the oxidation of the metal and the reduction of an oxidizing agent (e.g., oxygen, water)
  • Example: In the corrosion of iron, $Fe$ is oxidized to $Fe^{2+}$ at the anode, while $O_2$ is reduced to $OH^-$ at the cathode
• Electroplating uses electrolysis to deposit a thin layer of a metal onto a conductive surface
  • Example: In the electroplating of silver, $Ag^+$ ions are reduced to $Ag$ metal at the cathode, while a sacrificial silver anode is oxidized to $Ag^+$
• Electrochemical sensors and biosensors detect the presence and concentration of specific analytes based on changes in electrode potential
  • Example: A glucose biosensor uses the enzyme glucose oxidase to catalyze the oxidation of glucose, generating a current proportional to the glucose concentration

Common Mistakes and Troubleshooting

• Incorrectly identifying the anode and cathode in an electrochemical cell
  • Remember: Oxidation occurs at the anode, and reduction occurs at the cathode
• Confusing the sign conventions for reduction and oxidation potentials
  • Reduction potentials are more positive for stronger oxidizing agents, while oxidation potentials are more negative for stronger reducing agents
• Neglecting to consider the stoichiometry of the redox reaction when using the Nernst equation
  • Ensure that the reaction quotient ($Q$) is raised to the power of the stoichiometric coefficients
• Failing to account for the concentration of all species involved in the redox reaction
  • Include the concentrations (or partial pressures) of both reactants and products in the Nernst equation
• Using non-standard conditions without adjusting the electrode potentials accordingly
  • Apply the Nernst equation to calculate the electrode potential under non-standard conditions
• Overlooking the presence of interfering species or side reactions that may affect the electrode potential
  • Consider the possibility of competing redox reactions or the formation of complexes or precipitates that may alter the concentration of free ions
• Improper handling or maintenance of reference electrodes
  • Ensure that reference electrodes are properly stored, cleaned, and calibrated to maintain their accuracy and stability