Electrochemistry

• Electrochemical Cells
  • Galvanic / Voltaic Cell
    • Converts Chemical Energy to Electrical Energy
    • Spontaneous Redox Reaction ($\Delta G < 0$)
    • Example: Daniell Cell
      • Anode: Zinc (Oxidation, negative electrode)
      • Cathode: Copper (Reduction, positive electrode)
      • Salt Bridge: Completes circuit, maintains electrical neutrality
  • Electrolytic Cell
    • Converts Electrical Energy to Chemical Energy
    • Non-spontaneous Redox Reaction ($\Delta G > 0$)
    • Example: Electrolysis of molten $\text{NaCl}$
• Electrode Potential & Cell Potential
  • Standard Electrode Potential ($E^\circ$)
    • Measured at 298 K, 1 bar pressure, 1 M concentration
  • Standard Hydrogen Electrode (SHE)
    • Reference electrode with assigned potential of $0.00\text{ V}$
  • Electrochemical Series
    • Arrangement of electrodes in order of increasing/decreasing $E^\circ$ values
    • Applications: Predicting spontaneity, displacing metals
  • EMF of a Cell ($E_{\text{cell}}$)
    • $E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}$ ($E_{\text{right}} - E_{\text{left}}$)
• Nernst Equation
  • Effect of Concentration and Temperature on Cell Potential
  • Mathematical Formula: $E = E^\circ - \frac{RT}{nF} \ln Q$
  • Relation with Gibbs Free Energy ($\Delta G$): $\Delta G = -nFE_{\text{cell}}$
  • Relation with Equilibrium Constant ($K_c$): $E^\circ_{\text{cell}} = \frac{RT}{nF} \ln K_c$
• Conductance in Electrolytic Solutions
  • Resistance ($R$): Measured in Ohms ($\Omega$)
  • Resistivity ($\rho$): Resistance of 1 cm cube ($R = \rho \frac{l}{A}$)
  • Conductance ($G$): Reciprocal of Resistance ($G = \frac{1}{R}$)
  • Conductivity ($\kappa$ or Kappa): Reciprocal of Resistivity ($\kappa = \frac{1}{\rho}$)
  • Molar Conductivity ($\Lambda_m$)
    • Formula: $\Lambda_m = \frac{\kappa \times 1000}{M}$
    • Units: $\text{S cm}^2 \text{ mol}^{-1}$
  • Variation with Dilution
    • Conductivity ($\kappa$) decreases (decrease in number of ions per unit volume)
    • Molar Conductivity ($\Lambda_m$) increases (due to increased dissociation/mobility)
• Kohlrausch’s Law
  • Limiting molar conductivity ($\Lambda_m^\circ$) of an electrolyte is the sum of molar conductivities of its ions
  • Applications:
    • Calculation of $\Lambda_m^\circ$ for weak electrolytes
    • Calculation of Degree of Dissociation ($\alpha$) and Dissociation Constant ($K_a$)
• Electrolysis & Faraday's Laws
  • First Law of Electrolysis
    • Mass deposited ($m$) is directly proportional to charge ($Q$): $m = ZQ = ZIt$
  • Second Law of Electrolysis
    • Masses of different substances deposited by same charge are proportional to their equivalent masses
• Commercial Cells / Batteries
  • Primary Batteries (Non-rechargeable)
    • Dry Cell (Leclanché cell): Zn-C battery
    • Mercury Cell: Used in low current devices like watches
  • Secondary Batteries (Rechargeable)
    • Lead Storage Battery: Used in automobiles (Lead anode, $\text{PbO}_2$ cathode, $\text{H}_2\text{SO}_4$ electrolyte)
    • Nickel-Cadmium (Ni-Cd) Cell
  • Fuel Cells
    • Converts energy of combustion directly to electrical energy
    • Example: Hydrogen-Oxygen Fuel Cell (used in Apollo space missions)
• Corrosion
  • Electrochemical phenomenon
  • Rusting of Iron:
    • Oxidation at anode: $\text{Fe} \rightarrow \text{Fe}^{2+} + 2e^-$
    • Reduction at cathode (in presence of $\text{O}_2$ and $\text{H}^+$): $\text{O}_2 + 4H^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$
  • Methods of Prevention: Barrier protection, sacrificial anode, galvanization, electrical protection