Electrochemical cells and fuel cells are game-changers in energy conversion. They turn chemical energy into electrical power through redox reactions, with electrons moving between electrodes. The magic happens thanks to the Gibbs free energy and cell potential.

Fuel cells take this concept further, offering clean power for various applications. From hydrogen-powered cars to natural gas-fueled power plants, these devices are reshaping our energy landscape. Their efficiency depends on factors like temperature, pressure, and catalysts.

Electrochemical Cells

Principles of electrochemical cells

• Convert chemical energy into electrical energy through redox reactions
  • Involve transfer of electrons between species
  • Oxidation releases electrons at anode (zinc electrode)
  • Reduction accepts electrons at cathode (copper electrode)
• Gibbs free energy ($\Delta G$) determines spontaneity and maximum electrical work
  • Negative $\Delta G$ indicates spontaneous reaction and positive electrical work (galvanic cell)
  • Positive $\Delta G$ indicates non-spontaneous reaction and negative electrical work (electrolytic cell)
• Relationship between $\Delta G$ and cell potential ($E_{cell}$) given by $\Delta G = -nFE_{cell}$
  • $n$ is number of electrons transferred per mole of reaction
  • $F$ is Faraday's constant (96,485 C/mol)

EMF calculation using Nernst equation

• Relates cell potential ($E_{cell}$) to standard cell potential ($E_{cell}^{\circ}$) and concentrations of reactants and products
  • Nernst equation $E_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q$
  • $R$ is universal gas constant (8.314 J/mol·K)
  • $T$ is absolute temperature (K)
  • $Q$ is reaction quotient, ratio of product concentrations to reactant concentrations raised to stoichiometric coefficients
• Standard cell potential ($E_{cell}^{\circ}$) determined by difference between standard reduction potentials of half-reactions
  • $E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}$
  • Standard reduction potentials listed in reference tables for various half-reactions (hydrogen electrode, silver chloride electrode)

Fuel Cells

Fuel cell types and applications

• Electrochemical devices convert chemical energy of fuels directly into electrical energy
• Common types
  • Proton exchange membrane fuel cells (PEMFCs)
    • Use hydrogen as fuel and oxygen as oxidant
    • Applications in transportation (vehicles) and portable power (laptops)
  • Solid oxide fuel cells (SOFCs)
    • Use hydrocarbons (natural gas) or hydrogen as fuel and oxygen as oxidant
    • Applications in stationary power generation (power plants)
  • Molten carbonate fuel cells (MCFCs)
    • Use hydrocarbons as fuel and oxygen as oxidant
    • Applications in large-scale power generation (industrial facilities)
• Consist of anode, cathode, and electrolyte
  • Fuel oxidized at anode, releasing electrons
  • Oxidant reduced at cathode, accepting electrons
  • Electrolyte allows transfer of ions between electrodes (proton exchange membrane, solid oxide, molten carbonate)

Thermodynamics of fuel cell reactions

• Efficiency determined by ratio of electrical energy output to chemical energy input
  • Efficiency = $\frac{Electrical : energy : output}{Chemical : energy : input}$
• Thermodynamic efficiency limited by Gibbs free energy change of reaction
  • Maximum thermodynamic efficiency = $\frac{\Delta G}{\Delta H}$
  • $\Delta H$ is enthalpy change of reaction
• Factors affecting efficiency
  1. Operating temperature
     • Higher temperatures improve efficiency by increasing reaction rates and reducing activation losses
  2. Pressure
     • Higher pressures increase efficiency by improving mass transport and reducing concentration losses
  3. Catalyst
     • Effective catalysts (platinum) reduce activation energy and improve reaction kinetics
  4. Fuel and oxidant composition
     • Impurities in fuel or oxidant reduce efficiency by causing side reactions or poisoning catalyst