19.3 Electrochemical reactions and fuel cells

Electrochemical Cells

Electrochemical cells convert chemical energy into electrical energy through redox reactions. Understanding how they work connects core thermodynamic ideas (Gibbs free energy, enthalpy, entropy) to real devices like batteries and fuel cells.

Principles of Electrochemical Cells

Every electrochemical cell runs on the same basic idea: electrons transfer between chemical species through an external circuit, and that electron flow is usable electrical work.

• Oxidation occurs at the anode, where a species loses electrons (e.g., zinc dissolving: $Zn \rightarrow Zn^{2+} + 2e^-$)
• Reduction occurs at the cathode, where a species gains electrons (e.g., copper depositing: $Cu^{2+} + 2e^- \rightarrow Cu$)

The Gibbs free energy change ($\Delta G$) tells you whether the reaction is spontaneous and how much electrical work the cell can do:

• Negative $\Delta G$: the reaction is spontaneous, and the cell produces electrical work on its own. This is a galvanic (voltaic) cell.
• Positive $\Delta G$: the reaction is non-spontaneous, and you must supply electrical energy to drive it. This is an electrolytic cell.

The link between $\Delta G$ and the cell's voltage is:

$\Delta G = -nFE_{cell}$

• $n$ = number of moles of electrons transferred in the balanced reaction
• $F$ = Faraday's constant (96,485 C/mol)
• $E_{cell}$ = cell potential in volts

Notice the negative sign: a positive cell potential gives a negative $\Delta G$, confirming spontaneity.

EMF Calculation Using the Nernst Equation

Under standard conditions (1 M concentrations, 1 atm, 25 °C), you can look up the standard cell potential:

$E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}$

Both values come from tables of standard reduction potentials (measured relative to the standard hydrogen electrode, SHE, which is defined as 0.00 V).

When conditions aren't standard, the Nernst equation adjusts the cell potential:

$E_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q$

• $R$ = 8.314 J/(mol·K)
• $T$ = absolute temperature in K
• $Q$ = reaction quotient (products over reactants, each raised to their stoichiometric coefficients)

At 25 °C, this simplifies to a commonly used form:

$E_{cell} = E_{cell}^{\circ} - \frac{0.02569}{n} \ln Q$

or equivalently, using base-10 logarithms:

$E_{cell} = E_{cell}^{\circ} - \frac{0.05916}{n} \log Q$

How to use it step by step:

1. Write the balanced overall cell reaction and identify $n$.

2. Look up $E_{cathode}^{\circ}$ and $E_{anode}^{\circ}$ from a table of standard reduction potentials.

3. Calculate $E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}$.

4. Write the expression for $Q$ from the balanced reaction.

5. Plug everything into the Nernst equation to find $E_{cell}$.

Fuel Cells

Fuel cells are electrochemical devices that convert the chemical energy of a continuously supplied fuel directly into electricity. Unlike a battery, which stores a fixed amount of reactant, a fuel cell keeps running as long as fuel and oxidant are fed in.

Fuel Cell Types and Applications

All fuel cells share the same basic structure: an anode (where fuel is oxidized), a cathode (where the oxidant is reduced), and an electrolyte that allows ions to move between the two while forcing electrons through an external circuit.

The main types differ in their electrolyte material, operating temperature, and fuel flexibility:

• Proton Exchange Membrane Fuel Cells (PEMFCs)
  • Fuel: hydrogen; Oxidant: oxygen (from air)
  • Operate at relatively low temperatures (~80 °C)
  • The electrolyte is a solid polymer membrane that conducts protons ($H^+$)
  • Used in vehicles (e.g., Toyota Mirai) and portable power systems
• Solid Oxide Fuel Cells (SOFCs)
  • Fuel: hydrogen or hydrocarbons (natural gas); Oxidant: oxygen
  • Operate at high temperatures (600–1000 °C), which allows direct use of hydrocarbon fuels
  • The electrolyte is a ceramic that conducts oxide ions ($O^{2-}$)
  • Used in stationary power generation (buildings, power plants)
• Molten Carbonate Fuel Cells (MCFCs)
  • Fuel: hydrocarbons; Oxidant: oxygen
  • Operate at high temperatures (~650 °C)
  • The electrolyte is a molten carbonate salt that conducts carbonate ions ($CO_3^{2-}$)
  • Used in large-scale industrial power generation

Thermodynamics of Fuel Cell Reactions

A fuel cell's thermodynamic efficiency is the fraction of a fuel's total chemical energy that can theoretically be converted to electrical work. It's set by the ratio:

$\text{Maximum thermodynamic efficiency} = \frac{\Delta G}{\Delta H}$

• $\Delta G$ = Gibbs free energy change of the overall reaction (the maximum useful work)
• $\Delta H$ = enthalpy change of the reaction (the total chemical energy released)

Because $\Delta G = \Delta H - T\Delta S$, some energy is always "lost" to the $T\Delta S$ term. For the hydrogen fuel cell reaction ($2H_2 + O_2 \rightarrow 2H_2O$), the maximum thermodynamic efficiency at 25 °C is about 83%. That's notably higher than a typical heat engine, which is limited by the Carnot efficiency.

Factors that affect real-world efficiency:

1. Operating temperature — Higher temperatures generally improve reaction kinetics and reduce voltage losses from slow electrode reactions (activation losses). However, for some reactions the theoretical maximum efficiency actually decreases with temperature because $T\Delta S$ grows.
2. Pressure — Higher pressures push more reactant to the electrode surfaces, reducing concentration losses and slightly increasing the equilibrium cell voltage (as predicted by the Nernst equation with gas-phase $Q$).
3. Catalyst quality — Catalysts like platinum lower the activation energy for electrode reactions, reducing the voltage you "waste" getting the reaction started. Catalyst cost is a major practical barrier for PEMFCs.
4. Fuel and oxidant purity — Impurities (e.g., carbon monoxide in hydrogen feed) can poison the catalyst surface or cause unwanted side reactions, both of which lower efficiency and shorten cell life.