7.3 Nernst equation and concentration cells

The Nernst equation helps us understand how cell potential changes when conditions aren't standard. It connects cell potential to concentrations of reactants and products, letting us predict real-world behavior in batteries and fuel cells.

Concentration cells use the same redox couple at different concentrations to generate electricity. These cells have practical applications in pH meters, sensors, and studying biological systems. Understanding their potential helps us harness concentration gradients for energy.

Nernst Equation and Cell Potential

Nernst equation for nonstandard conditions

• Relates cell potential under nonstandard conditions to standard cell potential and concentrations of reactants and products
• Nernst equation: $E_{\text{cell}} = E_{\text{cell}}^{\circ} - \frac{RT}{nF} \ln Q$
  • $E_{\text{cell}}$ represents cell potential under nonstandard conditions
  • $E_{\text{cell}}^{\circ}$ represents standard cell potential
  • $R$ represents ideal gas constant (8.314 J/mol·K)
  • $T$ represents temperature in Kelvin
  • $n$ represents number of electrons transferred in balanced redox equation
  • $F$ represents Faraday's constant (96,485 C/mol)
  • $Q$ represents reaction quotient, ratio of product concentrations to reactant concentrations raised to their stoichiometric coefficients
• Simplified Nernst equation at 25°C (298 K): $E_{\text{cell}} = E_{\text{cell}}^{\circ} - \frac{0.0592}{n} \log Q$
• Allows calculation of cell potential when concentrations deviate from standard conditions (1 M for solutes, 1 atm for gases)
• Useful for predicting cell potential in real-world applications (batteries, fuel cells)

Cell potential and thermodynamic relationships

• Cell potential ($E_{\text{cell}}$), Gibbs free energy change ($\Delta G$), and equilibrium constant ($K$) are interconnected
• Relationship between $E_{\text{cell}}$ and $\Delta G$: $\Delta G = -nFE_{\text{cell}}$
  • $n$ represents number of electrons transferred in balanced redox equation
  • $F$ represents Faraday's constant (96,485 C/mol)
• Relationship between $\Delta G$ and $K$: $\Delta G^{\circ} = -RT \ln K$
  • $R$ represents ideal gas constant (8.314 J/mol·K)
  • $T$ represents temperature in Kelvin
• Positive cell potential ($E_{\text{cell}} > 0$) indicates negative Gibbs free energy change ($\Delta G < 0$) and spontaneous reaction
• Negative cell potential ($E_{\text{cell}} < 0$) indicates positive Gibbs free energy change ($\Delta G > 0$) and nonspontaneous reaction
• Larger positive cell potential corresponds to more negative Gibbs free energy change and larger equilibrium constant, indicating greater tendency for reaction to proceed towards products
• Understanding these relationships allows prediction of reaction spontaneity and equilibrium position based on cell potential measurements

Concentration Cells

Concentration cells and applications

• Electrochemical cell where both half-cells contain same redox couple but at different concentrations
  • Half-cell with higher concentration acts as cathode
  • Half-cell with lower concentration acts as anode
• Electrons flow from anode to cathode, driven by concentration difference
• Applications of concentration cells include:
  • Measuring concentration of ions in solution (pH meters)
  • Determining solubility product of sparingly soluble salts (silver chloride)
  • Studying behavior of ions in biological systems (nerve impulse transmission)
  • Developing sensors for environmental monitoring and medical diagnostics (glucose sensors)
• Concentration cells provide a means to convert chemical energy into electrical energy based on concentration gradients

Potential calculation of concentration cells

• Potential of concentration cell calculated using modified Nernst equation
• Concentration cell potential: $E_{\text{cell}} = \frac{RT}{nF} \ln \frac{[\text{X}]_{\text{cathode}}}{[\text{X}]_{\text{anode}}}$
  • $R$ represents ideal gas constant (8.314 J/mol·K)
  • $T$ represents temperature in Kelvin
  • $n$ represents number of electrons transferred in balanced redox equation
  • $F$ represents Faraday's constant (96,485 C/mol)
  • $[\text{X}]_{\text{cathode}}$ and $[\text{X}]_{\text{anode}}$ represent concentrations of redox species in cathode and anode half-cells, respectively
• Simplified concentration cell potential equation at 25°C (298 K): $E_{\text{cell}} = \frac{0.0592}{n} \log \frac{[\text{X}]_{\text{cathode}}}{[\text{X}]_{\text{anode}}}$
• Potential of concentration cell depends only on concentration ratio of redox species in two half-cells
• Independent of standard reduction potentials of half-reactions
• Allows determination of unknown concentrations by measuring cell potential and knowing one concentration (electrolyte concentration in lead-acid batteries)