Lecture on Calculating Cell Potential Using the Nernst Equation

Key Equations

• Non-standard Cell Potential (E)

  • Formula: [E = E^\circ - \frac{RT}{nF} \ln Q]
  • Constants:
    • (R = 8.3145) (Universal Gas Constant)
    • (F = 96485) (Faraday's Constant in Coulombs)
  • Variables:
    • (T) = Temperature in Kelvin
    • (n) = Number of moles of electrons transferred

• Standard Cell Potential ((E^\circ))

  • Concentrations of ions = 1 mole/liter

• Simplified Equation at 298 K

  • [E = E^\circ - \frac{0.0591}{n} \log Q]

Reaction Quotient (Q)

• (Q) is the ratio of the concentrations of products to reactants.
• (Q) considers initial concentrations, not equilibrium concentrations.

Cell Potential Changes

• Comparing Non-standard and Standard Potentials:
  • If reactant concentration increases or product concentration decreases, (E > E^\circ).
  • If reactant concentration decreases or product concentration increases, (E < E^\circ).

Example Calculations

• Example 1:

  • Calculate (Q) using concentrations of (Al^{3+}) and (Cu^{2+}).
  • Determine number of electrons, (n), from half-reaction balancing.
  • Calculate (E) using given temperatures and concentrations.

• Example 2: Determining (CuSO_4) Concentration

  • Find (n) from balanced half-reactions.
  • Convert temperature to Kelvin for calculations.
  • Use the given cell potential and standard cell potential to find (Q).
  • Calculate unknown concentrations using (Q).

pH Calculation Using Cell Potential

• Find number of electrons (n) by balancing reactions.
• Use the Nernst equation to solve for (Q) and then concentration of (H^+).
• Calculate pH using the formula (\text{pH} = -\log[H^+]).

Derivation of the Nernst Equation

• Start from (\Delta G = \Delta G^\circ + RT \ln Q).
• Substituting (\Delta G = -nFE) into the equation.
• Use change of base formula for logarithms to derive different forms of the Nernst equation.

Important Points

• When non-standard conditions apply (temperatures other than 298 K), use the full form of the Nernst equation.
• Solids and pure liquids are not included in the reaction quotient.
• Ensure correct balancing of all half-reactions to find (n).
• Remember to convert all temperatures to Kelvin when using these calculations.

This lecture provides a comprehensive understanding of how to apply the Nernst equation to calculate cell potentials under various conditions. Understanding how changes in concentration affect cell potential is crucial for predicting reaction spontaneity.