Electrochemistry Equations

Electrochemistry equations connect chemical reactions with electrical energy, crucial for understanding processes in Physical Chemistry II. Key concepts include the Nernst equation, Gibbs free energy, and various laws that describe reaction kinetics and mass transport in electrochemical systems.

1. Nernst equation

   • Relates the cell potential (E) to the standard electrode potential (E°) and the concentrations of reactants and products.
   • Formula: E = E° - (RT/nF) ln(Q), where Q is the reaction quotient.
   • Temperature (T) and the number of electrons transferred (n) are crucial for accurate calculations.
   • Useful for predicting the direction of spontaneous reactions under non-standard conditions.

2. Gibbs free energy and cell potential relationship

   • The relationship is given by ΔG = -nFE, where ΔG is the change in Gibbs free energy, n is the number of moles of electrons, F is Faraday's constant, and E is the cell potential.
   • A negative ΔG indicates a spontaneous reaction, correlating with a positive cell potential.
   • Understanding this relationship helps in determining the feasibility of electrochemical reactions.

3. Standard reduction potentials

   • Standard reduction potentials (E°) are measured under standard conditions (1 M concentration, 1 atm pressure, 25°C).
   • They provide a reference for comparing the tendency of different species to gain electrons (be reduced).
   • The more positive the E°, the greater the species' affinity for electrons and the stronger the oxidizing agent.

4. Faraday's laws of electrolysis

   • First law: The amount of substance transformed at an electrode during electrolysis is directly proportional to the quantity of electricity passed.
   • Second law: The amounts of different substances transformed by the same quantity of electricity are proportional to their equivalent weights.
   • These laws quantify the relationship between electric charge and chemical change in electrochemical processes.

5. Butler-Volmer equation

   • Describes the current density (j) as a function of overpotential (η) in an electrochemical reaction.
   • Formula: j = j0 [exp(αaFη/RT) - exp(-αcFη/RT)], where j0 is the exchange current density, αa and αc are the anodic and cathodic transfer coefficients.
   • Essential for understanding reaction kinetics and the effects of overpotential on current flow.

6. Tafel equation

   • A simplification of the Butler-Volmer equation at high overpotentials, relating current density to overpotential.
   • Formula: η = a + b log(j), where a and b are constants specific to the reaction.
   • Useful for determining the kinetics of electrochemical reactions and estimating activation energy.

7. Fick's laws of diffusion

   • First law: The flux of a species is proportional to the concentration gradient (J = -D(dC/dx)).
   • Second law: Describes how concentration changes over time due to diffusion (∂C/∂t = D(∂²C/∂x²)).
   • Fundamental for understanding mass transport in electrochemical systems.

8. Cottrell equation

   • Describes the current response of an electrochemical cell to a step change in potential, particularly in diffusion-controlled processes.
   • Formula: I(t) = (nFAD^1/2C)/(π^1/2t^1/2), where I(t) is the current at time t, A is the electrode area, and D is the diffusion coefficient.
   • Important for analyzing transient electrochemical behavior.

9. Levich equation

   • Relates the limiting current in an electrochemical reaction to the rotation rate of the electrode and the diffusion of reactants.
   • Formula: I_lim = 0.62nFAD^2/3ω^1/2ν^−1/6, where ω is the angular velocity and ν is the kinematic viscosity.
   • Key for understanding mass transport effects in rotating disk electrodes.

10. Randles-Sevcik equation

    • Describes the peak current in cyclic voltammetry as a function of scan rate and concentration.
    • Formula: I_p = (2.69 × 10^5)n^3/2AD^1/2Cν^1/2, where I_p is the peak current, n is the number of electrons, A is the electrode area, D is the diffusion coefficient, C is the concentration, and ν is the scan rate.
    • Useful for characterizing electrochemical systems and determining kinetic parameters.