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Butler-Volmer Electrochemical Kinetics Calculator

The Butler-Volmer equation is the cornerstone of modern electrode kinetics in electrochemistry.

Reversible exchange current density at zero overpotential.

Symmetry factor / charge transfer coefficient (typically 0.5).

Number of electrons in the rate-determining step.

Absolute electrolyte temperature (298.15 K = 25°C).

Electrode overpotential η = E - Eeq (positive for anodic, negative for cathodic).

Calculated Result
6.858e-1 A/m²

Net Current Density (i)

Anodic Branch Current (ia)

7.001e-1 A/m²

Cathodic Branch Current (ic)

1.428e-2 A/m²

Charge Transfer Resistance (Rct)

0.1285 Ω·m²

Tafel Anodic Slope (βa)

59.2 mV/dec

Linear Approximation (i_lin)

3.892e-1 A/m²

Calculation Breakdown

  1. Butler-Volmer Kinetic Equationi = i0·[exp(α·nFη/RT) - exp(-(1-α)·nFη/RT)]
  2. Branch Current Contributionsia = 7.00e-1 A/m², ic = 1.43e-2 A/m²
  3. Charge Transfer ResistanceRct = RT / (n·F·i0) = 0.1285 Ω·m²

What Is the Butler-Volmer Electrochemical Kinetics Calculator?

The Butler-Volmer equation describes how electrical potential across an electrode/electrolyte double layer drives electron transfer.

It accounts for both the forward (anodic) and reverse (cathodic) reaction rates simultaneously.

How Does the Butler-Volmer Electrochemical Kinetics Calculator Work?

At low overpotentials (|η| < 10 mV), the equation linearizes to Ohm’s law with charge transfer resistance Rct = RT / (n·F·i0).

At high overpotentials, the reverse term becomes negligible, reducing to the logarithmic Tafel equation.

Butler-Volmer Electrochemical Kinetics Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

i = i_0 \left[ \exp\left( \frac{\alpha n F \eta}{R T} \right) - \exp\left( -\frac{(1 - \alpha) n F \eta}{R T} \right) \right]

Fundamental Butler-Volmer activation overpotential relationship.

How to Use the Butler-Volmer Electrochemical Kinetics Calculator

  1. Specify exchange current density, transfer coefficient α, electron stoichiometry, and applied overpotential.
  2. Inspect net current density, partial currents, and charge transfer resistance.

Step-by-Step Example Calculation

Anodic Dissolution Overpotential

Input Values:

exchangeCurrentDensityA:0.05
apparentChargeTransferAlpha:0.5
numberOfElectronsTransferred:2
temperatureKelvin:298.15
overpotentialVolts:0.06
Worked Steps: Evaluates net current response and charge transfer resistance.

Understanding Your Result

A positive overpotential drives net anodic oxidation, while negative overpotential drives reduction.

Factors That Affect the Result

  • Electrocatalysts increase exchange current density i0 by orders of magnitude, lowering required overpotential.

When Should You Use This Calculator?

  • Electrochemical impedance spectroscopy (EIS), fuel cell polarization curve modeling, and battery kinetics.

Assumptions & Limitations

  • Valid for activation-controlled single-step charge transfer processes without mass transport limitations.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact microscopic formulation derived from transition state theory.

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