Tafel Equation: Overpotential, Tafel Slope and Exchange Current Density

By Aniket Bhardwaj · 30 October 2026 · Electrochemistry: Electrode Kinetics

The Nernst equation tells you the potential of an electrode at equilibrium. It says nothing about how fast a reaction runs when current flows. Electrode kinetics fills this gap, and the Tafel equation is its most useful working result. It appears in CSIR-NET physical chemistry, in GATE electrochemistry, and in the language of batteries, electrolysers and corrosion. This page explains each symbol and works four numericals.

Overpotential and the Butler–Volmer idea

Overpotential (η) is the extra potential applied beyond the equilibrium value to drive a reaction at a useful rate: η = E − E_eq. The current density j (current per unit area) depends on η through the Butler–Volmer equation:

j = j₀ [ exp(α_aFη/RT) − exp(−α_cFη/RT) ]

j₀ = exchange current density. At equilibrium the forward and reverse currents are equal and opposite, and each has magnitude j₀. A large j₀ means a fast, easy reaction.
α = transfer coefficient (symmetry factor), usually near 0.5 for a one-electron step. α_a + α_c = 1 for a single-step, single-electron reaction.
F = Faraday constant, 96485 C/mol; R = 8.314 J K⁻¹ mol⁻¹; T in kelvin.

The Tafel equation

When |η| is large (roughly more than 100 mV in a typical one-electron case), one exponential term becomes negligible. Taking logarithms of the remaining term gives, for the cathodic branch:

|η| = a + b log₁₀ |j| where b = 2.303 RT / (αF) and a = −b log₁₀ j₀

A plot of |η| against log₁₀|j| is a straight line. The slope is b (the Tafel slope, in V per decade of current). Extrapolating the line back to η = 0 gives log j₀ as the intercept on the log j axis. This is how j₀ is found from experiment.

Worked example 1: Tafel slope from α

Find the Tafel slope at 298.15 K for α = 0.5.

b = 2.303 × 8.314 × 298.15 / (0.5 × 96485) = 5708.7 / 48242.5 = 0.1183 V per decade, about 118 mV/decade.

A smaller α gives a larger slope. For α = 0.25 the slope would be double: about 237 mV/decade.

Worked example 2: α and j₀ from two data points

In the Tafel region (practice data at 298.15 K): |η| = 0.30 V at j = 1.0 × 10⁻³ A cm⁻², and |η| = 0.42 V at j = 1.0 × 10⁻² A cm⁻². Find the Tafel slope, α and j₀.

The current changes by exactly one decade (from 10⁻³ to 10⁻²), and η rises by 0.12 V, so b = 0.12 V/decade.

α = 2.303RT/(bF) = 5708.7 / (0.12 × 96485) = 5708.7 / 11578.2 = 0.493, about 0.5.

For j₀: η = b log(j/j₀). At the first point: 0.30 = 0.12 × log(10⁻³/j₀), so log(10⁻³/j₀) = 2.5.

log j₀ = −3 − 2.5 = −5.5, so j₀ = 10^−5.5 = 3.2 × 10⁻⁶ A cm⁻².

Worked example 3: overpotential needed for a target current

With the same line as in Example 2, find the overpotential needed to reach j = 0.10 A cm⁻².

The intercept: a = −b log j₀ = −0.12 × (−5.5) = 0.66 V.

η = a + b log j = 0.66 + 0.12 × log(0.10) = 0.66 + 0.12 × (−1) = 0.54 V.

Check from the data: from 10⁻² to 10⁻¹ is one more decade, so η = 0.42 + 0.12 = 0.54 V. It matches. Extrapolation outside the measured range should be treated with care, because mass transport and resistance can bend the line at high current.

Worked example 4: the linear region near equilibrium

For very small |η| (a few mV), the Butler–Volmer expression reduces to j ≈ j₀ Fη / RT. For j₀ = 3.16 × 10⁻⁶ A cm⁻², find j when η = 5 mV at 298.15 K.

Fη/RT = 96485 × 0.005 / (8.314 × 298.15) = 482.4 / 2478.8 = 0.1946.

j = 3.16 × 10⁻⁶ × 0.1946 = 6.1 × 10⁻⁷ A cm⁻².

Here current is proportional to η (Ohm-like), while the Tafel region is logarithmic. The two regions are different limiting cases of one equation.

Common mistakes

Using the Tafel equation near equilibrium. It needs a large η; for small η, use the linear form.
Using ln instead of log₁₀ without changing the slope. The 2.303 factor converts between them.
Confusing j₀ with the limiting current. j₀ measures the speed at equilibrium; the limiting current is set by diffusion.
Taking a smaller slope to mean a slower reaction. A smaller slope and larger j₀ both mean easier kinetics.
Dropping the unit of area. Use A cm⁻² consistently.

Exam relevance

Question type	Key step
Tafel slope from α	b = 2.303RT/(αF)
α from a plot	Measure slope, then invert
j₀ from an intercept	log j₀ = −a/b
Overpotential for a given j	η = a + b log j