Butler–Volmer equation & Current density

At 298 K the exchange current density (i_o) of an electrode having a surface area of 5 cm², used in an electrodeposition process is 0.79 mA cm^–2.

Estimate the applied current through the electrode if the overpotential (η) is 5 mV.

 

Required formula derived from the Butler–Volmer equation is:

i = (i_o η F) / (R T)

where, ‘i’ is the applied current density (mA cm^–2)

i_o is exchange current density = 0.79 mA cm^–2

η is overpotential = 5 mV

F is Faraday = 96485 C mol^–1

R is gas constant = 8.314 J K^–1 mol^–1

T is temperature (in K) = 298 K

Current density = Current (mA) / Surface area (cm²)

Surface area = 5 cm²

 

Substituting these values in the equation, value of the applied current density is:

i = (0.79 mA cm^–2 × 5 mV × 96485 C mol^–1) / (8.314 J K^–1 mol^–1 × 298 K).

 

Since, Joule = Volt × Coulomb or J = V × C.

So, i = (0.79 mA cm^–2 × 5 mV × 96485 C mol^–1) / (8.314 V C K^–1 mol^–1 × 298 K)

 

And, 1 V = 1000 mV

i = (0.79 mA cm^–2 × 5 mV × 96485 C mol^–1) / (8.314 × 1000 mV C K^–1 mol^–1 × 298 K)

 

Hence, i = 0.15 mA cm^–2

And the applied current (mA) = Current density × Surface area.

 

So, the applied current = 0.15 mA cm^–2 × 5 cm² = 0.75 mA.

By,
Dr. M Kanagasabapathy
Associate Professor of Chemistry
Rajapalayam Rajus' College
Madurai Kamaraj University
Rajapalayam (TN) India