Warburg coefficient

The Warburg coefficient (or Warburg constant; denoted or ) is the diffusion coefficient of ions in solution, associated to the Warburg element, . The Warburg coefficient has units of

The value of can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance () against the reciprocal of the square root of the angular frequency (). This relation should always yield a straight line, as it is unique for a Warburg.

Alternatively, the value of can be found by:

where

• is the ideal gas constant;
• is the thermodynamic temperature;
• is the Faraday constant;
• is the valency;
• is the diffusion coefficient of the species, where subscripts and stand for the oxidized and reduced species respectively;
• is the concentration of the and species in the bulk;
• is the concentration of the electrolyte;
• denotes the surface area;
• denotes the fraction of the and species present.

The equation for applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.

References