Warburg coefficient

The Warburg coefficient (or Warburg constant), formula_1, is the diffusion coefficient of ions in solution, associated to the Warburg element, formula_2. The Warburg coefficient, formula_1, also written as, formula_4, has the units of formula_5
The value of formula_1 can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance (formula_7) against the reciprocal of the square root of the frequency (formula_8). This relation should always yield a straight line, as it is unique for a Warburg.
Alternatively, the value of formula_1 can be found by:
formula_10
where formula_7 is the ideal gas constant, formula_12 is the thermodynamic temperature, formula_13 is the Faraday constant, formula_14 is the valency, formula_15 is the diffusion coefficient of the species where subscripts formula_16 and formula_7 stand for the oxidized and reduced species respectively, formula_18 is the concentration of the formula_16 and formula_7 species in the bulk, C is the concentration of the electrolyte, formula_21 denotes the surface area and formula_22 denotes the fraction of the formula_7 and formula_16 species present.
The equation for formula_1 applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.