Warburg coefficient

The Warburg coefficient (or Warburg constant; denoted Template:Math or Template:Mvar) is the diffusion coefficient of ions in solution, associated to the Warburg element, Template:Math. The Warburg coefficient has units of $\mathrm{\Omega }/\sqrt{\text{seconds}}=\mathrm{\Omega }{s}^{-1/2}$

The value of Template:Math can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance (Template:Mvar) against the reciprocal of the square root of the frequency ($1/\sqrt{\omega }$). This relation should always yield a straight line, as it is unique for a Warburg.

Alternatively, the value of Template:Math can be found by:

$$A_W=\frac{RT}{A{n}^2{F}^2\sqrt{2}}(\frac{1}{C_{\mathrm{O}}^b\sqrt{D_{\mathrm{O}}}}+\frac{1}{C_{\mathrm{R}}^b\sqrt{D_{\mathrm{R}}}})=\frac{RT}{A{n}^2{F}^2\mathrm{\Theta }C\sqrt{2D}}$$

where

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

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

References

• Template:Cite book

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