# Randles–Ševčík Equation

Last Updated: 10/27/20 by Random Electrochemist

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• Randles,
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• peak current,
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### 1Randles-Ševčík Equation

There are many resources that describe the detailed background, derivation, and applications of the Randles-Ševčík equation.   Here, we present just a snippet to get you started.

In a voltammetric experiment where a potential sweep is applied to the working electrode using a potentiostat (e.g., LSV or CV ), the peak current $i_p$ observed for a voltammogram follows the Randles-Ševčík equation,

$\displaystyle i_p=0.4463{\left( \frac{F^3}{RT}\right)}^{1/2}n^{3/2}AD_O^{1/2}C_O^*\upsilon^{1/2}$

where $F$ is Faraday's constant, $R$ is the universal gas constant, $T$ is the absolute temperature, $n$ is the number of electrons involved in the redox half-reaction being studied, $D_O$ is the diffusion coefficient for the redox active species, $C_O$ is the molar concentration of the redox active species, $A$ is the surface area of the electrode, and $\upsilon$ is the rate at which the potential is being swept.

The Randles-Ševčík equation is often written in an abbreviated form under the assumption that the temperature is fixed at 298.15 K (25℃).  For work at this particular temperature, the constants appearing at the beginning of the equation can be combined, allowing the equation to be written more simply as follows:

$\displaystyle i_p=(2.68648\times 10^5)n^{3/2}AD_O^{1/2}C_O^*{\upsilon}^{1/2}$

The constant appearing at the beginning of this simplified version of the equation is understood to have units (e.g., 2.69 × 105 C mol-1V-1/2).
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### 2References

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