# Randles–Sevcik Equation Calculator

Created by Luis Fernando
Reviewed by Davide Borchia
Based on research by
Piero Zanello Inorganic Electrochemistry: Theory, Practice and Application The Royal Society of Chemistry (2003)See 1 more source
Noémie Elgrishi, Kelley J. Rountree, Brian D. McCarthy, Eric S. Rountree, Thomas T. Eisenhart, and Jillian L. Dempsey A Practical Beginner’s Guide to Cyclic Voltammetry Journal of Chemical Education (2018)
Last updated: Jul 01, 2022

Welcome to our Randles-Sevcik equation calculator, where you'll be able to calculate any of the variables of that formula.

Of course, the Randles-Sevcik equation units are interchangeable, and you can, for example, use meters instead of centimeters as long as you keep dimensional homogeneity.

The calculation of this equation has different applications:

• As we'll see in the next section, the calculation of the Randles-Sevcik equation can help us distinguish whether an analyte is freely diffusing or absorbed in an electrode.
• We can also use the Randles-Sevcik equation to find the diffusion coefficient of the oxidized analyte.
• If we want to know if our electrochemical process is irreversible, the Randles-Sevcik equation can give insights into that: you will learn how the Randles-Sevcik plot describes such processes.

If you're interested in other handy tools from chemistry, our fret efficiency calculator offers a quick estimation of the resonance energy transfer efficiency and critical distance from the spectral overlap and other known parameters.

## The role of the Randles-Sevcik equation in electrochemistry.

Electrochemistry is the branch of physical chemistry that, using electrodes, studies the relationship between chemical reactions and electricity. Within this branch, we can find different methods to perform that study: voltammetry is the most common one, in which we study current as a function of applied potential in the electrodes. This current-voltage relationship is represented using a graph called voltammogram.

We can find different types of voltammetry, but we will focus on the cyclic voltammetry. In cyclic voltammetry, we apply an increasing and decreasing cyclic potential over time, as in the following image:

The voltammogram generated in this process is called cyclic voltammogram and typically has this form:

As long as the process is reversible and involves freely diffusing redox species, the previous plot will correspond to the Randles-Sevcik equation.

If you want to learn more about electrochemistry, our Nernst equation calculator can be of great help.

## Can I use the Randles-Sevcik equation for irreversible processes?

The calculation of the Randles-Sevcik equation applies only to reversible processes. To be more precise, this equation is valid for electrochemically reversible electron transfer processes that involve freely diffusing redox species.

As you can note from the equation, the Randles-Sevcik plot of $i_{\text{p}}$ vs. $v^{1/2}$ should be linear, and a deviation from this linearity can indicate two things:

1. Electrochemical quasi-reversibility.
2. Electron transfer occurs not via free diffusion but through surface-absorbed species.

## How to calculate the Randles-Sevcik equation, and its units.

The following one is the Randles-Sevcik equation and its units

$\footnotesize i_{\text{p}} = 0.4463\ A\ C^0 \left(\frac{n^3\ F^3\ v\ D_0}{R\ T}\right)^{1/2}$

where:

• $A$ — Electrode surface area (cm2);
• $C^0$ — Bulk concentration of the analyte (mol/cm3);
• $n$ — Number of electrons transferred in the redox event;
• $F$ — Faraday's constant (C/mol);
• $v$ — Scan rate (V/s);
• $D_0$ — Diffusion coefficient of the oxidized analyte (cm2/s);
• $R$Ideal gas constant (J/(mol K)); and
• $T$ — Absolute temperature (K).

🔎 The Randles-Sevcik equation derivation relies on applying the Laplace transform to the second Fick's law. You can consult the Randles-Sevcik equation derivation in the work of .

Luis Fernando
Electrode suface area (A)
in²
Concentration (C⁰)
mM
Electrons involved (n)
Scan rate (v)
V/s
Diffusion coefficient (D₀)
cm²
/s
Temperature (T)
°F
Maximum current (iₚ)
µA
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