# Randles–Sevcik Equation Calculator

*“Inorganic Electrochemistry: Theory, Practice and Application“*The Royal Society of Chemistry (2003)See 1 more source

*“A Practical Beginner’s Guide to Cyclic Voltammetry“*Journal of Chemical Education (2018)

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**.

🔎 You can learn more about the current-voltage relationship in

.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:

- Electrochemical
**quasi-reversibility**. - 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

where:

- $A$ — Electrode surface area (
**cm**);^{2} - $C^0$ — Bulk concentration of the analyte (
**mol/cm**);^{3} - $n$ — 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 (
**cm**);^{2}/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 .