Electrochemistry is a complex science that has multiple concepts and equations to remember. In this post, we have gathered the top 10 equations in electrochemistry used daily in the lab so that you can use it as a cheat sheet when you need it.
Top 10 Equations in Electrochemistry
1. The Nernst Equation
You probably have guessed that the Nernst equation would get in the top 10 list of equations in electrochemistry. And the truth is that is probably the most used in labs all over the world daily – even by non-electrochemists!
This equation describes the potential of an electrochemical cells based on the reduction potential and concentration of redox species in a solution.
It has numerous applications in energy, electrolysis and sensing. But it is perhaps most known for its application in ion-selective electrodes like the pH meter.
Where:
E is the cell potential in V,
E0 is the standard cell potential in V
R is the gas constant, 8.314 J/Kmol,
T is the temperature in K,
n is the number of electrons involved in the reaction
F is the Faraday constant, 96485 C/mol
Q is the reaction quotient, which describes the ratio of the product of the reaction to the reactants and is dimensionless
2. The Cottrell Equation
The second equation to hit our top 10 equations in electrochemistry is the Cottrell equation.
We have decided to give it the 2nd position on our top 10 because of its versatility and common use in experiments. Especially with SPEs.
The Cottrell equation describes the current-time transient in potentiostatic experiments in what is known as “depletion conditions”. That is, when the concentration redox molecule being oxidised or reduced decays as a result of the electrochemical reaction.
This equation has multiple applications in electrodeposition, fuel cells and biosensors.
Where:
i is the current in A,
n is the number of electrons in the reduction or oxidation reaction of the analyte,
F is the Faraday Constant, 96485 C/mol,
A is the area of the planar electrode in cm2 ,
C0 is the initial concentration of the analyte being reduced or oxidized,
D is the diffusion coefficient for the analyte in cm2/s,
3. Faraday’s Law of Electrolysis
Ever wondered how to quantify the amount of material deposited or stripped during an electrolysis reactions? You can do so with Faraday’s Law of Electrolysis, our number 3 in the top 10 equations in electrochemistry.
Faraday’s Law of electrolysis describes the relationship between the total charge passed during electrolysis and the amount of mass deposited or dissolved during electrolysis.
Where:
m is the mass deposited or dissolved during electrolysis in g,
M is the atomic mass of the chemical species being deposited or dissolved in g/mol
Q is the total electric charge passed during electrolysis in C,
F is Faraday’s Constant, 96485 C/mol,
and n is the number of electrons involved in the reaction.
4. The Tafel Equation
Next on our list of the top 10 equations in electrochemistry is the Tafel equation.
The Tafel equation is perhaps the most commonly used expression to describe electrochemical kinetics.
While it is often used in the study of corrosion, it can also be used for studying electrode reaction kinetics, fuel cells and batteries.
Where:
η is the overpotential in V,
A is the Tafel slope in V,
i is the current density in A/m2 ,
and i0 is the exchange current density in A/m2 .
The +/- sign in the equation describes whether the analysis is an anodic (+) or cathodic (-) process.
5. Corrosion rate
While there are several ways to calculate corrosion rates, none is faster than the electrochemical corrosion rate calculation. For this reason, this equation is in our top 5 equations in electrochemistry.
Traditional methods for measuring corrosion, while accurate, can take anything from weeks to years before results are obtained. But with electrochemistry, they can be obtained within a few hours or even minutes!
The results from electrochemical corrosion studies can then be turned into corrosion rates with the equation below:
Where:
i is the corrosion current, which can be obtained from the Tafel equation, the Butler-Volmer equation or the Stern-Geary equation,
M is the atomic mass in g/mol
n is the number of electrons of the corrosion reaction
F is Faraday’s constant 96485 C/mol
ρ is the density of the material being corroded in g/cm3
and A is the exposed area in cm2
6. Diffusion Layer Thickness Equation
The next equation of our top 10 equations in electrochemistry is often missed during experimental design, but can certainly help troubleshoot when problems arise: the diffusion layer thickness equation.
The diffusion layer thickness is a critical physical parameters that influences the total amount of molecules that can be either oxidized or reduced. As such, it is of utmost importance in electrodeposition, sensing and energy storage/generation.
It can be calculated as follows:
where:
l is the diffusion layer thickness in cm,
D is the diffusion coefficient of the analyte/reactant, in cm2/s
and t is time in s.
7. Randles-Sevcik Equation
Number 7 in our list of top equations in electrochemistry is the Randles-Sevcik equation.
The Randles-Sevcik equation describes the behavior of a reduction/oxidation reaction in linear sweep potentiometry. It explains the relationship between the peak current, the surface area of the electrode, the concentration of the redox species and the scan rate used for collectinf the data.
This equation has been used to characterize electrode materials as well as novel redox molecules. But its applications go beyond, and can certainly help in the development of sensing devices and surface coatings.
Where:
ip is the peak current of the redox reaction in the voltammogram in A
n is the number of electrons of the reaction
F is Faraday’s Constant, 96485 C/mol
A is the surface area of the working electrode in cm2
C is the concentration of the redox species in mol/cm3
v is the scan rate used to collect the voltammogram in V/s
D is the diffusion coefficient of the redox species in cm2/s
R is the Gas Constant 8.3144 J/molK
and T is the temperature in K
8. The Anson Equation
While most may not agree to have the Anson Equation in the top 10 equations in electrochemistry due to its connections to the Cottrell equation, we think that its applicability grants it its well-deserved spot.
The Anson equation describes the relationship between charge and time in experiments where a constant potential is applied in depletion conditions.
Monitoring charge-time transients has a great importance in electrodeposition/electrostripping, electrochemical energy storage and sensors, and its used daily in industry.
where:
Q is the charge in Coulombs,
n is the number of electrons involved in the oxidation or reduction reaction,
F is Faraday’s Constant, 96485 C/mol,
A is the area of the planar electrode in cm2 ,
C is the initial concentration of the analyte being reduced or oxidized, in mol/cm3,
D is the diffusion coefficient for the analyte in cm2/s,
and t is the time in seconds.
9. The Butler-Volmer Equation
In the 9th position of our top 10 equations in electrochemistry we have the Butler-Volmer equation.
Similar to the Tafel equation, the Butler-Volmer equation describes the relationship between the current passing through an electrode and the potential applied to it in electrochemistry experiments. However, the latter is a more complete expression and thus applicable to more complex systems.
While not as straightforward to use as the previous ones described in this list, the Butler-Volmer equation is used mainly in the modeling and analysis of batteries and corrosion.
Where:
i is the current passing through the electrode in A,
i0 is the exchange current density in A,
αf and αr are the forward (anodic) and reverse (cathodic) transfer coefficients in dimensionless units,
E is the potential difference across the electrode in V,
E0 is the equilibrium potential in V,
n is the number of electrons involved in the reaction,
F is Faraday’s constant, 96485 C/mol,
R is the gas constant, 8.314 J/Kmol
and T is the temperature in K.
10. The Stern-Geary Equation
Finally, in the last position of our top 10 equations in electrochemistry we have the Stern-Geary Equation.
The Stern-Geary equation, like the Tafel equation and the Butler-Volmer equation, is a model to describe corrosion processes using an electrochemical approach. In this case, however, it describes the relationship between the corrosion current of a system and the polarisation resistance instead of the potential.
Where:
icorr is the corrosion current in mA,
Rpol is the polarisation resistance in Ω,
βanodic is the anodic Tafel slope in mV/decade,
βcathodic is the cathodic Tafel slope in mV/decade
To sum up, these are the top 10 equations in electrochemistry that every electrochemist should know about. While there are certainly other important equations in electrochemistry, the ones that we made the top 10 are the most used on a day to day basis.
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