Formula in electrochemistry is the Nernst Equation support in figuring out an electrochemical cell’s electrode potential in unusual circumstances. It shows that how temperature, the concentration of the reactive species, and the cell potential and standard cell potential relate to one another.
Preamble of Nernst Equation
The electrode potential in an electrochemical cell is the potential difference between two electrodes. Temperature and the ion concentration in the solution are two examples of variables that affect this potential.
When the parameters differ from the normal conditions (1M concentration, 1 atm pressure, and 298K temperature), we may determine the electrode potential using the Nernst Equation, which was developed by the German scientist Walther Nernst.
The idea of Gibbs free energy and how it relates to electrical work is the basis for the equation.
Nernst Equation: Mathematical Expression
The Nernst equation is expressed as: E = E0− RT / nF ln Q
Where:
E = Electrode potential under given conditions (V)
E0 = Standard electrode potential (V)
R = Universal gas constant (8.314 J/mol·K)
T = Temperature in Kelvin (K)
n = Number of electrons transferred in the redox reaction
F = Faraday’s constant (96,485 C/mol)
Q = Reaction quotient, which represents the ratio of the concentration of products to reactants.
Since logarithms are commonly expressed in base 10, we can rewrite the equation as:
E = E0 − 0.0591 / n log Q (at 298K)
This form is particularly useful for solving numerical problems at standard room temperature (25°C or 298K).
Reaction Quotient (Q)
The reaction quotient Q is defined as:
Q = [Products]coefficients / [Reactants]coefficients
For example, in the redox reaction: Zn2 + 2e−→ Zn
The reaction quotient is: Q = [Zn2+] / [Zn]
Since solid Zn has an activity of 1, the equation simplifies to:
Q = [Zn2+]
This means that the electrode potential depends on the concentration of Zn²⁺ ions.
Application of Nernst Equation to Electrochemical Cells
For a complete electrochemical cell, the cell potential can be calculated by using equation: Ecell = Ecathode − Eanode
Using the Nernst equation, we can determine the cell potential at any concentration or temperature.
For example, in a Daniell cell:
Zn + Cu2 + → Zn2 + Cu
The standard cell potential is:
E0cell = E0cathode− E0anode
Substituting the values:
E0cell = (+0.34V) − (−0.76V) = + 1.10V
Using the Nernst equation:
Ecell = E0cell − 0.0591 / n log Q
Ecell = 1.10 − 0.0591 / 2 log [Zn2+] / [Cu2+]
This equation helps in determining the cell potential for different ion concentrations.
Importance of the Nernst Equation
Cell Potential Prediction: The formula helps in figuring out an electrochemical cell’s potential under unusual circumstances.
pH Determination: The Nernst equation, which is helpful in measuring pH, is used to compute the hydrogen electrode potential.
Concentration Cells: The Nernst equation can be used to evaluate cells with identical electrodes but different ion concentrations.
Biological Redox Reactions: The equation is used in biological systems such as ATP (Adenosine triphosphate is a nucleoside triphosphate that provides energy to drive and support many processes in living cells, such as muscle contraction, nerve impulse propagation, and chemical synthesis.) production and nerve signal transmission. Formula: C10H16N5O13P3
Design of Batteries and Fuel Cells: It aids in maximising battery and fuel cell performance.
Limitations of the Nernst Equation
The equation makes the assumption that optimal behavior will occur, which may not necessarily be the case for actual solutions.
Activity Rather than Concentration: Using ion activity rather than concentration improves the equation’s accuracy.
High Dilution Restrictions: Ion interactions cause deviations at very low concentrations.
Summary:-
An essential tool in electrochemistry is the Nernst Equation enables us to compute electrode potentials under a variety of circumstances. It can be used for everything from measuring pH to know the battery performance. Despite certain drawbacks, it is on the other hand a basic equation for examining redox reactions and electrochemical cells.
Note:- Relation between free energy and cell potential:
Types of reaction | DeltaG | E | Types of cell |
Spontaneous | -ve | +ve | Galvanic |
Non-Spontaneous | +ve | -ve | Electrolytic |
Equilibrium | 0 | 0 | Dead battery |
A mathematical method known as the Nernst Equation is used to determine the electrode potential of an electrochemical cell or half-cell in unusual circumstances. It is significant because it takes into consideration how temperature and ion concentration affect cell potential.
The Nernst Equation is: E = E0 − RT / nF ln Q
At 298K (25°C), it simplifies to: E = E0 − 0.0591 / n log Q
where E is the electrode potential, E0 is the standard electrode potential, n is the number of electrons transferred, and Q is the reaction quotient.
Temperature affects the term RT / nF in the equation. As temperature increases, the value of this term increases, impacting the overall cell potential. This means that electrode potentials vary with changes in temperature.
The ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient, is known as the reaction quotient Q. It helps in figuring out how much a reaction has deviated from equilibrium.
The hydrogen electrode potential is given by:
E = E0 − 0.0591 / n log [H+]
Since pH is defined as pH = −log[H+], the Nernst Equation is useful in measuring pH values in electrochemical systems.
It makes the assumption that ions in solution behave optimally.
It may not be accurate for highly concentrated solutions because it relies on concentration rather than activity.
Interactions between ions in less-than-ideal solutions are not taken into consideration.