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The Nernst Equation
In electrochemistry, the Nernst equation can be used to determine the reduction potential of an electrochemical cell.
Learning Objective

Recall the Nernst equation
Key Points
 In electrochemistry, the Nernst equation can be used to determine the reduction potential of a halfcell in an electrochemical cell.
 The Nernst equation can also be used to determine the total voltage (electromotive force) for a full electrochemical cell.
 The Nernst equation gives a formula that relates the numerical values of the concentration gradient to the electric gradient that balances it.
Terms

electromotive force
Voltage generated by a battery or by a varying magnetic field.

voltage
The amount of electrostatic potential between two points in space.

electrochemical cell
A container containing an electrolyte and two electrodes; used to produce direct current electricity. One or more of them constitute a battery.

electrochemistry
The science of the chemistry associated with the flow of electricity, especially at the surface of an electrode.
Full Text
In electrochemistry, the Nernst equation can be used, in conjunction with other information, to determine the reduction potential of a halfcell in an electrochemical cell. It can also be used to determine the total voltage, or electromotive force, for a full electrochemical cell. It is named after the German physical chemist who first formulated it, Walther Nernst.
Electrochemical cell
Schematic of an electrochemical cell.
The Nernst equation gives a formula that relates the electromotive force of a nonstandard cell to the concentrations of species in solution:
In this equation:
 E is the electromotive force of the nonstandard cell
 E^{o} is the electromotive force of the standard cell
 n is the number of moles of electrons transferred in the reaction
ln Q is the natural log of
Example
Find the cell potential of a galvanic cell based on the following reduction halfreactions where [Ni^{2+}] = 0.030 M and [Pb^{2+}] = 0.300 M.
Ni^{2+} + 2 e → Ni, E^{0} = 0.25 V
Pb^{2+} + 2 e → Pb, E^{0} = 0.13 V
First, find the electromotive force for the standard cell, which assumes concentrations of 1 M.
In order for this reaction to run spontaneously (positive E^{o} cell) the nickel must be oxidized and therefore its reaction needs to be reversed. The added halfreactions with the adjusted E^{0} cell are:
The number of moles of electrons transferred is 2 and Q is
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Key Term Reference
 Nernst equation
 Appears in these related concepts: Concentration of Cells and Thermodynamics of Redox Reactions
 coefficient
 Appears in these related concepts: Factoring General Quadratics, What Are Polynomials?, and Introduction to Variables
 concentration
 Appears in these related concepts: Calculating Equilibrium Concentrations , Molarity, and Diffusion
 electron
 Appears in these related concepts: Periods 1 through 3, Electrolytic Properties, and Microscopy
 galvanic cell
 Appears in these related concepts: Free Energy and Cell Potential, Predicting the Products of Electrolysis, and Electrolytic Cells
 halfcell
 Appears in these related concepts: Equilibrium Constant and Cell Potential, Electrochemical Cell Notation, and Voltaic Cells
 halfreactions
 Appears in these related concepts: Predicting Spontaneous Direction of a Redox Reaction, Balancing Redox Equations, and Predicting if a Metal Will Dissolve in Acid
 mole
 Appears in these related concepts: Converting between Mass and Number of Moles, Molar Mass of Compounds, and Concept of Osmolality and Milliequivalent
 reduction
 Appears in these related concepts: Balancing Redox Equations, Anaerobiosis and N2 Fixation, and Electron Donors and Acceptors in Anaerobic Respiration
 solid
 Appears in these related concepts: Types of Synthetic Organic Polymers, Metagenomics, and Three States of Matter
Sources
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Cite This Source
Source: Boundless. “The Nernst Equation.” Boundless Chemistry. Boundless, 26 May. 2016. Retrieved 26 Jul. 2016 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/electrochemistry18/cellpotentials130/thenernstequation5187510/