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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

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

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

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

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
Key Term Reference
 Nernst equation
 Appears in these related concepts: Equilibrium Constant and Cell Potential and Thermodynamics of Redox Reactions
 coefficient
 Appears in these related concepts: Trinomials of the Form ax^2 + bx + c, Where a is Not Equal to 1, Balancing Chemical Equations, and Polynomials: Introduction, Addition, and Subtraction
 concentration
 Appears in these related concepts: Calculating Equilibrium Concentrations , Factors that Affect Reaction Rate, and Molarity
 electron
 Appears in these related concepts: Periods 1 through 3, The Pauli Exclusion Principle, and Overview of Atomic Structure
 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: Concentration of Cells, Electrochemical Cell Notation, and Voltaic Cells
 halfreactions
 Appears in these related concepts: Balancing Redox Equations, Predicting Spontaneous Direction of a Redox Reaction, and Standard Reduction Potentials
 mole
 Appears in these related concepts: MoletoMole Conversions, Converting between Mass and Number of Moles, and Concept of Osmolality and Milliequivalent
 reduction
 Appears in these related concepts: Anaerobiosis and N2 Fixation, Nitrogen Fixation Mechanism, and Oxidation States
 solid
 Appears in these related concepts: Viscosity, Metagenomics, and Three States of Matter
Sources
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Cite This Source
Source: Boundless. “The Nernst Equation.” Boundless Chemistry. Boundless, 21 Jul. 2015. Retrieved 22 Jul. 2015 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/electrochemistry18/cellpotentials130/thenernstequation5187510/