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Physical law in electrochemistry
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction
Nernst_equation
Equation used to calculate the electromigration of ions in a fluid
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends
Nernst–Planck_equation
German physical chemist (1864–1941)
1920 Nobel Prize in Chemistry. He is also known for developing the Nernst equation in 1887. He studied physics and mathematics at the University of Zurich
Walther_Nernst
Type of thermodynamic potential
the equilibrium constant and reaction quotient for that reaction (Nernst equation), where Δ r G {\displaystyle \Delta _{\mathrm {r} }G} , Gibbs free
Gibbs_free_energy
Plot of thermodynamically stable phases of an aqueous electrochemical system
respect to the standard hydrogen electrode (SHE) as calculated by the Nernst equation. The "H" stands for hydrogen, although other standards may be used
Pourbaix_diagram
Reference redox electrode used under standard conditions
lower for more concentrated solutions. As the general form of the Nernst equation at equilibrium is the following: E cell = E cell ⊖ − R T z F ln K
Standard_hydrogen_electrode
Generalization of the Nernst equation for the membrane potential
}{z}}\log {\frac {X_{o}}{X_{i}}}&\end{aligned}}} which is the Nernst equation. Goldman's equation seeks to determine the voltage Em across a membrane. A Cartesian
Goldman_equation
Measure of the tendency of a substance to gain or lose electrons
global combined equation no longer contains electrons. The E h {\displaystyle E_{h}} and pH of a solution are related by the Nernst equation as commonly represented
Reduction_potential
Branch of physical chemistry
chemical reaction producing the voltage. He constructed an equation, known as Nernst equation, which related the voltage of a cell to its properties. In
Electrochemistry
Equation characterising electrochemical kinetics
large changes in current. Advanced Simulation Library Nernst equation Goldman equation Tafel equation For example, if the mass transfer rate is due to diffusion
Butler–Volmer_equation
Standard apparent reduction potentials (E°') in biochemistry at pH 7
ratio of the reduced (Red) and oxidized (Ox) forms according to the Nernst equation and the thermal voltage. When an oxidizer (Ox) accepts a number z of
Table of standard reduction potentials for half-reactions important in biochemistry
Table_of_standard_reduction_potentials_for_half-reactions_important_in_biochemistry
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Equation used in cyclic voltammetry
the species at the electrode surface is also changed, as set by the Nernst equation. Therefore, a faster voltage sweep causes a larger concentration gradient
Randles–Sevcik_equation
Expression of the ionic flux across a cell membrane
most accurately defined by the Nernst–Planck equation and the GHK flux equation is a solution to the Nernst–Planck equation with the assumptions listed below
Goldman–Hodgkin–Katz flux equation
Goldman–Hodgkin–Katz_flux_equation
Equation relating the rate of an electrochemical reaction to the overpotential
potential as well. The Tafel equation can be also written as: where n is the number of electrons exchanged, like in the Nernst equation, k is the rate constant
Tafel_equation
Electrochemical device
charged. Actual half-cell potentials must be calculated by using the Nernst equation as the solutes are unlikely to be in their standard states: E h a
Galvanic_cell
Measure of the level of acidity or basicity of an aqueous solution
measure pH, respond to activity. The electrode potential, E, follows the Nernst equation for the hydrogen cation, which can be expressed as: E = E 0 + R T F
PH
Early 20th century thermochemistry theory
{\displaystyle \lim _{T\to 0}\Delta S=0} The above equation is a modern statement of the theorem. Nernst often used a form that avoided the concept of entropy
Nernst_heat_theorem
Physical constant equivalent to the Boltzmann constant, but in different units
in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The gas constant is
Gas_constant
Electric potential difference between interior and exterior of a biological cell
Functions of the Cell Membrane Nernst/Goldman Equation Simulator Nernst Equation Calculator Goldman-Hodgkin-Katz Equation Calculator Electrochemical Driving
Membrane_potential
Simple battery made with a lemon for educational purposes
from the cell was reduced as predicted using the Nernst equation for the model. The Nernst equation essentially says how much the voltage drops as more
Lemon_battery
Data values of standard electrode potential
Variations from these ideal conditions affect measured voltage via the Nernst equation. Electrode potentials of successive elementary half-reactions cannot
Standard electrode potential (data page)
Standard_electrode_potential_(data_page)
Physical constant relating particle kinetic energy with temperature
voltage is also important in plasmas and electrolyte solutions (e.g. the Nernst equation); in both cases it provides a measure of how much the spatial distribution
Boltzmann_constant
Technique in chemistry and manufacturing
the difference of the electrode potentials as calculated using the Nernst equation. Applying additional voltage, referred to as overpotential, can increase
Electrolysis
Method of analyzing electrochemical reactions
quotient This equation describes how the changes in applied potential will alter the concentration ratio. However, the Nernst equation is limited, as
Voltammetry
Static membrane potential in biology
This equation resembles the Nernst equation, but has a term for each permeant ion. Also, z has been inserted into the equation, causing the intracellular
Resting_potential
Membrane potential at which ionic current reverses
PMID 5119107. S2CID 34404730. Nernst/Goldman Equation Simulator Nernst Equation Calculator Goldman-Hodgkin-Katz Equation Calculator Electrochemical Driving
Reversal_potential
Mathematical function, inverse of an exponential function
scientific formulas, such as the Tsiolkovsky rocket equation, the Fenske equation, or the Nernst equation. Scientific quantities are often expressed as logarithms
Logarithm
voltage (minimum voltage required to drive the reaction) is given by the Nernst equation: E = − Δ G n F = Δ G R e d − Δ G O x n F {\displaystyle E=-{\frac {\Delta
Thermoneutral_voltage
Reference electrode
E_{{\ce {Hg2Cl2/Hg, Cl-}}}^{0}=+0.27\ {\ce {V}}.\\\end{cases}}} The Nernst equation for the balanced reaction is: E cell = E 1 2 cathode − E 1 2 anode
Saturated_calomel_electrode
Measuring electric potential of a solution as titrant is added
of Mn+ changes, the Ecell changes correspondingly according to the Nernst equation. Thus the potentiometric titration involve measurement of Ecell with
Potentiometric_titration
Equation in Brownian motion
expressions of the equivalent conductivity of an electrolyte the Nernst–Einstein equation is derived: Λ e = z i 2 F 2 R T ( D + + D − ) . {\displaystyle
Einstein relation (kinetic theory)
Einstein_relation_(kinetic_theory)
Any process that modulates the potential difference across a post-synaptic membrane
potentials and the membrane's permeability to each ion. The Nernst equation and Goldman equation can calculate membrane potential differences based on ion
Postsynaptic_potential
Expression of monatomic ideal gas entropy
The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. It is named for Hugo Martin Tetrode (1895–1931) and Otto Sackur
Sackur–Tetrode_equation
Electro-chemical device
1996. doi:10.1038/s41598-025-31696-6. PMC 12808214. PMID 41372487. "Nernst Equation". Chemistry LibreTexts. October 2, 2013. Retrieved February 8, 2026
Electrochemical_cell
Type of electrochemical cell
in the liquid phase. Cell voltage is chemically determined by the Nernst equation and ranges, in practical applications, from 1.0 to 2.43 volts. The
Flow_battery
Fuel cell that produces electricity by oxidization
voltage E m a x {\displaystyle E_{max}} = maximum voltage given by the Nernst equation i m a x {\displaystyle i_{max}} = maximum current density (for given
Solid_oxide_fuel_cell
Electricity-induced chemical reaction
pH 7 ([H+] = 1.0×10−7 M), the potential is unchanged based on the Nernst equation. The thermodynamic standard cell potential can be obtained from standard-state
Electrolysis_of_water
Hypothetical type of nuclear reaction
000 atmospheres. John R. Huizenga says they had misinterpreted the Nernst equation, leading them to believe that there was enough pressure to bring deuterons
Cold_fusion
Equation describing a state of matter under a given set of conditions
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given
Equation_of_state
Galvanic cell
One can calculate the potential developed by such a cell using the Nernst equation. A concentration cell produces a small voltage as it attempts to reach
Concentration_cell
Electrode that is pH-sensitive
described by the semi-empirical Nikolsky-Shultz-Eisenman equation, an extension to the Nernst equation. It is given by: E = E 0 + R T z i F ln [ a i + ∑
Glass_electrode
Common type of reference electrode in electrochemistry
reaction has been proven to obey these equations in solutions of pH values between 0 and 13.5. The Nernst equation below shows the dependence of the potential
Silver_chloride_electrode
Branch of electrochemistry
Walther Nernst, who derived the Nernst equation and detected ionic conduction in heterovalently doped zirconia, which he applied in his Nernst lamp. Another
Solid_state_ionics
Néel Nernst effect (a.k.a. Nernst–Ettingshausen effect) – Walther Hermann Nernst and Albert von Ettingshausen Nernst equation – Walther Hermann Nernst Neupert
Scientific phenomena named after people
Scientific_phenomena_named_after_people
Adages and sayings named after a person
substances. Named after Claude-Louis Navier and George Gabriel Stokes. Nernst equation: A chemical and thermodynamic relationship that permits the calculation
List_of_eponymous_laws
perturbation 1889 – Walther Nernst relates the voltage of electrochemical cells to their chemical thermodynamics via the Nernst equation 1889 – Svante Arrhenius
Timeline_of_thermodynamics
ln a H + {\displaystyle E=E^{0}+{\frac {RT}{2F}}\ln a_{H^{+}}} (Nernst equation) The quinhydrone electrode provides an alternative to the most commonly
Quinhydrone_electrode
the German scientist Max Planck: Boltzmann–Planck equation Fokker–Planck equation Nernst–Planck equation Kelvin–Planck statement of the second law of thermodynamics
List of things named after Max Planck
List_of_things_named_after_Max_Planck
Measure of an acid's strength in solution
less than two in aqueous solution with a glass electrode, because the Nernst equation breaks down at such low pH values. To determine pK values of less than
Acid_dissociation_constant
Electrochemical interface that is either polarisable or polarised
ion transfer reactions Heterogeneous electron transfer reactions The Nernst equation for an ion transfer reaction reads Δ o w ϕ = ϕ w − ϕ o = Δ o w ϕ i
ITIES
Plating process
the perspective of thermodynamics, the process is governed by the Nernst equation: E = E 0 − ( 0.592 | 2 ) l o g ( Q ) {\displaystyle E=E^{0}-({0.592}|{2})log(Q)}
Electroless_deposition
Electromotive force of a cell built of two electrodes
Absolute electrode potential Electric potential Galvani potential Nernst equation Overpotential Potential difference (voltage) Standard electrode potential
Electrode_potential
Propagation of action potentials along the myelinated axons of neurons
descriptions of redirect targets Goldman equation – Generalization of the Nernst equation for the membrane potential Hindmarsh–Rose model – Of the spiking-bursting
Saltatory_conduction
Genetic disorder causing muscles to delay relaxing after contraction
-80 mV, becomes more depolarized (depolarization), according to the Nernst equation. In skeletal muscle fibers the equilibrium potential for Cl− is around
Myotonia_congenita
Subdiscipline of chemistry concerned with chemical equilibrium
species}}]}{[{\text{reduced species}}]}}} This is an example of the Nernst equation. The potential is known as a reduction potential. Standard electrode
Equilibrium_chemistry
Neuron communication by electric impulses
introduce the Nernst equation for resting potential across the membrane; this was generalized by David E. Goldman to the eponymous Goldman equation in 1943
Action_potential
Austrian mathematician and theoretical physicist (1844–1906)
Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his
Ludwig_Boltzmann
Class of enzymes
HOX + R−H → H2O + R−X From the perspective of thermodynamics, the Nernst equation confirms that hydrogen peroxide can oxidize chloride (E°= 1.36 V),
Haloperoxidase
Behaviour of charged particles near a semi-permeable membrane
flow into the cell and tissue swelling occurs. Chemical equilibrium Nernst equation Double layer (biology) Osmotic pressure Diffusion equilibrium "Gibbs–Donnan
Gibbs–Donnan_effect
Electromotive force of a half reaction cell versus standard hydrogen electrode
potential) as given in the table of standard electrode potential. Nernst equation Pourbaix diagram Solvated electron Standard electrode potential (data
Standard_electrode_potential
Sensor of ion concentration in a solution
dependent on the logarithm of the ionic activity, according to the Nernst equation. Analysis with ISEs expands throughout a range of technological fields
Ion-selective_electrode
Quantity in chemistry and engineering
{\partial G}{\partial \xi }}\right)_{p,T}} This formula leads to the Nernst equation when applied to the oxidation-reduction reaction which generates the
Extent_of_reaction
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References
List of scientific equations named after people
List_of_scientific_equations_named_after_people
When the ratio of reactants to products of a chemical reaction is constant with time
asymptotically but in the form of a damped oscillation . The related Nernst equation in electrochemistry gives the difference in electrode potential as
Chemical_equilibrium
Intensive physical property of substances
Electrochemical gradient Fermi level Membrane potential Nernst equation Poisson–Boltzmann equation Reduction potential Standard electrode potential Guggenheim
Electrochemical_potential
is at fixed composition and the electrode response is given by the Nernst equation: E = E0 − RT/F ln aF−, where: E is the measured cell potential, E0
Fluoride_selective_electrode
Instrument measuring acidity or alkalinity of solutions
across the glass bulb is linearly related to the pH according to the Nernst equation. The reference electrode is insensitive to the pH of the solution,
PH_meter
axonal membrane to ions. Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane. In 1907, Louis Lapicque
History_of_neuroscience
Electrical action produced by a non-electrical source
G=-n_{0}F_{0}{\mathcal {E}}} which is used in the derivation of the Nernst equation. Although an electrical potential difference (voltage) is sometimes
Electromotive_force
Combination of the diffusion and convection (advection) equations
Buckley–Leverett equation Burgers' equation Conservation equations Double diffusive convection Incompressible Navier–Stokes equations Natural convection Nernst–Planck
Convection–diffusion_equation
Group of transport proteins
concentration increases the reversal potential for chloride, given by the Nernst equation. Later in development expression of NKCC1 is reduced, while expression
Na–K–Cl_cotransporter
Study of neural function
ions are held back. Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane. In 1907, Prof. Louis Lapicque
Neurophysiology
Captured energy for later usage
or discharge the cell. Cell voltage is chemically determined by the Nernst equation and ranges, in practical applications, from 1.0 V to 2.2 V. Storage
Energy_storage
Mackey-Glass equations McKendrick–von Foerster equation in age structure modeling Nernst–Planck equation in ion flux across biological membranes Price equation in
List of named differential equations
List_of_named_differential_equations
High-temperature fuel cells
+ 1 2 O 2 = H 2 O {\displaystyle H_{2}+{\frac {1}{2}}O_{2}=H_{2}O} Nernst Equation: E = E o + R T 2 F l o g P H 2 P O 2 1 2 P H 2 O + R T 2 F l o g P
Molten_carbonate_fuel_cell
Law of physics
chemist Walther Nernst during the years 1906 to 1912 and is therefore often referred to as the Nernst heat theorem, or sometimes the Nernst-Simon heat theorem
Third_law_of_thermodynamics
Class of electrodes
(dissolution of the metal or cathodic deposition of the copper-ions). The Nernst equation below shows the dependence of the potential of the copper-copper(II)
Copper–copper(II) sulfate electrode
Copper–copper(II)_sulfate_electrode
Voltmeter
The concentration of the analyte can then be calculated from the Nernst equation. Many varieties of this basic principle exist for quantitative measurements
Potentiometer (measuring instrument)
Potentiometer_(measuring_instrument)
equilibrium Topology Game Theory John Forbes Nash Nernst equation Electrochemistry Walther Nernst Newton's law of cooling Newton's law of universal gravitation
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Equation of the state of a hypothetical ideal gas
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior
Ideal_gas_law
Mechanical side-effects of an electrochemical process
(such as in a stationary battery) – with a depolarizer. Depolarizer Nernst equation Stern, M.; Geary, A. L. (1957), "Electrochemical Polarization I. A
Polarization (electrochemistry)
Polarization_(electrochemistry)
Common thermodynamic equations and quantities in thermodynamics, using mathematical notation, are as follows: Many of the definitions below are also used
Table of thermodynamic equations
Table_of_thermodynamic_equations
chemical reaction producing the current. He constructed an equation, known as Nernst Equation, which describes the relation of a battery cell's voltage
History_of_electrochemistry
electrode is calibrated using activity standards it is assumed that the Nernst equation applies in the form E = E 0 + R T n F ln { A } {\displaystyle E=E^{0}+{\frac
Determination of equilibrium constants
Determination_of_equilibrium_constants
American chemical engineer
measurements of impedance and ion diffusivity (which is calculated using the Nernst equation). In 2018 she returned to the University of Texas at Austin, where
Joan_Brennecke
Place in Kuyavian-Pomeranian Voivodeship, Poland
Kudłacz-Gloc (born 1985), handball player Walther Nernst (1864–1941), chemist, Nobel Prize winner for the Nernst equation Franciszek Nogalski (1911–1939), Roman
Wąbrzeźno
Probe which tests for biological molecules
logarithmic response relative to the analyte concentration (governed by the Nernst equation). This allows potentiometric sensors to feature an exceptionally wide
Biosensor
Belgian electrochemist and corrosion specialist
Pourbaix Diagrams are thermodynamic charts constructed using the Nernst equation and visualize the relationship between possible phases of a system
Marcel_Pourbaix
Potential resulting from the Donnan equilibrium
to dissolved plasma proteins.[citation needed] Chemical equilibrium Nernst equation Double Layer (biospecific) "Donnan potential" p. 167. in "D". Electrochemical
Donnan_potential
Relations between flows and forces, or gradients, in thermodynamic systems
difference) coefficients are equal. For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager relations are closely connected to the
Onsager_reciprocal_relations
of the redox reactions through the Nernst equation: Eh=E0-(RT/nF)ln([Reductants]a/[Oxidants]b[H+]b) This equation allows for the calculation of the extent
Chemistry_of_wetland_dredging
Concept in applied mathematics
Central Difference Methods Archived 5 November 2013 at the Wayback Machine A Conservative Finite Difference Scheme for Poisson–Nernst–Planck Equations
Central_differencing_scheme
Research institute in Leipzig, Germany
Effectiveness of Jons") in 1889. In his habilitation, Nernst published the Nernst equation named after him. Nernst received the Nobel Prize in Chemistry for the
Wilhelm_Ostwald_Institute
Observational basis of thermodynamics
established. Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated by Walther Nernst over the period 1906–1912
Laws_of_thermodynamics
flows between them. The potentiometric response is governed by the Nernst equation in that the potential is proportional to the logarithm of the concentration
Biotransducer
Mathematical descriptions of molecular diffusion
Advection Churchill–Bernstein equation Diffusion False diffusion Gas exchange Mass flux Maxwell–Stefan diffusion Nernst–Planck equation Osmosis Vallero, Daniel
Fick's_laws_of_diffusion
particular ion across the cell membrane. It can be calculated using the Nernst equation. Estrogen A steroid hormone that, in addition to reproductive functions
Glossary_of_neuroscience
Describes how neurons transmit electric signals
neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable
Hodgkin–Huxley_model
Mathematical model of a dendrite
Dendrite Hodgkin–Huxley model Membrane potential Monodomain model Nernst–Planck equation Patch clamp Saltatory conduction Soliton model in neuroscience Douglas
Cable_theory
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