5802:
4562:
applied taking care to first express the relationship as a function of pH. The second factor to be considered are the values of the concentrations taken into account in the Nernst equation. To define a formal reduction potential for a biochemical reaction, the pH value, the concentrations values and the hypotheses made on the activity coefficients must always be explicitly indicated. When using, or comparing, several formal reduction potentials they must also be internally consistent.
6677:
5413:
6253:
1928:
4589:
6244:
5797:{\displaystyle E_{\mathrm {m} }={\frac {RT}{F}}\ln {\left({\frac {\displaystyle \sum _{i}^{N}P_{\mathrm {M} _{i}^{+}}\left_{\mathrm {out} }+\displaystyle \sum _{j}^{M}P_{\mathrm {A} _{j}^{-}}\left_{\mathrm {in} }}{\displaystyle \sum _{i}^{N}P_{\mathrm {M} _{i}^{+}}\left_{\mathrm {in} }+\displaystyle \sum _{j}^{M}P_{\mathrm {A} _{j}^{-}}\left_{\mathrm {out} }}}\right)},}
8388:
9276:
1741:
6672:{\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {rP_{\mathrm {K} ^{+}}\left_{\mathrm {out} }+P_{\mathrm {Na} ^{+}}\left_{\mathrm {out} }+P_{\mathrm {Cl} ^{-}}\left_{\mathrm {in} }}{rP_{\mathrm {K} ^{+}}\left_{\mathrm {in} }+P_{\mathrm {Na} ^{+}}\left_{\mathrm {in} }+P_{\mathrm {Cl} ^{-}}\left_{\mathrm {out} }}}\right)}.}
1735:
5943:
4343:
1309:
6945:
1593:
10019:
779:
10428:
7573:
of the system (here an idealized system is considered for better understanding, so that activities are posited very close to the true concentrations. Fundamental statistical proof of the mentioned linearity goes beyond the scope of this section, but to see this is true it is simpler to consider usual
5903:
The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides
4561:
The main factor affecting the formal reduction potentials in biochemical or biological processes is most often the pH. To determine approximate values of formal reduction potentials, neglecting in a first approach changes in activity coefficients due to ionic strength, the Nernst equation has to be
8123:
3494:
Formal reduction potentials are applied to simplify calculations of a considered system under given conditions and measurements interpretation. The experimental conditions in which they are determined and their relationship to the standard reduction potentials must be clearly described to avoid to
2175:
When wishing to use simple concentrations in place of activities, but that the activity coefficients are far from unity and can no longer be neglected and are unknown or too difficult to determine, it can be convenient to introduce the notion of the "so-called" standard formal reduction potential
4573:
versus SHE (pH = 0) with formal reduction potentials (pH = 7). Definitions must be clearly expressed and carefully controlled, especially if the sources of data are different and arise from different fields (e.g., picking and mixing data from classical electrochemistry and microbiology textbooks
5113:
is the same for both reduction reactions because they share the same linear relationship as a function of pH and the slopes of their lines are the same. This can be directly verified on a
Pourbaix diagram. For other reduction reactions, the value of the formal reduction potential at a pH of 7,
4719:
When solving the Nernst equation for each corresponding reduction reaction (need to revert the water oxidation reaction producing oxygen), both equations have a similar form because the number of protons and the number of electrons involved within a reaction are the same and their ratio is one
4569:, with different underlying hypotheses). When working at the frontier between inorganic and biological processes (e.g., when comparing abiotic and biotic processes in geochemistry when microbial activity could also be at work in the system), care must be taken not to inadvertently directly mix
8582:
10172:
In dilute solutions, the Nernst equation can be expressed directly in the terms of concentrations (since activity coefficients are close to unity). But at higher concentrations, the true activities of the ions must be used. This complicates the use of the Nernst equation, since estimation of
7411:
219:). The chemical activity of a dissolved species corresponds to its true thermodynamic concentration taking into account the electrical interactions between all ions present in solution at elevated concentrations. For a given dissolved species, its chemical activity (a) is the product of its
10152:
2319:
9018:
1401:. Because activity coefficients tend to unity at low concentrations, or are unknown or difficult to determine at medium and high concentrations, activities in the Nernst equation are frequently replaced by simple concentrations and then, formal standard reduction potentials
1599:
3328:
1153:
6738:
1466:
2422:
2160:
5148:
of the half-reaction. The determination of the formal reduction potential at pH = 7 for a given biochemical half-reaction requires thus to calculate it with the corresponding Nernst equation as a function of pH. One cannot simply apply an offset of -414 mV to the
10192:
becomes very low, and there may be no thermodynamic equilibrium necessary for Nernst equation to hold. The electrode is called unpoised in such case. Other effects tend to take control of the electrochemical behavior of the system, like the involvement of the
3164:
The formal potential is thus the reversible potential of an electrode at equilibrium immersed in a solution where reactants and products are at unit concentration. If any small incremental change of potential causes a change in the direction of the reaction,
9847:
626:
4167:
1923:{\displaystyle E_{\text{red}}=\underbrace {\left(E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {\gamma _{\text{Red}}}{\gamma _{\text{Ox}}}}\right)} _{E_{\text{red}}^{\ominus '}}-{\frac {RT}{zF}}\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}}
2558:
will vary from medium to medium. Several definitions of the formal reduction potential can be found in the literature, depending on the pursued objective and the experimental constraints imposed by the studied system. The general definition of
6239:{\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {rP_{\mathrm {K} ^{+}}\left_{\mathrm {out} }+P_{\mathrm {Na} ^{+}}\left_{\mathrm {out} }}{rP_{\mathrm {K} ^{+}}\left_{\mathrm {in} }+P_{\mathrm {Na} ^{+}}\left_{\mathrm {in} }}}\right)}.}
10593:
5374:
2516:
is often a more convenient, but conditional, form of the standard reduction potential, taking into account activity coefficients and specific conditions characteristics of the reaction medium. Therefore, its value is a conditional value,
8399:
4607:
of the electrolyte (otherwise non-interacting). Above the top line oxygen will bubble off of the electrode until water is totally consumed. Likewise, below the bottom line hydrogen will bubble off of the electrode until water is totally
7793:
7222:
4083:
10032:
5904:
of the membrane. The greater this ratio the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion. A similar expression exists that includes
7161:
3966:
863:
2216:
10173:
non-ideal activities of ions generally requires experimental measurements. The Nernst equation also only applies when there is no net current flow through the electrode. The activity of ions at the electrode surface changes
8853:
10337:
5180:
5174:
3504:
2713:
331:
8383:{\displaystyle \Delta S_{\mathrm {rxn} }={\big (}yS(\mathrm {Y} )+zS(\mathrm {Z} ){\big )}-{\big (}aS(\mathrm {A} )+bS(\mathrm {B} ){\big )}=\Delta S_{\mathrm {rxn} }^{\ominus }-k\ln {\frac {^{y}^{z}}{^{a}^{b}}}.}
5940:), altering the constraints for applying GHK equation. The other variables are the same as above. The following example includes two ions: potassium (K) and sodium (Na). Chloride is assumed to be in equilibrium.
4823:
10918:
10693:
3085:
7886:
7559:
8066:
2959:
2324:
2062:
9767:
6743:
9604:
8928:
3006:
2906:
2641:
420:
7965:
3333:
The term formal concentration (F) is now largely ignored in the current literature and can be commonly assimilated to molar concentration (M), or molality (m) in case of thermodynamic calculations.
2859:
514:
9271:{\displaystyle {\begin{aligned}E&=E^{\ominus }-{\frac {kT}{ze}}\ln {\frac {}{}}\\&=E^{\ominus }-{\frac {RT}{zF}}\ln {\frac {}{}}\\&=E^{\ominus }-{\frac {RT}{zF}}\ln Q_{r}.\end{aligned}}}
7033:
4420:
3243:
9852:
9023:
7227:
9686:
5014:
3605:
3544:
3489:
3444:
3122:
2753:
2678:
2594:
2556:
2514:
2462:
2211:
2055:
1991:
1436:
9457:
3652:
4885:
1730:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\left(\ln {\frac {\gamma _{\text{Red}}}{\gamma _{\text{Ox}}}}+\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}\right)}
167:
5047:
4918:
4667:
here beside (the simplest possible version of a
Pourbaix diagram), the water stability domain (grey surface) is delimited in term of redox potential by two inclined red dashed lines:
4338:{\displaystyle E_{h}=E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {0.05916}{z}}\log \left({\frac {\{C\}^{c}\{D\}^{d}}{\{A\}^{a}\{B\}^{b}}}\right)-{\frac {0.05916\,h}{z}}{\text{pH}}}
4004:
10580:: A formal potential is defined as the potential of a half-cell, measured against the standard hydrogen electrode, when the total concentration of each oxidation state is one formal.
5228:
1304:{\displaystyle E=E^{\ominus }-{\frac {V_{T}}{z}}\ln {\frac {a_{\text{Red}}}{a_{\text{Ox}}}}=E^{\ominus }-{\frac {\lambda V_{T}}{z}}\log _{10}{\frac {a_{\text{Red}}}{a_{\text{Ox}}}}.}
6940:{\displaystyle {\begin{aligned}{\frac {}{}}&={\frac {\exp \left(-/kT\right)}{\exp \left(-/kT\right)}}\\&=\exp \left({\frac {\mu _{\mathrm {c} }}{kT}}\right).\end{aligned}}}
1588:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln \left({\frac {\gamma _{\text{Red}}}{\gamma _{\text{Ox}}}}{\frac {C_{\text{Red}}}{C_{\text{Ox}}}}\right)}
1130:
7666:
9535:
9490:
9394:
9013:
4116:
9341:
5111:
5080:
4951:
4547:
4489:
4450:
4378:
3820:
3679:
2780:
2018:
576:
7060:
3377:
9309:
8093:
3407:
784:
10014:{\displaystyle {\begin{aligned}0&=E^{\ominus }-{\frac {RT}{zF}}\ln K\\{\frac {RT}{zF}}\ln K&=E^{\ominus }\\\ln K&={\frac {zFE^{\ominus }}{RT}}\end{aligned}}}
774:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln Q_{r}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {a_{\text{Red}}}{a_{\text{Ox}}}}.}
3044:
1954:
1459:
6731:, is equivalent to the probability of being oxidized (giving electrons) over the probability of being reduced (taking electrons), which we can write in terms of the
4516:
4159:
3793:
3760:
3724:
8770:
4012:
537:
associated with the electrochemical reaction is defined as the decrease in Gibbs free energy per coulomb of charge transferred, which leads to the relationship
10730:
4655:(oxidation of water oxygen atoms). The same may occur if a reductant stronger than hydrogen (e.g., metallic Na) or an oxidant stronger than oxygen (e.g., F
3840:
6701:
and that have a standard potential of zero, and in which the activities are well represented by the concentrations (i.e. unit activity coefficient). The
7800:
8577:{\displaystyle Q_{r}={\frac {\displaystyle \prod _{j}a_{j}^{\nu _{j}}}{\displaystyle \prod _{i}a_{i}^{\nu _{i}}}}\approx {\frac {^{z}^{y}}{^{a}^{b}}},}
7499:
7990:
7406:{\displaystyle {\begin{aligned}E&=E^{\ominus }-{\frac {kT}{e}}\ln {\frac {}{}}\\&=E^{\ominus }-{\frac {RT}{F}}\ln {\frac {}{}}.\end{aligned}}}
5912:
where the transport ratio would be 2/3, so r equals 1.5 in the formula below. The reason why we insert a factor r = 1.5 here is that current density
10147:{\displaystyle \log _{10}K={\frac {zE^{\ominus }}{\lambda V_{T}}}={\frac {zE^{\ominus }}{0.05916{\text{ V}}}}\quad {\text{at }}T=298.15~{\text{K}}}
3491:
cannot be referred as an immutable standard potential but needs to be systematically determined for each specific set of experimental conditions.
253:
8858:
7891:
455:
6952:
2314:{\displaystyle E_{\text{red}}^{\ominus '}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {\gamma _{\text{Red}}}{\gamma _{\text{Ox}}}}}
7652:. In this sense there is no difference in statistical properties of ideal gas atoms compared with the dissolved species of a solution with
4768:
10559:
Brown, Raymond A.; Swift, Ernest H. (1949). "The formal potential of the antimonous-antimonic half cell in hydrochloric acid solutions".
4828:
Note that the slopes of the two water stability domain upper and lower lines are the same (-59.16 mV/pH unit), so they are parallel on a
3049:
3340:, where at this point the concentration of Ox (the oxidized species) and Red (the reduced species) at the electrode surface are equal.
4832:. As the slopes are negative, at high pH, both hydrogen and oxygen evolution requires a much lower reduction potential than at low pH.
17:
10244:
claimed their original calculation was affected by a misinterpretation of the Nernst equation. He cited a paper about Pd–Zr alloys.
10332:
10956:
9697:
9543:
10412:
Bard, Allen J.; Faulkner, Larry R. (2001). "Chapter 2. Potentials and
Thermodynamics of Cells – See: 2.1.6 Formal Potentials".
2964:
2914:
2864:
2599:
378:
10897:
2819:
239:, also denoted here below with square brackets ) of all the dissolved species of interest are sufficiently low and that their
10843:
10630:
10366:
3323:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}={\frac {1\,\mathrm {M} _{\text{red}}}{1\,\mathrm {M} _{\text{ox}}}}=1}
3173:, the system is close to equilibrium, reversible and is at its formal potential. When the formal potential is measured under
10184:
At very low concentrations of the potential-determining ions, the potential predicted by Nernst equation approaches toward
4383:
7620:
takes place. It follows from the definition of entropy and from the condition of constant temperature and quantity of gas
8946:
6713:
of this solution is the difference between the energy barriers for taking electrons from and for giving electrons to the
10535:
2321:
So that the Nernst equation for the half-cell reaction can be correctly formally written in terms of concentrations as:
10951:
9618:
5114:
commonly referred for biochemical reactions, also depends on the slope of the corresponding line in a
Pourbaix diagram
6691:
For simplicity, we will consider a solution of redox-active molecules that undergo a one-electron reversible reaction
4971:
10800:
10774:
9281:
8096:
5223:
across a membrane. This potential is determined using the concentration of the ion both inside and outside the cell:
4596:
2417:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}-{\frac {RT}{zF}}\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}}
2155:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}-{\frac {RT}{zF}}\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}}
9409:
3214:
In this case, as for the standard reduction potentials, the concentrations of dissolved species remain equal to one
540:
2521:, that it depends on the experimental conditions and because the ionic strength affects the activity coefficients,
7656:
equaling one: particles freely "hang around" filling the provided volume), which is inversely proportional to the
7460:. To convert to the molar quantities given in most chemistry textbooks, it is simply necessary to multiply by the
3625:
4845:
10453:
3573:
3512:
3457:
3412:
3090:
2721:
2646:
2562:
2524:
2482:
2430:
2179:
2023:
1959:
1404:
10251:
systems and can be used, for example, to assess whether a particular reaction will go to completion or not. At
5908:(the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See:
5020:
4891:
3977:
131:
3654:
fixed arbitrarily to zero by convention, it is no longer the case at a pH of 7. Then, the reduction potential
2464:
is the reduction potential that applies to a half reaction under a set of specified conditions such as, e.g.,
5217:
The Nernst equation has a physiological application when used to calculate the potential of an ion of charge
10902:
5857:
units, though the units strictly don't matter, as the ion concentration terms become a dimensionless ratio),
10327:
10157:
8767:
is the temperature of the system. Using these relations, we can now write the change in Gibbs free energy,
7567:
is the number of states available to the molecule. The number of states must vary linearly with the volume
4570:
4353:, and exponents are shown in the conventional manner. This equation is the equation of a straight line for
3972:
3555:
2170:
1090:
900:
62:
2680:
is also determined at pH 7, as e.g. for redox reactions important in biochemistry or biological systems.
10282:
9499:
9465:
9369:
5050:
4921:
4600:
4519:
4091:
3823:
3682:
3619:
3199:
4565:
Problems may occur when mixing different sources of data using different conventions or approximations (
10307:
9772:
Starting from the Nernst equation, one can also demonstrate the same relationship in the reverse way.
8598:
5200:
3570:
better corresponding to real conditions than the standard state. Formal standard reduction potentials (
46:
10454:"Redox potentials of proteins and other compounds of bioelectrochemical interest in aqueous solutions"
9784:
9780:
6718:
5379:
66:
9355:, and complexing agents) and is the potential that is actually measured in an electrochemical cell.
5089:
5058:
4929:
4525:
4467:
4428:
4356:
3798:
3657:
2758:
1996:
10189:
10174:
9314:
3349:
9287:
8610:, and the denominator is a similar product of reactant activities. All activities refer to a time
8071:
5932:(K) = 0 (as for both ions flux by electrochemical force is compensated by that by the pump, i.e. J
3382:
10946:
9609:
The sign is negative, because the considered system performs the work and thus releases energy.
4759:
respectively), so it simplifies when solving the Nernst equation expressed as a function of pH.
1132:
is approximately 25.693 mV. The Nernst equation is frequently expressed in terms of base-10
938:
623:
charge. This immediately leads to the Nernst equation, which for an electrochemical half-cell is
5369:{\displaystyle E={\frac {RT}{zF}}\ln {\frac {}{}}=2.3026{\frac {RT}{zF}}\log _{10}{\frac {}{}}.}
10507:
8585:
4612:
To illustrate the dependency of the reduction potential on pH, one can simply consider the two
3015:
2683:
74:
10815:
10790:
10764:
10618:
7624:
that the change in the number of states must be proportional to the relative change in volume
10717:
7788:{\displaystyle S=k\ln \ (\mathrm {constant} \times V)=-k\ln \ (\mathrm {constant} \times c).}
5909:
4628:
4131:
1939:
1444:
4693:
Higher stability line with oxygen gas evolution due to water oxygen oxidation at very high E
10763:
Bard, Allen J.; Inzelt, György; Scholz, Fritz, eds. (2012-10-02), "Karaoglanoff equation",
10737:[On Oxidation and Reduction Processes in the Electrolysis of Iron Salt Solutions],
10260:
10252:
10161:
9808:
9776:
9397:
9344:
8617:
7653:
4494:
4350:
4137:
4078:{\displaystyle E_{\text{red}}^{\ominus }({\text{volt}})=-{\frac {\Delta G^{\ominus }}{zF}}}
3771:
3738:
3702:
3344:
3223:
3207:
3150:
1933:
1394:
1054:
364:
337:
240:
220:
58:
5408:
under the constraints that total current density driven by electrochemical force is zero:
4671:
Lower stability line with hydrogen gas evolution due to the proton reduction at very low E
8:
10317:
10287:
10256:
8634:
may be replaced by a concentration term, .In an electrochemical cell, the cell potential
7657:
3231:
3215:
3174:
3128:
918:
880:
224:
50:
10619:"Table 14-4 Standard Reduction Potentials for Some Biochemically Import Half-Reactions"
10475:
10302:
10277:
8641:
7575:
7425:
6702:
5872:
5383:
5212:
5188:
5134:
4742:
4724:
2782:
of the half-reaction at unity concentration ratio of the oxidized and reduced species (
1332:
Similarly to equilibrium constants, activities are always measured with respect to the
1145:
10912:
7156:{\displaystyle \mu _{\mathrm {c} }=\mu _{\mathrm {c} }^{\ominus }+kT\ln {\frac {}{}}.}
3961:{\displaystyle a\,A+b\,B+h\,{\ce {H+}}+z\,e^{-}\quad {\ce {<=>}}\quad c\,C+d\,D}
10876:
10839:
10796:
10770:
10626:
10568:
10483:
10372:
10362:
10322:
10198:
10194:
9795:
9364:
8722:
8684:
8393:
7461:
7434:
6714:
5405:
5401:
4119:
3612:
3198:"A formal potential is defined as the potential of a half-cell, measured against the
3146:
612:
526:
426:
247:
as commonly done when simplifying, or idealizing, a reaction for didactic purposes:
190:
173:
10859:
Huot, J. Y. (1989). "Electrolytic
Hydrogenation and Amorphization of Pd-Zr Alloys".
10735:"Über Oxydations- und Reduktionsvorgänge bei der Elektrolyse von Eisensaltzlösungen"
5400:
When the membrane is permeable to more than one ion, as is inevitably the case, the
5382:(i.e., no net flux of ions), and if the cell is permeable to only one ion, then the
858:{\displaystyle E_{\text{cell}}=E_{\text{cell}}^{\ominus }-{\frac {RT}{zF}}\ln Q_{r}}
781:
For a complete electrochemical reaction (full cell), the equation can be written as
10913:
DoITPoMS Teaching and
Learning Package- "The Nernst Equation and Pourbaix Diagrams"
10868:
10831:
10746:
10681:
10465:
10312:
10297:
10241:
10240:. In reality, only 10,000–20,000 atmospheres were achieved. The American physicist
8718:
7452:
6732:
5896:
5395:
5175:
Table of standard reduction potentials for half-reactions important in biochemistry
4829:
4617:
4592:
4583:
3731:
3694:
3505:
Table of standard reduction potentials for half-reactions important in biochemistry
2714:
Table of standard reduction potentials for half-reactions important in biochemistry
2473:
1141:
583:
90:
78:
38:
10470:
7169:
to convert from chemical potentials to electrode potentials, and remembering that
4556:
10247:
The Nernst equation allows the calculation of the extent of reaction between two
10233:
10221:. Fleischmann and Pons, claiming that cold fusion could exist, calculated that a
3203:
3181:
the activity of each dissolved species is 1 mol/L, T = 298.15 K = 25 °C = 77 °F,
1085:
4574:
without paying attention to the different conventions on which they are based).
10237:
10024:
9348:
3563:
3447:
2469:
1333:
436:
86:
31:
4599:(STP). The vertical scale (ordinate) is the electrode potential relative to a
3730:
of a solution are related by the Nernst equation as commonly represented by a
10940:
10880:
10838:(2 ed.). Oxford and New York: Oxford University Press. pp. 33, 47.
10750:
10572:
10487:
10479:
10292:
10178:
5192:
5145:
4632:
3336:
The formal potential is also found halfway between the two peaks in a cyclic
995:
244:
232:
10376:
10232:
electrolysis cell could achieve up to 10 atmospheres of pressure inside the
8848:{\displaystyle \Delta G=\Delta H-T\Delta S=\Delta G^{\ominus }+kT\ln Q_{r},}
7978:
is unity (e.g., 1 atm or 1 M), it will merely cancel the units of
10907:
10661:
7443:
4549:= 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P
3551:
3547:
948:
530:
243:
are close to unity, their chemical activities can be approximated by their
10338:
Standard apparent reduction potentials in biochemistry at pH 7 (data page)
10217:
The Nernst equation has been involved in the scientific controversy about
8099:
and denotes the concentration of A. The change in entropy for a reaction
5865:
is the intracellular concentration of that ion (in moles per cubic meter),
3681:
of a hydrogen electrode operating at pH 7 is -0.413 V with respect to the
3446:, and because they depend on experimental conditions such as temperature,
326:{\displaystyle Q_{r}={\frac {a_{\text{Red}}}{a_{\text{Ox}}}}={\frac {}{}}}
10229:
10218:
8721:. There is a negative sign because a spontaneous reaction has a negative
7421:
5850:
4595:
for water, including stability regions for water, oxygen and hydrogen at
3615:
or to fuel microbial activity under some conditions is feasible or not.
3337:
1009:
10209:
The expression of time dependence has been established by
Karaoglanoff.
7797:
The change in entropy from some state 1 to another state 2 is therefore
3688:
10268:
of the reaction to be calculated and hence the extent of the reaction.
5184:
3127:
The formal reduction potential makes possible to more simply work with
1133:
10872:
10181:
and resistive loss terms which contribute to the measured potential.
10222:
10188:. This is physically meaningless because, under such conditions, the
7987:. We can, therefore, write the entropy of an arbitrary molecule A as
7579:
4636:
3827:
1327:
198:
82:
54:
10734:
9347:
of the dissolved species under given experimental conditions (T, P,
5404:
can be determined from the
Goldman equation, which is a solution of
4818:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-0.05916\ pH}
2057:
and the concentrations in the simplest form of the Nernst equation:
8758:
4640:
3219:
3132:
3080:{\displaystyle {\frac {\gamma _{\text{red}}}{\gamma _{\text{ox}}}}}
2213:) which is related to the standard reduction potential as follows:
1336:(1 mol/L for solutes, 1 atm for gases, and T = 298.15 K,
991:
620:
228:
10236:
of the metal of the cathode, enough pressure to cause spontaneous
7881:{\displaystyle \Delta S=S_{2}-S_{1}=-k\ln {\frac {c_{2}}{c_{1}}},}
10225:
10197:
in electricity transfer and electrode equilibria, as analyzed by
7554:{\displaystyle S\ {\stackrel {\mathrm {def} }{=}}\ k\ln \Omega ,}
7491:
5827:
4644:
1005:
209:
8061:{\displaystyle S(\mathrm {A} )=S^{\ominus }(\mathrm {A} )-k\ln,}
4588:
5886:
5876:
4753:
4648:
4557:
Main factors affecting the formal standard reduction potentials
3149:. Because molar and molal concentrations were once referred as
981:
3498:
2684:
Determination of the formal standard reduction potential when
10248:
8645:
7211:, we obtain the Nernst equation for the one-electron process
5823:
4652:
4613:
4553:= 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0).
3608:
3567:
3137:
70:
7415:
7057: = 1, we need to add in this additional constant:
4452:
at higher pH values. This is observed for the reduction of O
1993:
and called the formal standard reduction potential, so that
10617:
Voet, Donald; Voet, Judith G.; Pratt, Charlotte W. (2016).
9762:{\displaystyle E_{cell}^{\ominus }={\frac {RT}{zF}}\ln {K}}
5819:
10416:(2 ed.). New York: John Wiley & Sons. p. 52.
10212:
9599:{\displaystyle \Delta G^{\ominus }=-zFE_{cell}^{\ominus }}
9496:) transferred during the reaction and the cell potential (
5181:
important redox reactions in biochemistry and microbiology
4659:) enters in contact with water and reacts with it. In the
3830:
equation, conventionally written as a reduction reaction (
10623:
8923:{\displaystyle E=E^{\ominus }-{\frac {kT}{ze}}\ln Q_{r}.}
5196:
3618:
While, standard reduction potentials always refer to the
3566:
pH of 0. The advantage is to defining a more appropriate
3001:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}=1}
2954:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}}
2901:{\displaystyle {\frac {a_{\text{red}}}{a_{\text{ox}}}}=1}
2636:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}=1}
2427:
According to Wenzel (2020), a formal reduction potential
415:{\displaystyle K={\frac {a_{\text{Red}}}{a_{\text{Ox}}}}}
7960:{\displaystyle S_{2}=S_{1}-k\ln {\frac {c_{2}}{c_{1}}}.}
5841:
is the permeability for that ion (in meters per second),
3562:
of most physiological and intracellular fluids than the
2854:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }}
509:{\displaystyle \Delta G=\Delta G^{\ominus }+RT\ln Q_{r}}
101:
10429:"4. Table of Standard State Electrochemical Potentials"
10259:(emf) of the two half cells are equal. This allows the
9358:
9352:
8932:
This is the more general form of the Nernst equation.
7028:{\displaystyle \mu _{\mathrm {c} }=kT\ln {\frac {}{}}.}
5854:
4604:
3763:
3727:
3559:
3451:
2465:
10414:
Electrochemical methods: Fundamentals and applications
3920:
3834:, electrons accepted by an oxidant on the left side):
2164:
1340:, 25 °C or 77 °F). The chemical activity of a species
425:
The standard thermodynamics also says that the actual
10035:
9850:
9700:
9621:
9546:
9502:
9468:
9412:
9372:
9317:
9290:
9021:
8949:
8861:
8773:
8737:. The Gibbs free energy is related to the entropy by
8584:
where the numerator is a product of reaction product
8452:
8418:
8402:
8126:
8074:
7993:
7894:
7803:
7669:
7502:
7225:
7063:
6955:
6741:
6256:
5946:
5702:
5622:
5543:
5460:
5416:
5231:
5092:
5061:
5023:
4974:
4932:
4894:
4848:
4771:
4762:
The result can be numerically expressed as follows:
4528:
4497:
4470:
4431:
4415:{\displaystyle -0.05916\,\left({\frac {h}{z}}\right)}
4386:
4359:
4170:
4140:
4094:
4015:
3980:
3843:
3801:
3774:
3741:
3705:
3689:
Expression of the Nernst equation as a function of pH
3660:
3628:
3576:
3515:
3460:
3415:
3385:
3352:
3246:
3093:
3052:
3018:
2967:
2917:
2867:
2822:
2761:
2724:
2649:
2602:
2565:
2527:
2485:
2433:
2327:
2219:
2182:
2065:
2026:
1999:
1962:
1942:
1744:
1602:
1469:
1447:
1407:
1156:
1093:
1004:
is the
Faraday constant, the magnitude of charge (in
787:
629:
543:
458:
381:
256:
134:
10390:
Wahl (2005). "A Short History of Electrochemistry".
5386:
must be equal to the Nernst potential for that ion.
5144:
involved in the reduction reaction, and thus on the
10204:
9492:
is also equal to the product of the total charge (
5849:is the extracellular concentration of that ion (in
4577:
2755:can be defined as the measured reduction potential
1047:
is the reaction quotient of the cell reaction, and,
10792:Introduction to Polarography and Allied Techniques
10536:"Origins of electrochemical potentials — PalmSens"
10146:
10013:
9761:
9680:
9598:
9529:
9484:
9451:
9388:
9335:
9303:
9270:
9007:
8922:
8847:
8576:
8382:
8087:
8060:
7959:
7880:
7787:
7553:
7405:
7155:
7027:
6939:
6671:
6238:
5796:
5368:
5105:
5074:
5041:
5008:
4965:O the here above mentioned relationship becomes:
4945:
4912:
4879:
4817:
4603:electrode. The horizontal scale (abscissa) is the
4541:
4510:
4483:
4444:
4414:
4372:
4337:
4153:
4110:
4077:
3998:
3960:
3814:
3787:
3754:
3718:
3673:
3646:
3599:
3538:
3483:
3438:
3401:
3371:
3322:
3116:
3079:
3038:
3000:
2953:
2900:
2853:
2774:
2747:
2672:
2635:
2588:
2550:
2508:
2456:
2416:
2313:
2205:
2154:
2049:
2012:
1985:
1948:
1922:
1729:
1587:
1453:
1430:
1328:Form with activity coefficients and concentrations
1303:
1124:
857:
773:
570:
508:
414:
325:
161:
10836:Cold Fusion: The Scientific Fiasco of the Century
9681:{\displaystyle -zFE_{cell}^{\ominus }=-RT\ln {K}}
6949:Taking the natural logarithm of both sides gives
3928:
3927:
3910:
3909:
3495:confuse them with standard reduction potentials.
49:relationship that permits the calculation of the
10938:
10762:
10686:
10350:
7420:Quantities here are given per molecule, not per
5009:{\displaystyle E_{\text{red}}=1.229-0.05916\ pH}
4839:the here above mentioned relationship becomes:
3622:(SHE), with = 1 M corresponding to a pH 0, and
10407:
10405:
7969:If state 1 is at standard conditions, in which
3153:, it could explain the origin of the adjective
1441:Taking into account the activity coefficients (
185:), also often called the ion activity product (
9452:{\displaystyle \Delta G^{\ominus }=-RT\ln {K}}
6721:. The ratio of oxidized to reduced molecules,
77:(often approximated by concentrations) of the
10616:
10500:
8251:
8207:
8197:
8153:
10729:
10411:
10402:
8392:We define the ratio in the last term as the
4616:determining the water stability domain in a
4295:
4288:
4279:
4272:
4261:
4254:
4245:
4238:
3647:{\displaystyle E_{\text{red H+}}^{\ominus }}
10361:. Columbus, OH: American Chemical Society.
8711:is the number of electrons transferred and
6248:When chloride (Cl) is taken into account,
4880:{\displaystyle E_{\text{red}}=-0.05916\ pH}
4460:O, or OH, and for the reduction of H into H
3499:Formal standard reduction potential at pH 7
2424:and likewise for the full cell expression.
2020:can be directly expressed as a function of
1353:, is related to the measured concentration
435:is related to the free energy change under
10585:
10558:
10529:
10527:
10420:
9311:is often replaced by the formal potential
5168:
3600:{\displaystyle E_{\text{red}}^{\ominus '}}
3539:{\displaystyle E_{\text{red}}^{\ominus '}}
3484:{\displaystyle E_{\text{red}}^{\ominus '}}
3439:{\displaystyle E_{\text{red}}^{\ominus '}}
3117:{\displaystyle E_{\text{red}}^{\ominus '}}
2748:{\displaystyle E_{\text{red}}^{\ominus '}}
2673:{\displaystyle E_{\text{red}}^{\ominus '}}
2589:{\displaystyle E_{\text{red}}^{\ominus '}}
2551:{\displaystyle E_{\text{red}}^{\ominus '}}
2509:{\displaystyle E_{\text{red}}^{\ominus '}}
2457:{\displaystyle E_{\text{red}}^{\ominus '}}
2206:{\displaystyle E_{\text{red}}^{\ominus '}}
2050:{\displaystyle E_{\text{red}}^{\ominus '}}
1986:{\displaystyle E_{\text{red}}^{\ominus '}}
1431:{\displaystyle E_{\text{red}}^{\ominus '}}
162:{\displaystyle {\ce {Ox + ze- -> Red}}}
69:, the number of electrons involved in the
10610:
10552:
10469:
10357:Orna, Mary Virginia; Stock, John (1989).
10356:
9807:) attains the special value known as the
7416:Using thermodynamics (chemical potential)
6686:
5042:{\displaystyle E_{\text{red}}^{\ominus }}
4913:{\displaystyle E_{\text{red}}^{\ominus }}
4393:
4320:
4126:is the number of electrons involved, and
3999:{\displaystyle E_{\text{red}}^{\ominus }}
3954:
3944:
3886:
3867:
3857:
3847:
3298:
3280:
349:of the activity of the reaction product (
10919:"20.5: Gibbs energy and redox reactions"
10852:
10830:
10694:"20.5: Gibbs energy and redox reactions"
10561:Journal of the American Chemical Society
10533:
10445:
10333:Standard electrode potential (data page)
4953:= -0.414 V for the reduction of protons.
4587:
3558:measured at pH 7, a value closer to the
2718:The formal standard reduction potential
1066:is the activity of the reduced form and
235:(C): a = γ C. So, if the concentration (
121:) to be converted in its reduced form (
10524:
10383:
10283:Dependency of reduction potential on pH
10213:Significance in other scientific fields
10201:and B. Damaskin, Sergio Trasatti, etc.
5082:= +0.815 V for the reduction of oxygen.
4631:by applying a sufficient difference of
3903:
3202:, when the total concentration of each
125:), the half-reaction is expressed as:
14:
10939:
10908:Interactive Nernst/Goldman Java Applet
10861:Journal of the Electrochemical Society
10788:
10591:
10426:
7663:, so we can also write the entropy as
5183:, the Nernst equation is also used in
3509:Formal standard reduction potentials (
3226:(F). So, expressing the concentration
3194:According to Brown and Swift (1949):
1084:At room temperature (25 °C), the
4134:. The Nernst equation relates pH and
3607:) allow to more easily estimate if a
3409:are included in the formal potential
1125:{\displaystyle V_{T}={\frac {RT}{F}}}
1075:is the activity of the oxidized form.
102:General form with chemical activities
10858:
10625:(5th ed.). Wiley. p. 466.
10451:
10389:
9359:Relation to the chemical equilibrium
5853:per cubic meter, to match the other
4380:as a function of pH with a slope of
2596:refers to its value determined when
994:transferred in the cell reaction or
9530:{\displaystyle E_{cell}^{\ominus }}
9485:{\displaystyle \Delta G^{\ominus }}
9389:{\displaystyle \Delta G^{\ominus }}
9008:{\displaystyle Q_{r}={\frac {}{}},}
8616:. Under certain circumstances (see
5924:(K) is no longer zero, but rather J
5389:
5206:
4647:(reduction of water protons) while
4111:{\displaystyle \Delta G^{\ominus }}
2165:Formal standard reduction potential
1932:Where the first term including the
24:
10359:Electrochemistry, past and present
9547:
9469:
9413:
9373:
9192:
9189:
9176:
9173:
9170:
9104:
9101:
9088:
9085:
9082:
8992:
8989:
8976:
8973:
8970:
8804:
8795:
8783:
8774:
8554:
8536:
8516:
8498:
8360:
8342:
8322:
8304:
8274:
8271:
8268:
8259:
8242:
8222:
8188:
8168:
8142:
8139:
8136:
8127:
8048:
8025:
8001:
7888:so that the entropy of state 2 is
7804:
7769:
7766:
7763:
7760:
7757:
7754:
7751:
7748:
7713:
7710:
7707:
7704:
7701:
7698:
7695:
7692:
7545:
7525:
7522:
7519:
7386:
7383:
7370:
7367:
7364:
7303:
7300:
7287:
7284:
7281:
7140:
7137:
7124:
7121:
7118:
7085:
7070:
7012:
7009:
6996:
6993:
6990:
6962:
6910:
6775:
6772:
6759:
6756:
6753:
6652:
6649:
6646:
6630:
6627:
6608:
6605:
6589:
6586:
6570:
6567:
6548:
6545:
6529:
6526:
6510:
6491:
6473:
6470:
6454:
6451:
6432:
6429:
6413:
6410:
6407:
6391:
6388:
6369:
6366:
6350:
6347:
6344:
6328:
6309:
6219:
6216:
6200:
6197:
6178:
6175:
6159:
6156:
6140:
6121:
6103:
6100:
6097:
6081:
6078:
6059:
6056:
6040:
6037:
6034:
6018:
5999:
5776:
5773:
5770:
5749:
5725:
5693:
5690:
5669:
5645:
5614:
5611:
5590:
5566:
5534:
5531:
5528:
5507:
5483:
5423:
4518:to indicate that it refers to the
4095:
4051:
3301:
3283:
1079:
544:
468:
459:
85:respectively. It was named after
25:
10968:
10898:Nernst/Goldman Equation Simulator
10891:
10817:The Journal of Physical Chemistry
9282:standard temperature and pressure
4597:standard temperature and pressure
2643:. A more particular case is when
921:) at the temperature of interest,
10205:Time dependence of the potential
8597:, each raised to the power of a
4578:Examples with a Pourbaix diagram
3611:reaction supposed to occur in a
3145:, m) concentrations in place of
1461:) the Nernst equation becomes:
1057:for the relevant species, where
27:Physical law in electrochemistry
10824:
10808:
10782:
10756:
10723:
10711:
10639:
10121:
6814:barrier for gaining an electron
6717:that is setting the solution's
5049:= +1.229 V with respect to the
3940:
3897:
3222:(m), and so are said to be one
3169:from reduction to oxidation or
2479:The formal reduction potential
1148:, in which case it is written:
883:at the temperature of interest,
10957:Eponymous equations of physics
10769:, Springer, pp. 527–528,
10167:
9196:
9185:
9180:
9166:
9108:
9097:
9092:
9078:
8996:
8985:
8980:
8966:
8559:
8550:
8541:
8532:
8521:
8512:
8503:
8494:
8365:
8356:
8347:
8338:
8327:
8318:
8309:
8300:
8246:
8238:
8226:
8218:
8192:
8184:
8172:
8164:
8052:
8044:
8029:
8021:
8005:
7997:
7779:
7744:
7723:
7688:
7390:
7379:
7374:
7360:
7307:
7296:
7291:
7277:
7144:
7133:
7128:
7114:
7016:
7005:
7000:
6986:
6860:
6857:barrier for losing an electron
6852:
6817:
6809:
6779:
6768:
6763:
6749:
5818:is the membrane potential (in
5357:
5349:
5344:
5336:
5288:
5280:
5275:
5267:
5106:{\displaystyle E_{\text{red}}}
5075:{\displaystyle E_{\text{red}}}
4946:{\displaystyle E_{\text{red}}}
4542:{\displaystyle E_{\text{red}}}
4484:{\displaystyle E_{\text{red}}}
4445:{\displaystyle E_{\text{red}}}
4373:{\displaystyle E_{\text{red}}}
4349:where curly brackets indicate
4039:
4031:
3930:
3905:
3815:{\displaystyle E_{\text{red}}}
3674:{\displaystyle E_{\text{red}}}
2810:= 1) under given conditions.
2775:{\displaystyle E_{\text{red}}}
2013:{\displaystyle E_{\text{red}}}
586:) is a unit conversion factor
571:{\displaystyle \Delta G=-zFE.}
317:
311:
306:
300:
152:
13:
1:
10739:Zeitschrift für Elektrochemie
10471:10.5189/revpolarography.48.29
10427:Wenzel, Thomas (2020-06-09).
10343:
9336:{\displaystyle E^{\ominus '}}
8620:) each activity term such as
6681:
4835:For the reduction of H into H
4627:. When water is submitted to
4571:standard reduction potentials
4425:This equation predicts lower
3556:standard reduction potentials
3372:{\displaystyle \gamma _{red}}
904:half-cell reduction potential
208:) and the oxidized form (the
96:
93:who formulated the equation.
10592:Harvey, David (2020-06-15).
10328:Standard electrode potential
10158:standard electrode potential
9304:{\displaystyle E^{\ominus }}
8088:{\displaystyle S^{\ominus }}
7582:where the change of entropy
7494:of a molecule is defined as
5195:with respect to one type of
3973:standard reduction potential
3546:) are also commonly used in
3402:{\displaystyle \gamma _{ox}}
2171:Standard electrode potential
949:universal ideal gas constant
531:universal ideal gas constant
189:), is the ratio between the
63:standard electrode potential
7:
10820:. Cornell University. 1906.
10271:
10177:, and there are additional
5153:value (SHE) when the ratio
5051:standard hydrogen electrode
4922:standard hydrogen electrode
4520:standard hydrogen electrode
3824:standard hydrogen electrode
3683:standard hydrogen electrode
3620:standard hydrogen electrode
3200:standard hydrogen electrode
356:) by the reagent activity (
197:) of the reduced form (the
10:
10973:
10903:Nernst Equation Calculator
10766:Electrochemical Dictionary
10175:when there is current flow
8599:stoichiometric coefficient
5393:
5210:
5201:acid dissociation constant
5199:. It can be linked to the
5172:
4614:oxido-reduction equilibria
4581:
3692:
3502:
2711:
2472:, or the concentration of
2168:
29:
18:Formal reduction potential
10952:Electrochemical equations
10156:We have thus related the
9785:electrochemical potential
9781:thermodynamic equilibrium
8731:and a positive potential
7165:Dividing the equation by
6719:electrochemical potential
5380:thermodynamic equilibrium
5086:The offset of -414 mV in
4422:volt (pH has no units).
3039:{\displaystyle \ln {1}=0}
81:undergoing reduction and
10751:10.1002/bbpc.19060120105
10190:exchange current density
8855:and the cell potential,
7442:are used instead of the
5914:by electrochemical force
5378:When the membrane is in
47:chemical thermodynamical
30:Not to be confused with
10789:Zutshi, Kamala (2008),
8935:For the redox reaction
5169:Applications in biology
4491:is then often noted as
1949:{\displaystyle \gamma }
1454:{\displaystyle \gamma }
939:standard cell potential
917:is the cell potential (
372:of the half-reaction:
10458:Review of Polarography
10308:Nernst–Planck equation
10148:
10015:
9763:
9682:
9600:
9531:
9486:
9453:
9390:
9337:
9305:
9280:The cell potential at
9272:
9009:
8924:
8849:
8578:
8384:
8089:
8062:
7961:
7882:
7789:
7555:
7407:
7157:
7029:
6941:
6687:Using Boltzmann factor
6673:
6240:
5885:is the temperature in
5798:
5717:
5637:
5558:
5475:
5370:
5107:
5076:
5043:
5010:
4957:For the reduction of O
4947:
4914:
4888:because by convention
4881:
4819:
4609:
4543:
4512:
4485:
4446:
4416:
4374:
4339:
4155:
4112:
4079:
4000:
3962:
3816:
3789:
3756:
3720:
3675:
3648:
3601:
3540:
3485:
3440:
3403:
3373:
3324:
3212:
3192:a standard potential.
3118:
3081:
3040:
3002:
2955:
2902:
2855:
2776:
2749:
2674:
2637:
2590:
2552:
2510:
2458:
2418:
2315:
2207:
2156:
2051:
2014:
1987:
1950:
1924:
1731:
1589:
1455:
1432:
1317:= ln(10) ≈ 2.3026 and
1305:
1126:
980:is the temperature in
859:
775:
572:
510:
416:
327:
163:
10718:J. Electroanal. Chem.
10512:TheFreeDictionary.com
10164:of a redox reaction.
10149:
10016:
9764:
9683:
9601:
9532:
9487:
9454:
9391:
9345:activity coefficients
9343:, which includes the
9338:
9306:
9273:
9010:
8925:
8850:
8694:only by a constant:
8579:
8385:
8090:
8063:
7962:
7883:
7790:
7654:activity coefficients
7556:
7408:
7158:
7030:
6942:
6735:for these processes:
6674:
6241:
5910:sodium-potassium pump
5799:
5703:
5623:
5544:
5461:
5406:G-H-K influx equation
5371:
5108:
5077:
5044:
5011:
4948:
4915:
4882:
4820:
4591:
4544:
4513:
4511:{\displaystyle E_{h}}
4486:
4447:
4417:
4375:
4340:
4156:
4154:{\displaystyle E_{h}}
4113:
4080:
4001:
3963:
3822:expressed versus the
3817:
3790:
3788:{\displaystyle E_{h}}
3757:
3755:{\displaystyle E_{h}}
3721:
3719:{\displaystyle E_{h}}
3676:
3649:
3602:
3541:
3486:
3441:
3404:
3374:
3345:activity coefficients
3325:
3196:
3151:formal concentrations
3119:
3082:
3041:
3003:
2956:
2903:
2856:
2777:
2750:
2675:
2638:
2591:
2553:
2511:
2459:
2419:
2316:
2208:
2157:
2052:
2015:
1988:
1951:
1934:activity coefficients
1925:
1732:
1590:
1456:
1433:
1362:via the relationship
1306:
1127:
860:
776:
573:
533:. The cell potential
511:
452:by the relationship:
417:
328:
241:activity coefficients
227:(mol/L solution), or
164:
10923:Chemistry LibreTexts
10795:, pp. 127–128,
10720:, 79 (1977), 259-266
10698:Chemistry LibreTexts
10598:Chemistry LibreTexts
10594:"2.2: Concentration"
10452:Kano, Kenji (2002).
10433:Chemistry LibreTexts
10261:equilibrium constant
10257:electromotive forces
10253:chemical equilibrium
10162:equilibrium constant
10033:
9848:
9809:equilibrium constant
9777:chemical equilibrium
9698:
9619:
9544:
9500:
9466:
9410:
9398:equilibrium constant
9370:
9315:
9288:
9019:
8947:
8859:
8771:
8618:chemical equilibrium
8400:
8124:
8072:
7991:
7892:
7801:
7667:
7500:
7223:
7061:
6953:
6739:
6254:
5944:
5899:(coulombs per mole).
5414:
5229:
5187:for calculating the
5090:
5059:
5021:
4972:
4930:
4892:
4846:
4769:
4688:(cathode: reduction)
4633:electrical potential
4526:
4495:
4468:
4429:
4384:
4357:
4168:
4138:
4092:
4013:
3978:
3841:
3799:
3772:
3739:
3703:
3658:
3626:
3574:
3513:
3458:
3413:
3383:
3350:
3244:
3188:= 1 bar) it becomes
3091:
3050:
3046:, and that the term
3016:
2965:
2915:
2865:
2820:
2759:
2722:
2647:
2600:
2563:
2525:
2483:
2431:
2325:
2217:
2180:
2063:
2024:
1997:
1960:
1940:
1742:
1600:
1467:
1445:
1405:
1395:activity coefficient
1154:
1091:
785:
627:
541:
456:
379:
365:equilibrium constant
338:chemical equilibrium
254:
221:activity coefficient
132:
67:absolute temperature
10318:Reduction potential
10288:Electrode potential
9724:
9654:
9595:
9526:
8484:
8450:
8284:
8097:standard conditions
7095:
5763:
5739:
5683:
5659:
5604:
5580:
5521:
5497:
5038:
4909:
4799:
4643:is produced at the
4639:immersed in water,
4211:
4030:
3995:
3916:
3795:explicitly denotes
3643:
3596:
3535:
3480:
3435:
3175:standard conditions
3113:
2950:
2850:
2744:
2669:
2585:
2547:
2505:
2453:
2360:
2257:
2239:
2202:
2098:
2046:
1982:
1864:
1780:
1630:
1497:
1427:
919:electromotive force
881:reduction potential
815:
714:
657:
619:is the fundamental
191:chemical activities
110:) accepts a number
61:reaction) from the
51:reduction potential
10508:"Formal potential"
10303:Membrane potential
10278:Concentration cell
10144:
10011:
10009:
9794:and therefore the
9759:
9701:
9678:
9631:
9596:
9572:
9527:
9503:
9482:
9462:At the same time,
9449:
9396:is related to the
9386:
9333:
9301:
9268:
9266:
9005:
8920:
8845:
8683:is related to the
8642:chemical potential
8574:
8485:
8463:
8462:
8451:
8429:
8428:
8380:
8262:
8095:is the entropy at
8085:
8058:
7957:
7878:
7785:
7576:isothermal process
7551:
7453:Faraday's constant
7426:Boltzmann constant
7403:
7401:
7153:
7079:
7025:
6937:
6935:
6703:chemical potential
6669:
6236:
5897:Faraday's constant
5873:ideal gas constant
5794:
5783:
5782:
5747:
5723:
5667:
5643:
5621:
5620:
5588:
5564:
5505:
5481:
5384:membrane potential
5366:
5213:Reversal potential
5189:electric potential
5103:
5072:
5039:
5024:
5006:
4943:
4910:
4895:
4877:
4815:
4785:
4715:(anode: oxidation)
4610:
4539:
4508:
4481:
4442:
4412:
4370:
4335:
4197:
4151:
4132:Faraday's constant
4108:
4075:
4016:
3996:
3981:
3958:
3935:
3812:
3785:
3752:
3716:
3671:
3644:
3629:
3597:
3577:
3536:
3516:
3481:
3461:
3436:
3416:
3399:
3369:
3320:
3157:in the expression
3114:
3094:
3077:
3036:
2998:
2951:
2931:
2898:
2851:
2836:
2772:
2745:
2725:
2670:
2650:
2633:
2586:
2566:
2548:
2528:
2506:
2486:
2454:
2434:
2414:
2341:
2311:
2243:
2220:
2203:
2183:
2152:
2079:
2047:
2027:
2010:
1983:
1963:
1946:
1920:
1866:
1845:
1842:
1766:
1727:
1616:
1585:
1483:
1451:
1428:
1408:
1301:
1146:natural logarithms
1122:
855:
801:
771:
700:
643:
568:
506:
412:
363:) is equal to the
323:
159:
106:When an oxidizer (
10873:10.1149/1.2096700
10845:978-0-19-855817-0
10832:Huizenga, John R.
10632:978-1-118-91840-1
10534:PalmSens (2021).
10368:978-0-8412-1572-6
10323:Solvated electron
10199:Alexander Frumkin
10195:solvated electron
10142:
10138:
10125:
10119:
10116:
10087:
10005:
9929:
9896:
9796:reaction quotient
9746:
9365:Gibbs free energy
9243:
9200:
9155:
9112:
9067:
9000:
8899:
8723:Gibbs free energy
8685:Gibbs free energy
8569:
8486:
8453:
8419:
8394:reaction quotient
8375:
8120:is then given by
7952:
7873:
7743:
7687:
7535:
7530:
7508:
7462:Avogadro constant
7394:
7349:
7311:
7266:
7148:
7020:
6924:
6880:
6858:
6815:
6783:
6715:working electrode
6659:
6283:
6226:
5973:
5784:
5445:
5402:resting potential
5361:
5355:
5342:
5318:
5292:
5286:
5273:
5256:
5137:to the number of
5130:of the number of
5100:
5069:
5031:
4999:
4982:
4940:
4902:
4870:
4856:
4808:
4792:
4779:
4651:is formed at the
4536:
4478:
4439:
4406:
4367:
4333:
4328:
4305:
4223:
4204:
4191:
4120:Gibbs free energy
4073:
4037:
4023:
3988:
3937:
3872:
3809:
3668:
3636:
3613:metabolic process
3584:
3554:for referring to
3523:
3468:
3423:
3312:
3308:
3290:
3269:
3266:
3256:
3101:
3075:
3072:
3062:
2990:
2987:
2977:
2938:
2925:
2890:
2887:
2877:
2843:
2830:
2769:
2732:
2657:
2625:
2622:
2612:
2573:
2535:
2493:
2474:complexing agents
2441:
2412:
2409:
2399:
2382:
2348:
2335:
2309:
2306:
2296:
2279:
2250:
2227:
2190:
2150:
2147:
2137:
2120:
2086:
2073:
2034:
2007:
1970:
1918:
1915:
1905:
1888:
1852:
1832:
1829:
1819:
1802:
1773:
1760:
1758:
1752:
1720:
1717:
1707:
1687:
1684:
1674:
1652:
1623:
1610:
1578:
1575:
1565:
1554:
1551:
1541:
1519:
1490:
1477:
1415:
1296:
1293:
1283:
1259:
1221:
1218:
1208:
1191:
1142:common logarithms
1120:
990:is the number of
879:is the half-cell
837:
808:
795:
766:
763:
753:
736:
707:
679:
650:
637:
613:Avogadro constant
527:reaction quotient
427:Gibbs free energy
410:
407:
397:
321:
292:
289:
279:
174:reaction quotient
157:
145:
138:
16:(Redirected from
10964:
10933:
10931:
10930:
10885:
10884:
10856:
10850:
10849:
10828:
10822:
10821:
10812:
10806:
10805:
10786:
10780:
10779:
10760:
10754:
10753:
10733:(January 1906),
10731:Karaoglanoff, Z.
10727:
10721:
10715:
10709:
10708:
10706:
10705:
10690:
10684:
10682:Faraday constant
10679:
10659:
10643:
10637:
10636:
10614:
10608:
10607:
10605:
10604:
10589:
10583:
10582:
10567:(8): 2719–2723.
10556:
10550:
10549:
10547:
10546:
10531:
10522:
10521:
10519:
10518:
10504:
10498:
10497:
10495:
10494:
10473:
10449:
10443:
10442:
10440:
10439:
10424:
10418:
10417:
10409:
10400:
10399:
10387:
10381:
10380:
10354:
10313:Pourbaix diagram
10298:Goldman equation
10267:
10242:John R. Huizenga
10187:
10153:
10151:
10150:
10145:
10143:
10140:
10136:
10126:
10123:
10120:
10118:
10117:
10114:
10108:
10107:
10106:
10093:
10088:
10086:
10085:
10084:
10071:
10070:
10069:
10056:
10045:
10044:
10020:
10018:
10017:
10012:
10010:
10006:
10004:
9996:
9995:
9994:
9978:
9956:
9955:
9930:
9928:
9920:
9912:
9897:
9895:
9887:
9879:
9874:
9873:
9838:
9819:
9806:
9793:
9768:
9766:
9765:
9760:
9758:
9747:
9745:
9737:
9729:
9723:
9718:
9691:And therefore:
9687:
9685:
9684:
9679:
9677:
9653:
9648:
9605:
9603:
9602:
9597:
9594:
9589:
9559:
9558:
9536:
9534:
9533:
9528:
9525:
9520:
9495:
9491:
9489:
9488:
9483:
9481:
9480:
9458:
9456:
9455:
9450:
9448:
9425:
9424:
9402:
9395:
9393:
9392:
9387:
9385:
9384:
9342:
9340:
9339:
9334:
9332:
9331:
9330:
9310:
9308:
9307:
9302:
9300:
9299:
9277:
9275:
9274:
9269:
9267:
9260:
9259:
9244:
9242:
9234:
9226:
9221:
9220:
9205:
9201:
9199:
9195:
9183:
9179:
9164:
9156:
9154:
9146:
9138:
9133:
9132:
9117:
9113:
9111:
9107:
9095:
9091:
9076:
9068:
9066:
9058:
9050:
9045:
9044:
9014:
9012:
9011:
9006:
9001:
8999:
8995:
8983:
8979:
8964:
8959:
8958:
8942:
8940:
8929:
8927:
8926:
8921:
8916:
8915:
8900:
8898:
8890:
8882:
8877:
8876:
8854:
8852:
8851:
8846:
8841:
8840:
8816:
8815:
8766:
8756:
8750:
8736:
8730:
8719:Faraday constant
8716:
8710:
8704:
8693:
8682:
8676:
8675:
8673:
8672:
8667:
8664:
8639:
8633:
8631:
8630:
8615:
8609:
8596:
8583:
8581:
8580:
8575:
8570:
8568:
8567:
8566:
8557:
8549:
8548:
8539:
8530:
8529:
8528:
8519:
8511:
8510:
8501:
8492:
8487:
8483:
8482:
8481:
8471:
8461:
8449:
8448:
8447:
8437:
8427:
8417:
8412:
8411:
8389:
8387:
8386:
8381:
8376:
8374:
8373:
8372:
8363:
8355:
8354:
8345:
8336:
8335:
8334:
8325:
8317:
8316:
8307:
8298:
8283:
8278:
8277:
8255:
8254:
8245:
8225:
8211:
8210:
8201:
8200:
8191:
8171:
8157:
8156:
8147:
8146:
8145:
8116:
8112:
8108:
8104:
8094:
8092:
8091:
8086:
8084:
8083:
8067:
8065:
8064:
8059:
8051:
8028:
8020:
8019:
8004:
7986:
7977:
7966:
7964:
7963:
7958:
7953:
7951:
7950:
7941:
7940:
7931:
7917:
7916:
7904:
7903:
7887:
7885:
7884:
7879:
7874:
7872:
7871:
7862:
7861:
7852:
7835:
7834:
7822:
7821:
7794:
7792:
7791:
7786:
7772:
7741:
7716:
7685:
7662:
7651:
7650:
7648:
7647:
7639:
7636:
7623:
7619:
7617:
7615:
7614:
7606:
7603:
7572:
7566:
7560:
7558:
7557:
7552:
7533:
7532:
7531:
7529:
7528:
7516:
7511:
7506:
7489:
7476:
7459:
7450:
7441:
7432:
7412:
7410:
7409:
7404:
7402:
7395:
7393:
7389:
7377:
7373:
7358:
7350:
7345:
7337:
7332:
7331:
7316:
7312:
7310:
7306:
7294:
7290:
7275:
7267:
7262:
7254:
7249:
7248:
7216:
7215:
7210:
7209:
7207:
7206:
7201:
7198:
7189:
7187:
7186:
7181:
7178:
7168:
7162:
7160:
7159:
7154:
7149:
7147:
7143:
7131:
7127:
7112:
7094:
7089:
7088:
7075:
7074:
7073:
7056:
7054:
7053:
7046:
7034:
7032:
7031:
7026:
7021:
7019:
7015:
7003:
6999:
6984:
6967:
6966:
6965:
6946:
6944:
6943:
6938:
6936:
6929:
6925:
6923:
6915:
6914:
6913:
6903:
6885:
6881:
6879:
6878:
6874:
6867:
6859:
6856:
6836:
6835:
6831:
6824:
6816:
6813:
6793:
6784:
6782:
6778:
6766:
6762:
6747:
6733:Boltzmann factor
6730:
6728:
6727:
6712:
6697:
6678:
6676:
6675:
6670:
6665:
6664:
6660:
6658:
6657:
6656:
6655:
6643:
6639:
6638:
6633:
6619:
6618:
6617:
6616:
6611:
6594:
6593:
6592:
6583:
6579:
6578:
6573:
6559:
6558:
6557:
6556:
6551:
6534:
6533:
6532:
6523:
6519:
6518:
6513:
6502:
6501:
6500:
6499:
6494:
6479:
6478:
6477:
6476:
6467:
6463:
6462:
6457:
6443:
6442:
6441:
6440:
6435:
6418:
6417:
6416:
6404:
6400:
6399:
6394:
6380:
6379:
6378:
6377:
6372:
6355:
6354:
6353:
6341:
6337:
6336:
6331:
6320:
6319:
6318:
6317:
6312:
6297:
6284:
6279:
6271:
6266:
6265:
6245:
6243:
6242:
6237:
6232:
6231:
6227:
6225:
6224:
6223:
6222:
6213:
6209:
6208:
6203:
6189:
6188:
6187:
6186:
6181:
6164:
6163:
6162:
6153:
6149:
6148:
6143:
6132:
6131:
6130:
6129:
6124:
6109:
6108:
6107:
6106:
6094:
6090:
6089:
6084:
6070:
6069:
6068:
6067:
6062:
6045:
6044:
6043:
6031:
6027:
6026:
6021:
6010:
6009:
6008:
6007:
6002:
5987:
5974:
5969:
5961:
5956:
5955:
5907:
5894:
5884:
5870:
5864:
5848:
5840:
5822:, equivalent to
5817:
5803:
5801:
5800:
5795:
5790:
5789:
5785:
5781:
5780:
5779:
5767:
5762:
5757:
5752:
5741:
5740:
5738:
5733:
5728:
5716:
5711:
5698:
5697:
5696:
5687:
5682:
5677:
5672:
5661:
5660:
5658:
5653:
5648:
5636:
5631:
5619:
5618:
5617:
5608:
5603:
5598:
5593:
5582:
5581:
5579:
5574:
5569:
5557:
5552:
5539:
5538:
5537:
5525:
5520:
5515:
5510:
5499:
5498:
5496:
5491:
5486:
5474:
5469:
5459:
5446:
5441:
5433:
5428:
5427:
5426:
5396:Goldman equation
5390:Goldman equation
5375:
5373:
5372:
5367:
5362:
5360:
5356:
5353:
5347:
5343:
5341:ion outside cell
5340:
5334:
5329:
5328:
5319:
5317:
5309:
5301:
5293:
5291:
5287:
5284:
5278:
5274:
5272:ion outside cell
5271:
5265:
5257:
5255:
5247:
5239:
5222:
5207:Nernst potential
5165:differs from 1.
5163:
5162:
5158:
5140:
5133:
5128:
5127:
5123:
5112:
5110:
5109:
5104:
5102:
5101:
5098:
5081:
5079:
5078:
5073:
5071:
5070:
5067:
5048:
5046:
5045:
5040:
5037:
5032:
5029:
5015:
5013:
5012:
5007:
4997:
4984:
4983:
4980:
4952:
4950:
4949:
4944:
4942:
4941:
4938:
4919:
4917:
4916:
4911:
4908:
4903:
4900:
4886:
4884:
4883:
4878:
4868:
4858:
4857:
4854:
4830:Pourbaix diagram
4824:
4822:
4821:
4816:
4806:
4798:
4793:
4790:
4781:
4780:
4777:
4748:
4741:
4730:
4723:
4714:
4713:
4687:
4686:
4666:
4626:
4618:Pourbaix diagram
4593:Pourbaix diagram
4584:Pourbaix diagram
4548:
4546:
4545:
4540:
4538:
4537:
4534:
4517:
4515:
4514:
4509:
4507:
4506:
4490:
4488:
4487:
4482:
4480:
4479:
4476:
4451:
4449:
4448:
4443:
4441:
4440:
4437:
4421:
4419:
4418:
4413:
4411:
4407:
4399:
4379:
4377:
4376:
4371:
4369:
4368:
4365:
4344:
4342:
4341:
4336:
4334:
4331:
4329:
4324:
4315:
4310:
4306:
4304:
4303:
4302:
4287:
4286:
4270:
4269:
4268:
4253:
4252:
4236:
4224:
4216:
4210:
4205:
4202:
4193:
4192:
4189:
4180:
4179:
4160:
4158:
4157:
4152:
4150:
4149:
4129:
4125:
4118:is the standard
4117:
4115:
4114:
4109:
4107:
4106:
4084:
4082:
4081:
4076:
4074:
4072:
4064:
4063:
4062:
4049:
4038:
4035:
4029:
4024:
4021:
4005:
4003:
4002:
3997:
3994:
3989:
3986:
3967:
3965:
3964:
3959:
3939:
3938:
3936:
3934:
3933:
3926:
3918:
3917:
3915:
3908:
3900:
3896:
3895:
3879:
3878:
3877:
3870:
3821:
3819:
3818:
3813:
3811:
3810:
3807:
3794:
3792:
3791:
3786:
3784:
3783:
3767:
3761:
3759:
3758:
3753:
3751:
3750:
3732:Pourbaix diagram
3725:
3723:
3722:
3717:
3715:
3714:
3695:Pourbaix diagram
3680:
3678:
3677:
3672:
3670:
3669:
3666:
3653:
3651:
3650:
3645:
3642:
3637:
3634:
3606:
3604:
3603:
3598:
3595:
3594:
3585:
3582:
3545:
3543:
3542:
3537:
3534:
3533:
3524:
3521:
3490:
3488:
3487:
3482:
3479:
3478:
3469:
3466:
3445:
3443:
3442:
3437:
3434:
3433:
3424:
3421:
3408:
3406:
3405:
3400:
3398:
3397:
3378:
3376:
3375:
3370:
3368:
3367:
3329:
3327:
3326:
3321:
3313:
3311:
3310:
3309:
3306:
3304:
3293:
3292:
3291:
3288:
3286:
3275:
3270:
3268:
3267:
3264:
3258:
3257:
3254:
3248:
3236:
3229:
3187:
3144:
3123:
3121:
3120:
3115:
3112:
3111:
3102:
3099:
3086:
3084:
3083:
3078:
3076:
3074:
3073:
3070:
3064:
3063:
3060:
3054:
3045:
3043:
3042:
3037:
3029:
3007:
3005:
3004:
2999:
2991:
2989:
2988:
2985:
2979:
2978:
2975:
2969:
2960:
2958:
2957:
2952:
2949:
2948:
2939:
2936:
2927:
2926:
2923:
2907:
2905:
2904:
2899:
2891:
2889:
2888:
2885:
2879:
2878:
2875:
2869:
2860:
2858:
2857:
2852:
2849:
2844:
2841:
2832:
2831:
2828:
2809:
2808:
2806:
2805:
2799:
2796:
2781:
2779:
2778:
2773:
2771:
2770:
2767:
2754:
2752:
2751:
2746:
2743:
2742:
2733:
2730:
2707:
2706:
2704:
2703:
2697:
2694:
2679:
2677:
2676:
2671:
2668:
2667:
2658:
2655:
2642:
2640:
2639:
2634:
2626:
2624:
2623:
2620:
2614:
2613:
2610:
2604:
2595:
2593:
2592:
2587:
2584:
2583:
2574:
2571:
2557:
2555:
2554:
2549:
2546:
2545:
2536:
2533:
2515:
2513:
2512:
2507:
2504:
2503:
2494:
2491:
2463:
2461:
2460:
2455:
2452:
2451:
2442:
2439:
2423:
2421:
2420:
2415:
2413:
2411:
2410:
2407:
2401:
2400:
2397:
2391:
2383:
2381:
2373:
2365:
2359:
2358:
2349:
2346:
2337:
2336:
2333:
2320:
2318:
2317:
2312:
2310:
2308:
2307:
2304:
2298:
2297:
2294:
2288:
2280:
2278:
2270:
2262:
2256:
2251:
2248:
2238:
2237:
2228:
2225:
2212:
2210:
2209:
2204:
2201:
2200:
2191:
2188:
2161:
2159:
2158:
2153:
2151:
2149:
2148:
2145:
2139:
2138:
2135:
2129:
2121:
2119:
2111:
2103:
2097:
2096:
2087:
2084:
2075:
2074:
2071:
2056:
2054:
2053:
2048:
2045:
2044:
2035:
2032:
2019:
2017:
2016:
2011:
2009:
2008:
2005:
1992:
1990:
1989:
1984:
1981:
1980:
1971:
1968:
1955:
1953:
1952:
1947:
1929:
1927:
1926:
1921:
1919:
1917:
1916:
1913:
1907:
1906:
1903:
1897:
1889:
1887:
1879:
1871:
1865:
1863:
1862:
1853:
1850:
1843:
1838:
1834:
1833:
1831:
1830:
1827:
1821:
1820:
1817:
1811:
1803:
1801:
1793:
1785:
1779:
1774:
1771:
1754:
1753:
1750:
1736:
1734:
1733:
1728:
1726:
1722:
1721:
1719:
1718:
1715:
1709:
1708:
1705:
1699:
1688:
1686:
1685:
1682:
1676:
1675:
1672:
1666:
1653:
1651:
1643:
1635:
1629:
1624:
1621:
1612:
1611:
1608:
1594:
1592:
1591:
1586:
1584:
1580:
1579:
1577:
1576:
1573:
1567:
1566:
1563:
1557:
1555:
1553:
1552:
1549:
1543:
1542:
1539:
1533:
1520:
1518:
1510:
1502:
1496:
1491:
1488:
1479:
1478:
1475:
1460:
1458:
1457:
1452:
1437:
1435:
1434:
1429:
1426:
1425:
1416:
1413:
1400:
1392:
1383:
1361:
1352:
1343:
1324:≈ 0.05916 Volt.
1310:
1308:
1307:
1302:
1297:
1295:
1294:
1291:
1285:
1284:
1281:
1275:
1270:
1269:
1260:
1255:
1254:
1253:
1240:
1235:
1234:
1222:
1220:
1219:
1216:
1210:
1209:
1206:
1200:
1192:
1187:
1186:
1177:
1172:
1171:
1131:
1129:
1128:
1123:
1121:
1116:
1108:
1103:
1102:
1074:
1065:
1053:is the chemical
1052:
1046:
1035:
1034:
1032:
1029:
1026:
1022:
1003:
989:
979:
973:
972:
970:
967:
964:
961:
946:
936:
935:
934:
916:
898:
897:
896:
878:
864:
862:
861:
856:
854:
853:
838:
836:
828:
820:
814:
809:
806:
797:
796:
793:
780:
778:
777:
772:
767:
765:
764:
761:
755:
754:
751:
745:
737:
735:
727:
719:
713:
708:
705:
696:
695:
680:
678:
670:
662:
656:
651:
648:
639:
638:
635:
618:
610:
601:
584:Faraday constant
581:
577:
575:
574:
569:
536:
524:
515:
513:
512:
507:
505:
504:
480:
479:
451:
450:
449:
434:
421:
419:
418:
413:
411:
409:
408:
405:
399:
398:
395:
389:
370:
347:
332:
330:
329:
324:
322:
320:
309:
298:
293:
291:
290:
287:
281:
280:
277:
271:
266:
265:
231:(mol/kg water),
218:
207:
183:
168:
166:
165:
160:
158:
155:
151:
150:
143:
136:
124:
117:
109:
91:physical chemist
79:chemical species
39:electrochemistry
21:
10972:
10971:
10967:
10966:
10965:
10963:
10962:
10961:
10937:
10936:
10928:
10926:
10917:
10894:
10889:
10888:
10857:
10853:
10846:
10829:
10825:
10814:
10813:
10809:
10803:
10787:
10783:
10777:
10761:
10757:
10728:
10724:
10716:
10712:
10703:
10701:
10692:
10691:
10687:
10675:
10665:
10664:
10655:
10645:
10644:
10640:
10633:
10615:
10611:
10602:
10600:
10590:
10586:
10557:
10553:
10544:
10542:
10532:
10525:
10516:
10514:
10506:
10505:
10501:
10492:
10490:
10450:
10446:
10437:
10435:
10425:
10421:
10410:
10403:
10398:(8): 1820–1828.
10392:Galvanotechtnik
10388:
10384:
10369:
10355:
10351:
10346:
10274:
10263:
10234:crystal lattice
10215:
10207:
10185:
10170:
10139:
10122:
10113:
10109:
10102:
10098:
10094:
10092:
10080:
10076:
10072:
10065:
10061:
10057:
10055:
10040:
10036:
10034:
10031:
10030:
10008:
10007:
9997:
9990:
9986:
9979:
9977:
9970:
9958:
9957:
9951:
9947:
9940:
9921:
9913:
9911:
9908:
9907:
9888:
9880:
9878:
9869:
9865:
9858:
9851:
9849:
9846:
9845:
9837:
9829:
9824:
9818:
9812:
9804:
9799:
9787:
9754:
9738:
9730:
9728:
9719:
9705:
9699:
9696:
9695:
9673:
9649:
9635:
9620:
9617:
9616:
9590:
9576:
9554:
9550:
9545:
9542:
9541:
9521:
9507:
9501:
9498:
9497:
9493:
9476:
9472:
9467:
9464:
9463:
9444:
9420:
9416:
9411:
9408:
9407:
9400:
9380:
9376:
9371:
9368:
9367:
9361:
9323:
9322:
9318:
9316:
9313:
9312:
9295:
9291:
9289:
9286:
9285:
9265:
9264:
9255:
9251:
9235:
9227:
9225:
9216:
9212:
9203:
9202:
9188:
9184:
9169:
9165:
9163:
9147:
9139:
9137:
9128:
9124:
9115:
9114:
9100:
9096:
9081:
9077:
9075:
9059:
9051:
9049:
9040:
9036:
9029:
9022:
9020:
9017:
9016:
8988:
8984:
8969:
8965:
8963:
8954:
8950:
8948:
8945:
8944:
8938:
8936:
8911:
8907:
8891:
8883:
8881:
8872:
8868:
8860:
8857:
8856:
8836:
8832:
8811:
8807:
8772:
8769:
8768:
8762:
8752:
8738:
8732:
8725:
8712:
8706:
8695:
8688:
8678:
8668:
8665:
8663:
8657:
8656:
8654:
8649:
8644:available from
8635:
8629:
8626:
8625:
8624:
8621:
8611:
8607:
8602:
8594:
8589:
8562:
8558:
8553:
8544:
8540:
8535:
8531:
8524:
8520:
8515:
8506:
8502:
8497:
8493:
8491:
8477:
8473:
8472:
8467:
8457:
8443:
8439:
8438:
8433:
8423:
8416:
8407:
8403:
8401:
8398:
8397:
8368:
8364:
8359:
8350:
8346:
8341:
8337:
8330:
8326:
8321:
8312:
8308:
8303:
8299:
8297:
8279:
8267:
8266:
8250:
8249:
8241:
8221:
8206:
8205:
8196:
8195:
8187:
8167:
8152:
8151:
8135:
8134:
8130:
8125:
8122:
8121:
8118:
8114:
8110:
8106:
8102:
8079:
8075:
8073:
8070:
8069:
8047:
8024:
8015:
8011:
8000:
7992:
7989:
7988:
7985:
7979:
7976:
7970:
7946:
7942:
7936:
7932:
7930:
7912:
7908:
7899:
7895:
7893:
7890:
7889:
7867:
7863:
7857:
7853:
7851:
7830:
7826:
7817:
7813:
7802:
7799:
7798:
7747:
7691:
7668:
7665:
7664:
7660:
7646:
7640:
7637:
7635:
7629:
7628:
7626:
7625:
7621:
7613:
7607:
7604:
7602:
7596:
7595:
7593:
7583:
7568:
7564:
7518:
7517:
7512:
7510:
7509:
7501:
7498:
7497:
7488:
7478:
7475:
7465:
7455:
7446:
7437:
7435:electron charge
7428:
7418:
7400:
7399:
7382:
7378:
7363:
7359:
7357:
7338:
7336:
7327:
7323:
7314:
7313:
7299:
7295:
7280:
7276:
7274:
7255:
7253:
7244:
7240:
7233:
7226:
7224:
7221:
7220:
7213:
7212:
7202:
7199:
7194:
7193:
7191:
7182:
7179:
7174:
7173:
7171:
7170:
7166:
7136:
7132:
7117:
7113:
7111:
7090:
7084:
7083:
7069:
7068:
7064:
7062:
7059:
7058:
7051:
7050:
7048:
7044:
7038:
7008:
7004:
6989:
6985:
6983:
6961:
6960:
6956:
6954:
6951:
6950:
6934:
6933:
6916:
6909:
6908:
6904:
6902:
6898:
6883:
6882:
6863:
6855:
6848:
6844:
6837:
6820:
6812:
6805:
6801:
6794:
6792:
6785:
6771:
6767:
6752:
6748:
6746:
6742:
6740:
6737:
6736:
6725:
6724:
6722:
6711:
6705:
6695:
6689:
6684:
6645:
6644:
6634:
6626:
6625:
6621:
6620:
6612:
6604:
6603:
6602:
6598:
6585:
6584:
6574:
6566:
6565:
6561:
6560:
6552:
6544:
6543:
6542:
6538:
6525:
6524:
6514:
6509:
6508:
6504:
6503:
6495:
6490:
6489:
6488:
6484:
6480:
6469:
6468:
6458:
6450:
6449:
6445:
6444:
6436:
6428:
6427:
6426:
6422:
6406:
6405:
6395:
6387:
6386:
6382:
6381:
6373:
6365:
6364:
6363:
6359:
6343:
6342:
6332:
6327:
6326:
6322:
6321:
6313:
6308:
6307:
6306:
6302:
6298:
6296:
6292:
6291:
6272:
6270:
6261:
6257:
6255:
6252:
6251:
6215:
6214:
6204:
6196:
6195:
6191:
6190:
6182:
6174:
6173:
6172:
6168:
6155:
6154:
6144:
6139:
6138:
6134:
6133:
6125:
6120:
6119:
6118:
6114:
6110:
6096:
6095:
6085:
6077:
6076:
6072:
6071:
6063:
6055:
6054:
6053:
6049:
6033:
6032:
6022:
6017:
6016:
6012:
6011:
6003:
5998:
5997:
5996:
5992:
5988:
5986:
5982:
5981:
5962:
5960:
5951:
5947:
5945:
5942:
5941:
5939:
5935:
5931:
5927:
5923:
5919:
5905:
5892:
5882:
5868:
5863:
5860:
5847:
5844:
5839:
5833:
5816:
5810:
5769:
5768:
5758:
5753:
5748:
5743:
5742:
5734:
5729:
5724:
5722:
5718:
5712:
5707:
5689:
5688:
5678:
5673:
5668:
5663:
5662:
5654:
5649:
5644:
5642:
5638:
5632:
5627:
5610:
5609:
5599:
5594:
5589:
5584:
5583:
5575:
5570:
5565:
5563:
5559:
5553:
5548:
5527:
5526:
5516:
5511:
5506:
5501:
5500:
5492:
5487:
5482:
5480:
5476:
5470:
5465:
5458:
5454:
5453:
5434:
5432:
5422:
5421:
5417:
5415:
5412:
5411:
5398:
5392:
5354:ion inside cell
5352:
5348:
5339:
5335:
5333:
5324:
5320:
5310:
5302:
5300:
5285:ion inside cell
5283:
5279:
5270:
5266:
5264:
5248:
5240:
5238:
5230:
5227:
5226:
5218:
5215:
5209:
5177:
5171:
5160:
5156:
5155:
5152:
5138:
5131:
5125:
5121:
5120:
5097:
5093:
5091:
5088:
5087:
5066:
5062:
5060:
5057:
5056:
5055:So, at pH = 7,
5054:
5053:(SHE: pH = 1).
5033:
5028:
5022:
5019:
5018:
5016:
4979:
4975:
4973:
4970:
4969:
4964:
4960:
4937:
4933:
4931:
4928:
4927:
4926:So, at pH = 7,
4925:
4924:(SHE: pH = 1).
4904:
4899:
4893:
4890:
4889:
4887:
4853:
4849:
4847:
4844:
4843:
4838:
4794:
4789:
4776:
4772:
4770:
4767:
4766:
4757:
4746:
4739:
4737:
4728:
4721:
4711:
4707:
4703:
4702:
4696:
4685:
4682:2 H + 2 e ⇌ H
4681:
4680:
4674:
4664:
4660:
4658:
4624:
4620:
4586:
4580:
4559:
4552:
4533:
4529:
4527:
4524:
4523:
4502:
4498:
4496:
4493:
4492:
4475:
4471:
4469:
4466:
4465:
4463:
4459:
4455:
4436:
4432:
4430:
4427:
4426:
4398:
4394:
4385:
4382:
4381:
4364:
4360:
4358:
4355:
4354:
4330:
4316:
4314:
4298:
4294:
4282:
4278:
4271:
4264:
4260:
4248:
4244:
4237:
4235:
4231:
4215:
4206:
4201:
4188:
4184:
4175:
4171:
4169:
4166:
4165:
4145:
4141:
4139:
4136:
4135:
4127:
4123:
4102:
4098:
4093:
4090:
4089:
4065:
4058:
4054:
4050:
4048:
4034:
4025:
4020:
4014:
4011:
4010:
3990:
3985:
3979:
3976:
3975:
3929:
3922:
3921:
3919:
3911:
3904:
3902:
3901:
3899:
3898:
3891:
3887:
3873:
3869:
3868:
3842:
3839:
3838:
3806:
3802:
3800:
3797:
3796:
3779:
3775:
3773:
3770:
3769:
3746:
3742:
3740:
3737:
3736:
3734:
3710:
3706:
3704:
3701:
3700:
3697:
3691:
3665:
3661:
3659:
3656:
3655:
3638:
3633:
3627:
3624:
3623:
3587:
3586:
3581:
3575:
3572:
3571:
3526:
3525:
3520:
3514:
3511:
3510:
3507:
3501:
3471:
3470:
3465:
3459:
3456:
3455:
3426:
3425:
3420:
3414:
3411:
3410:
3390:
3386:
3384:
3381:
3380:
3357:
3353:
3351:
3348:
3347:
3305:
3300:
3299:
3294:
3287:
3282:
3281:
3276:
3274:
3263:
3259:
3253:
3249:
3247:
3245:
3242:
3241:
3234:
3227:
3204:oxidation state
3193:
3186:
3182:
3141:
3136:
3104:
3103:
3098:
3092:
3089:
3088:
3087:is included in
3069:
3065:
3059:
3055:
3053:
3051:
3048:
3047:
3025:
3017:
3014:
3013:
2984:
2980:
2974:
2970:
2968:
2966:
2963:
2962:
2941:
2940:
2935:
2922:
2918:
2916:
2913:
2912:
2884:
2880:
2874:
2870:
2868:
2866:
2863:
2862:
2845:
2840:
2827:
2823:
2821:
2818:
2817:
2804:
2800:
2797:
2795:
2791:
2790:
2788:
2787:
2766:
2762:
2760:
2757:
2756:
2735:
2734:
2729:
2723:
2720:
2719:
2716:
2710:
2702:
2698:
2695:
2693:
2689:
2688:
2686:
2685:
2660:
2659:
2654:
2648:
2645:
2644:
2619:
2615:
2609:
2605:
2603:
2601:
2598:
2597:
2576:
2575:
2570:
2564:
2561:
2560:
2538:
2537:
2532:
2526:
2523:
2522:
2496:
2495:
2490:
2484:
2481:
2480:
2444:
2443:
2438:
2432:
2429:
2428:
2406:
2402:
2396:
2392:
2390:
2374:
2366:
2364:
2351:
2350:
2345:
2332:
2328:
2326:
2323:
2322:
2303:
2299:
2293:
2289:
2287:
2271:
2263:
2261:
2252:
2247:
2230:
2229:
2224:
2218:
2215:
2214:
2193:
2192:
2187:
2181:
2178:
2177:
2173:
2167:
2144:
2140:
2134:
2130:
2128:
2112:
2104:
2102:
2089:
2088:
2083:
2070:
2066:
2064:
2061:
2060:
2037:
2036:
2031:
2025:
2022:
2021:
2004:
2000:
1998:
1995:
1994:
1973:
1972:
1967:
1961:
1958:
1957:
1941:
1938:
1937:
1912:
1908:
1902:
1898:
1896:
1880:
1872:
1870:
1855:
1854:
1849:
1844:
1826:
1822:
1816:
1812:
1810:
1794:
1786:
1784:
1775:
1770:
1765:
1761:
1759:
1749:
1745:
1743:
1740:
1739:
1714:
1710:
1704:
1700:
1698:
1681:
1677:
1671:
1667:
1665:
1658:
1654:
1644:
1636:
1634:
1625:
1620:
1607:
1603:
1601:
1598:
1597:
1572:
1568:
1562:
1558:
1556:
1548:
1544:
1538:
1534:
1532:
1531:
1527:
1511:
1503:
1501:
1492:
1487:
1474:
1470:
1468:
1465:
1464:
1446:
1443:
1442:
1418:
1417:
1412:
1406:
1403:
1402:
1398:
1397:of the species
1391:
1385:
1382:
1376:
1369:
1363:
1360:
1354:
1351:
1345:
1341:
1330:
1322:
1290:
1286:
1280:
1276:
1274:
1265:
1261:
1249:
1245:
1241:
1239:
1230:
1226:
1215:
1211:
1205:
1201:
1199:
1182:
1178:
1176:
1167:
1163:
1155:
1152:
1151:
1109:
1107:
1098:
1094:
1092:
1089:
1088:
1086:thermal voltage
1082:
1080:Thermal voltage
1073:
1067:
1064:
1058:
1050:
1045:
1039:
1030:
1027:
1024:
1020:
1018:
1013:
1001:
987:
977:
968:
965:
962:
959:
957:
952:
944:
933:
930:
929:
928:
924:
915:
909:
895:
892:
891:
890:
886:
877:
871:
849:
845:
829:
821:
819:
810:
805:
792:
788:
786:
783:
782:
760:
756:
750:
746:
744:
728:
720:
718:
709:
704:
691:
687:
671:
663:
661:
652:
647:
634:
630:
628:
625:
624:
616:
609:
603:
597:
587:
579:
542:
539:
538:
534:
523:
517:
500:
496:
475:
471:
457:
454:
453:
448:
446:
445:
444:
439:
429:
404:
400:
394:
390:
388:
380:
377:
376:
368:
362:
355:
346:
342:
310:
299:
297:
286:
282:
276:
272:
270:
261:
257:
255:
252:
251:
217:
213:
206:
202:
182:
178:
146:
142:
135:
133:
130:
129:
122:
115:
107:
104:
99:
53:of a reaction (
43:Nernst equation
35:
28:
23:
22:
15:
12:
11:
5:
10970:
10960:
10959:
10954:
10949:
10947:Walther Nernst
10935:
10934:
10915:
10910:
10905:
10900:
10893:
10892:External links
10890:
10887:
10886:
10867:(3): 630–635.
10851:
10844:
10823:
10807:
10801:
10781:
10775:
10755:
10722:
10710:
10685:
10673:
10653:
10638:
10631:
10609:
10584:
10551:
10523:
10499:
10444:
10419:
10401:
10382:
10367:
10348:
10347:
10345:
10342:
10341:
10340:
10335:
10330:
10325:
10320:
10315:
10310:
10305:
10300:
10295:
10290:
10285:
10280:
10273:
10270:
10238:nuclear fusion
10228:immersed in a
10214:
10211:
10206:
10203:
10169:
10166:
10135:
10132:
10129:
10112:
10105:
10101:
10097:
10091:
10083:
10079:
10075:
10068:
10064:
10060:
10054:
10051:
10048:
10043:
10039:
10025:standard state
10003:
10000:
9993:
9989:
9985:
9982:
9976:
9973:
9971:
9969:
9966:
9963:
9960:
9959:
9954:
9950:
9946:
9943:
9941:
9939:
9936:
9933:
9927:
9924:
9919:
9916:
9910:
9909:
9906:
9903:
9900:
9894:
9891:
9886:
9883:
9877:
9872:
9868:
9864:
9861:
9859:
9857:
9854:
9853:
9840:
9839:
9835:
9827:
9816:
9802:
9770:
9769:
9757:
9753:
9750:
9744:
9741:
9736:
9733:
9727:
9722:
9717:
9714:
9711:
9708:
9704:
9689:
9688:
9676:
9672:
9669:
9666:
9663:
9660:
9657:
9652:
9647:
9644:
9641:
9638:
9634:
9630:
9627:
9624:
9607:
9606:
9593:
9588:
9585:
9582:
9579:
9575:
9571:
9568:
9565:
9562:
9557:
9553:
9549:
9524:
9519:
9516:
9513:
9510:
9506:
9479:
9475:
9471:
9460:
9459:
9447:
9443:
9440:
9437:
9434:
9431:
9428:
9423:
9419:
9415:
9383:
9379:
9375:
9360:
9357:
9349:ionic strength
9329:
9326:
9321:
9298:
9294:
9263:
9258:
9254:
9250:
9247:
9241:
9238:
9233:
9230:
9224:
9219:
9215:
9211:
9208:
9206:
9204:
9198:
9194:
9191:
9187:
9182:
9178:
9175:
9172:
9168:
9162:
9159:
9153:
9150:
9145:
9142:
9136:
9131:
9127:
9123:
9120:
9118:
9116:
9110:
9106:
9103:
9099:
9094:
9090:
9087:
9084:
9080:
9074:
9071:
9065:
9062:
9057:
9054:
9048:
9043:
9039:
9035:
9032:
9030:
9028:
9025:
9024:
9004:
8998:
8994:
8991:
8987:
8982:
8978:
8975:
8972:
8968:
8962:
8957:
8953:
8919:
8914:
8910:
8906:
8903:
8897:
8894:
8889:
8886:
8880:
8875:
8871:
8867:
8864:
8844:
8839:
8835:
8831:
8828:
8825:
8822:
8819:
8814:
8810:
8806:
8803:
8800:
8797:
8794:
8791:
8788:
8785:
8782:
8779:
8776:
8661:
8627:
8605:
8592:
8573:
8565:
8561:
8556:
8552:
8547:
8543:
8538:
8534:
8527:
8523:
8518:
8514:
8509:
8505:
8500:
8496:
8490:
8480:
8476:
8470:
8466:
8460:
8456:
8446:
8442:
8436:
8432:
8426:
8422:
8415:
8410:
8406:
8379:
8371:
8367:
8362:
8358:
8353:
8349:
8344:
8340:
8333:
8329:
8324:
8320:
8315:
8311:
8306:
8302:
8296:
8293:
8290:
8287:
8282:
8276:
8273:
8270:
8265:
8261:
8258:
8253:
8248:
8244:
8240:
8237:
8234:
8231:
8228:
8224:
8220:
8217:
8214:
8209:
8204:
8199:
8194:
8190:
8186:
8183:
8180:
8177:
8174:
8170:
8166:
8163:
8160:
8155:
8150:
8144:
8141:
8138:
8133:
8129:
8101:
8082:
8078:
8057:
8054:
8050:
8046:
8043:
8040:
8037:
8034:
8031:
8027:
8023:
8018:
8014:
8010:
8007:
8003:
7999:
7996:
7983:
7974:
7956:
7949:
7945:
7939:
7935:
7929:
7926:
7923:
7920:
7915:
7911:
7907:
7902:
7898:
7877:
7870:
7866:
7860:
7856:
7850:
7847:
7844:
7841:
7838:
7833:
7829:
7825:
7820:
7816:
7812:
7809:
7806:
7784:
7781:
7778:
7775:
7771:
7768:
7765:
7762:
7759:
7756:
7753:
7750:
7746:
7740:
7737:
7734:
7731:
7728:
7725:
7722:
7719:
7715:
7712:
7709:
7706:
7703:
7700:
7697:
7694:
7690:
7684:
7681:
7678:
7675:
7672:
7644:
7633:
7611:
7600:
7550:
7547:
7544:
7541:
7538:
7527:
7524:
7521:
7515:
7505:
7486:
7473:
7417:
7414:
7398:
7392:
7388:
7385:
7381:
7376:
7372:
7369:
7366:
7362:
7356:
7353:
7348:
7344:
7341:
7335:
7330:
7326:
7322:
7319:
7317:
7315:
7309:
7305:
7302:
7298:
7293:
7289:
7286:
7283:
7279:
7273:
7270:
7265:
7261:
7258:
7252:
7247:
7243:
7239:
7236:
7234:
7232:
7229:
7228:
7152:
7146:
7142:
7139:
7135:
7130:
7126:
7123:
7120:
7116:
7110:
7107:
7104:
7101:
7098:
7093:
7087:
7082:
7078:
7072:
7067:
7042:
7024:
7018:
7014:
7011:
7007:
7002:
6998:
6995:
6992:
6988:
6982:
6979:
6976:
6973:
6970:
6964:
6959:
6932:
6928:
6922:
6919:
6912:
6907:
6901:
6897:
6894:
6891:
6888:
6886:
6884:
6877:
6873:
6870:
6866:
6862:
6854:
6851:
6847:
6843:
6840:
6834:
6830:
6827:
6823:
6819:
6811:
6808:
6804:
6800:
6797:
6791:
6788:
6786:
6781:
6777:
6774:
6770:
6765:
6761:
6758:
6755:
6751:
6745:
6744:
6709:
6699:
6698:
6688:
6685:
6683:
6680:
6668:
6663:
6654:
6651:
6648:
6642:
6637:
6632:
6629:
6624:
6615:
6610:
6607:
6601:
6597:
6591:
6588:
6582:
6577:
6572:
6569:
6564:
6555:
6550:
6547:
6541:
6537:
6531:
6528:
6522:
6517:
6512:
6507:
6498:
6493:
6487:
6483:
6475:
6472:
6466:
6461:
6456:
6453:
6448:
6439:
6434:
6431:
6425:
6421:
6415:
6412:
6409:
6403:
6398:
6393:
6390:
6385:
6376:
6371:
6368:
6362:
6358:
6352:
6349:
6346:
6340:
6335:
6330:
6325:
6316:
6311:
6305:
6301:
6295:
6290:
6287:
6282:
6278:
6275:
6269:
6264:
6260:
6235:
6230:
6221:
6218:
6212:
6207:
6202:
6199:
6194:
6185:
6180:
6177:
6171:
6167:
6161:
6158:
6152:
6147:
6142:
6137:
6128:
6123:
6117:
6113:
6105:
6102:
6099:
6093:
6088:
6083:
6080:
6075:
6066:
6061:
6058:
6052:
6048:
6042:
6039:
6036:
6030:
6025:
6020:
6015:
6006:
6001:
5995:
5991:
5985:
5980:
5977:
5972:
5968:
5965:
5959:
5954:
5950:
5937:
5933:
5929:
5925:
5921:
5917:
5901:
5900:
5890:
5880:
5866:
5861:
5858:
5845:
5842:
5837:
5831:
5814:
5793:
5788:
5778:
5775:
5772:
5766:
5761:
5756:
5751:
5746:
5737:
5732:
5727:
5721:
5715:
5710:
5706:
5701:
5695:
5692:
5686:
5681:
5676:
5671:
5666:
5657:
5652:
5647:
5641:
5635:
5630:
5626:
5616:
5613:
5607:
5602:
5597:
5592:
5587:
5578:
5573:
5568:
5562:
5556:
5551:
5547:
5542:
5536:
5533:
5530:
5524:
5519:
5514:
5509:
5504:
5495:
5490:
5485:
5479:
5473:
5468:
5464:
5457:
5452:
5449:
5444:
5440:
5437:
5431:
5425:
5420:
5394:Main article:
5391:
5388:
5365:
5359:
5351:
5346:
5338:
5332:
5327:
5323:
5316:
5313:
5308:
5305:
5299:
5296:
5290:
5282:
5277:
5269:
5263:
5260:
5254:
5251:
5246:
5243:
5237:
5234:
5211:Main article:
5208:
5205:
5170:
5167:
5150:
5096:
5084:
5083:
5065:
5036:
5027:
5005:
5002:
4996:
4993:
4990:
4987:
4978:
4962:
4958:
4955:
4954:
4936:
4920:= 0 V for the
4907:
4898:
4876:
4873:
4867:
4864:
4861:
4852:
4836:
4826:
4825:
4814:
4811:
4805:
4802:
4797:
4788:
4784:
4775:
4755:
4735:
4717:
4716:
4709:
4705:
4699:
4698:
4694:
4690:
4689:
4683:
4677:
4676:
4672:
4662:
4656:
4622:
4582:Main article:
4579:
4576:
4558:
4555:
4550:
4532:
4505:
4501:
4474:
4461:
4457:
4453:
4435:
4410:
4405:
4402:
4397:
4392:
4389:
4363:
4347:
4346:
4327:
4323:
4319:
4313:
4309:
4301:
4297:
4293:
4290:
4285:
4281:
4277:
4274:
4267:
4263:
4259:
4256:
4251:
4247:
4243:
4240:
4234:
4230:
4227:
4222:
4219:
4214:
4209:
4200:
4196:
4187:
4183:
4178:
4174:
4148:
4144:
4105:
4101:
4097:
4086:
4085:
4071:
4068:
4061:
4057:
4053:
4047:
4044:
4041:
4033:
4028:
4019:
3993:
3984:
3971:The half-cell
3969:
3968:
3957:
3953:
3950:
3947:
3943:
3932:
3925:
3914:
3907:
3894:
3890:
3885:
3882:
3876:
3866:
3863:
3860:
3856:
3853:
3850:
3846:
3805:
3782:
3778:
3749:
3745:
3713:
3709:
3690:
3687:
3664:
3641:
3632:
3593:
3590:
3580:
3564:standard state
3532:
3529:
3519:
3500:
3497:
3477:
3474:
3464:
3448:ionic strength
3432:
3429:
3419:
3396:
3393:
3389:
3366:
3363:
3360:
3356:
3331:
3330:
3319:
3316:
3303:
3297:
3285:
3279:
3273:
3262:
3252:
3184:
3139:
3131:(mol/L, M) or
3110:
3107:
3097:
3068:
3058:
3035:
3032:
3028:
3024:
3021:
3010:
3009:
2997:
2994:
2983:
2973:
2947:
2944:
2934:
2930:
2921:
2897:
2894:
2883:
2873:
2848:
2839:
2835:
2826:
2802:
2793:
2765:
2741:
2738:
2728:
2709:
2700:
2691:
2682:
2666:
2663:
2653:
2632:
2629:
2618:
2608:
2582:
2579:
2569:
2544:
2541:
2531:
2502:
2499:
2489:
2470:ionic strength
2450:
2447:
2437:
2405:
2395:
2389:
2386:
2380:
2377:
2372:
2369:
2363:
2357:
2354:
2344:
2340:
2331:
2302:
2292:
2286:
2283:
2277:
2274:
2269:
2266:
2260:
2255:
2246:
2242:
2236:
2233:
2223:
2199:
2196:
2186:
2166:
2163:
2143:
2133:
2127:
2124:
2118:
2115:
2110:
2107:
2101:
2095:
2092:
2082:
2078:
2069:
2043:
2040:
2030:
2003:
1979:
1976:
1966:
1945:
1911:
1901:
1895:
1892:
1886:
1883:
1878:
1875:
1869:
1861:
1858:
1848:
1841:
1837:
1825:
1815:
1809:
1806:
1800:
1797:
1792:
1789:
1783:
1778:
1769:
1764:
1757:
1748:
1725:
1713:
1703:
1697:
1694:
1691:
1680:
1670:
1664:
1661:
1657:
1650:
1647:
1642:
1639:
1633:
1628:
1619:
1615:
1606:
1583:
1571:
1561:
1547:
1537:
1530:
1526:
1523:
1517:
1514:
1509:
1506:
1500:
1495:
1486:
1482:
1473:
1450:
1424:
1421:
1411:
1389:
1380:
1374:
1367:
1358:
1349:
1334:standard state
1329:
1326:
1320:
1300:
1289:
1279:
1273:
1268:
1264:
1258:
1252:
1248:
1244:
1238:
1233:
1229:
1225:
1214:
1204:
1198:
1195:
1190:
1185:
1181:
1175:
1170:
1166:
1162:
1159:
1144:) rather than
1119:
1115:
1112:
1106:
1101:
1097:
1081:
1078:
1077:
1076:
1071:
1062:
1048:
1043:
1037:
1012:of electrons:
999:
985:
975:
942:
931:
922:
913:
907:
893:
884:
875:
852:
848:
844:
841:
835:
832:
827:
824:
818:
813:
804:
800:
791:
770:
759:
749:
743:
740:
734:
731:
726:
723:
717:
712:
703:
699:
694:
690:
686:
683:
677:
674:
669:
666:
660:
655:
646:
642:
633:
607:
595:
567:
564:
561:
558:
555:
552:
549:
546:
521:
503:
499:
495:
492:
489:
486:
483:
478:
474:
470:
467:
464:
461:
447:
437:standard state
423:
422:
403:
393:
387:
384:
360:
353:
344:
334:
333:
319:
316:
313:
308:
305:
302:
296:
285:
275:
269:
264:
260:
245:concentrations
215:
204:
180:
170:
169:
154:
149:
141:
114:of electrons (
103:
100:
98:
95:
87:Walther Nernst
71:redox reaction
32:Ernst equation
26:
9:
6:
4:
3:
2:
10969:
10958:
10955:
10953:
10950:
10948:
10945:
10944:
10942:
10924:
10920:
10916:
10914:
10911:
10909:
10906:
10904:
10901:
10899:
10896:
10895:
10882:
10878:
10874:
10870:
10866:
10862:
10855:
10847:
10841:
10837:
10833:
10827:
10819:
10818:
10811:
10804:
10802:9788122417913
10798:
10794:
10793:
10785:
10778:
10776:9783642295515
10772:
10768:
10767:
10759:
10752:
10748:
10744:
10741:(in German),
10740:
10736:
10732:
10726:
10719:
10714:
10699:
10695:
10689:
10683:
10678:
10672:
10668:
10663:
10658:
10652:
10648:
10642:
10634:
10628:
10624:
10620:
10613:
10599:
10595:
10588:
10581:
10579:
10574:
10570:
10566:
10562:
10555:
10541:
10537:
10530:
10528:
10513:
10509:
10503:
10489:
10485:
10481:
10477:
10472:
10467:
10463:
10459:
10455:
10448:
10434:
10430:
10423:
10415:
10408:
10406:
10397:
10393:
10386:
10378:
10374:
10370:
10364:
10360:
10353:
10349:
10339:
10336:
10334:
10331:
10329:
10326:
10324:
10321:
10319:
10316:
10314:
10311:
10309:
10306:
10304:
10301:
10299:
10296:
10294:
10293:Galvanic cell
10291:
10289:
10286:
10284:
10281:
10279:
10276:
10275:
10269:
10266:
10262:
10258:
10254:
10250:
10245:
10243:
10239:
10235:
10231:
10227:
10224:
10220:
10210:
10202:
10200:
10196:
10191:
10182:
10180:
10179:overpotential
10176:
10165:
10163:
10159:
10154:
10133:
10130:
10127:
10110:
10103:
10099:
10095:
10089:
10081:
10077:
10073:
10066:
10062:
10058:
10052:
10049:
10046:
10041:
10037:
10028:
10026:
10021:
10001:
9998:
9991:
9987:
9983:
9980:
9974:
9972:
9967:
9964:
9961:
9952:
9948:
9944:
9942:
9937:
9934:
9931:
9925:
9922:
9917:
9914:
9904:
9901:
9898:
9892:
9889:
9884:
9881:
9875:
9870:
9866:
9862:
9860:
9855:
9843:
9834:
9830:
9823:
9822:
9821:
9815:
9810:
9805:
9797:
9791:
9786:
9782:
9778:
9773:
9755:
9751:
9748:
9742:
9739:
9734:
9731:
9725:
9720:
9715:
9712:
9709:
9706:
9702:
9694:
9693:
9692:
9674:
9670:
9667:
9664:
9661:
9658:
9655:
9650:
9645:
9642:
9639:
9636:
9632:
9628:
9625:
9622:
9615:
9614:
9613:
9610:
9591:
9586:
9583:
9580:
9577:
9573:
9569:
9566:
9563:
9560:
9555:
9551:
9540:
9539:
9538:
9522:
9517:
9514:
9511:
9508:
9504:
9477:
9473:
9445:
9441:
9438:
9435:
9432:
9429:
9426:
9421:
9417:
9406:
9405:
9404:
9403:as follows:
9399:
9381:
9377:
9366:
9363:The standard
9356:
9354:
9350:
9346:
9327:
9324:
9319:
9296:
9292:
9283:
9278:
9261:
9256:
9252:
9248:
9245:
9239:
9236:
9231:
9228:
9222:
9217:
9213:
9209:
9207:
9160:
9157:
9151:
9148:
9143:
9140:
9134:
9129:
9125:
9121:
9119:
9072:
9069:
9063:
9060:
9055:
9052:
9046:
9041:
9037:
9033:
9031:
9026:
9015:and we have:
9002:
8960:
8955:
8951:
8933:
8930:
8917:
8912:
8908:
8904:
8901:
8895:
8892:
8887:
8884:
8878:
8873:
8869:
8865:
8862:
8842:
8837:
8833:
8829:
8826:
8823:
8820:
8817:
8812:
8808:
8801:
8798:
8792:
8789:
8786:
8780:
8777:
8765:
8760:
8755:
8749:
8745:
8741:
8735:
8729:
8724:
8720:
8715:
8709:
8703:
8699:
8692:
8686:
8681:
8671:
8660:
8652:
8647:
8643:
8638:
8632:
8619:
8614:
8608:
8600:
8595:
8587:
8571:
8563:
8545:
8525:
8507:
8488:
8478:
8474:
8468:
8464:
8458:
8454:
8444:
8440:
8434:
8430:
8424:
8420:
8413:
8408:
8404:
8395:
8390:
8377:
8369:
8351:
8331:
8313:
8294:
8291:
8288:
8285:
8280:
8263:
8256:
8235:
8232:
8229:
8215:
8212:
8202:
8181:
8178:
8175:
8161:
8158:
8148:
8131:
8100:
8098:
8080:
8076:
8055:
8041:
8038:
8035:
8032:
8016:
8012:
8008:
7994:
7982:
7973:
7967:
7954:
7947:
7943:
7937:
7933:
7927:
7924:
7921:
7918:
7913:
7909:
7905:
7900:
7896:
7875:
7868:
7864:
7858:
7854:
7848:
7845:
7842:
7839:
7836:
7831:
7827:
7823:
7818:
7814:
7810:
7807:
7795:
7782:
7776:
7773:
7738:
7735:
7732:
7729:
7726:
7720:
7717:
7682:
7679:
7676:
7673:
7670:
7659:
7658:concentration
7655:
7643:
7632:
7610:
7599:
7591:
7587:
7581:
7577:
7571:
7561:
7548:
7542:
7539:
7536:
7513:
7503:
7495:
7493:
7485:
7481:
7472:
7468:
7463:
7458:
7454:
7449:
7445:
7440:
7436:
7431:
7427:
7423:
7413:
7396:
7354:
7351:
7346:
7342:
7339:
7333:
7328:
7324:
7320:
7318:
7271:
7268:
7263:
7259:
7256:
7250:
7245:
7241:
7237:
7235:
7230:
7218:
7205:
7197:
7185:
7177:
7163:
7150:
7108:
7105:
7102:
7099:
7096:
7091:
7080:
7076:
7065:
7041:
7035:
7022:
6980:
6977:
6974:
6971:
6968:
6957:
6947:
6930:
6926:
6920:
6917:
6905:
6899:
6895:
6892:
6889:
6887:
6875:
6871:
6868:
6864:
6849:
6845:
6841:
6838:
6832:
6828:
6825:
6821:
6806:
6802:
6798:
6795:
6789:
6787:
6734:
6720:
6716:
6708:
6704:
6694:
6693:
6692:
6679:
6666:
6661:
6640:
6635:
6622:
6613:
6599:
6595:
6580:
6575:
6562:
6553:
6539:
6535:
6520:
6515:
6505:
6496:
6485:
6481:
6464:
6459:
6446:
6437:
6423:
6419:
6401:
6396:
6383:
6374:
6360:
6356:
6338:
6333:
6323:
6314:
6303:
6299:
6293:
6288:
6285:
6280:
6276:
6273:
6267:
6262:
6258:
6249:
6246:
6233:
6228:
6210:
6205:
6192:
6183:
6169:
6165:
6150:
6145:
6135:
6126:
6115:
6111:
6091:
6086:
6073:
6064:
6050:
6046:
6028:
6023:
6013:
6004:
5993:
5989:
5983:
5978:
5975:
5970:
5966:
5963:
5957:
5952:
5948:
5915:
5911:
5898:
5891:
5888:
5881:
5878:
5874:
5867:
5859:
5856:
5852:
5843:
5836:
5832:
5829:
5825:
5821:
5813:
5809:
5808:
5807:
5804:
5791:
5786:
5764:
5759:
5754:
5744:
5735:
5730:
5719:
5713:
5708:
5704:
5699:
5684:
5679:
5674:
5664:
5655:
5650:
5639:
5633:
5628:
5624:
5605:
5600:
5595:
5585:
5576:
5571:
5560:
5554:
5549:
5545:
5540:
5522:
5517:
5512:
5502:
5493:
5488:
5477:
5471:
5466:
5462:
5455:
5450:
5447:
5442:
5438:
5435:
5429:
5418:
5409:
5407:
5403:
5397:
5387:
5385:
5381:
5376:
5363:
5330:
5325:
5321:
5314:
5311:
5306:
5303:
5297:
5294:
5261:
5258:
5252:
5249:
5244:
5241:
5235:
5232:
5224:
5221:
5214:
5204:
5202:
5198:
5194:
5193:cell membrane
5190:
5186:
5182:
5176:
5166:
5164:
5147:
5146:stoichiometry
5143:
5136:
5129:
5118:on the ratio
5117:
5094:
5063:
5052:
5034:
5025:
5003:
5000:
4994:
4991:
4988:
4985:
4976:
4968:
4967:
4966:
4934:
4923:
4905:
4896:
4874:
4871:
4865:
4862:
4859:
4850:
4842:
4841:
4840:
4833:
4831:
4812:
4809:
4803:
4800:
4795:
4786:
4782:
4773:
4765:
4764:
4763:
4760:
4758:
4751:
4744:
4733:
4726:
4701:
4700:
4692:
4691:
4679:
4678:
4670:
4669:
4668:
4654:
4650:
4646:
4642:
4638:
4634:
4630:
4619:
4615:
4606:
4602:
4598:
4594:
4590:
4585:
4575:
4572:
4568:
4563:
4554:
4530:
4521:
4503:
4499:
4472:
4433:
4423:
4408:
4403:
4400:
4395:
4390:
4387:
4361:
4352:
4325:
4321:
4317:
4311:
4307:
4299:
4291:
4283:
4275:
4265:
4257:
4249:
4241:
4232:
4228:
4225:
4220:
4217:
4212:
4207:
4198:
4194:
4185:
4181:
4176:
4172:
4164:
4163:
4162:
4146:
4142:
4133:
4121:
4103:
4099:
4069:
4066:
4059:
4055:
4045:
4042:
4026:
4017:
4009:
4008:
4007:
3991:
3982:
3974:
3955:
3951:
3948:
3945:
3941:
3923:
3912:
3892:
3888:
3883:
3880:
3874:
3864:
3861:
3858:
3854:
3851:
3848:
3844:
3837:
3836:
3835:
3833:
3829:
3826:(SHE). For a
3825:
3803:
3780:
3776:
3765:
3747:
3743:
3733:
3729:
3711:
3707:
3696:
3686:
3684:
3662:
3639:
3630:
3621:
3616:
3614:
3610:
3591:
3588:
3578:
3569:
3565:
3561:
3557:
3553:
3549:
3530:
3527:
3517:
3506:
3496:
3492:
3475:
3472:
3462:
3453:
3449:
3430:
3427:
3417:
3394:
3391:
3387:
3364:
3361:
3358:
3354:
3346:
3341:
3339:
3334:
3317:
3314:
3295:
3277:
3271:
3260:
3250:
3240:
3239:
3238:
3233:
3225:
3221:
3217:
3211:
3209:
3205:
3201:
3195:
3191:
3180:
3176:
3172:
3168:
3162:
3160:
3156:
3152:
3148:
3143:
3134:
3130:
3125:
3108:
3105:
3095:
3066:
3056:
3033:
3030:
3026:
3022:
3019:
2995:
2992:
2981:
2971:
2945:
2942:
2932:
2928:
2919:
2911:
2910:
2909:
2895:
2892:
2881:
2871:
2846:
2837:
2833:
2824:
2814:
2811:
2785:
2763:
2739:
2736:
2726:
2715:
2681:
2664:
2661:
2651:
2630:
2627:
2616:
2606:
2580:
2577:
2567:
2542:
2539:
2529:
2520:
2500:
2497:
2487:
2477:
2475:
2471:
2467:
2448:
2445:
2435:
2425:
2403:
2393:
2387:
2384:
2378:
2375:
2370:
2367:
2361:
2355:
2352:
2342:
2338:
2329:
2300:
2290:
2284:
2281:
2275:
2272:
2267:
2264:
2258:
2253:
2244:
2240:
2234:
2231:
2221:
2197:
2194:
2184:
2172:
2162:
2141:
2131:
2125:
2122:
2116:
2113:
2108:
2105:
2099:
2093:
2090:
2080:
2076:
2067:
2058:
2041:
2038:
2028:
2001:
1977:
1974:
1964:
1956:) is denoted
1943:
1935:
1930:
1909:
1899:
1893:
1890:
1884:
1881:
1876:
1873:
1867:
1859:
1856:
1846:
1839:
1835:
1823:
1813:
1807:
1804:
1798:
1795:
1790:
1787:
1781:
1776:
1767:
1762:
1755:
1746:
1737:
1723:
1711:
1701:
1695:
1692:
1689:
1678:
1668:
1662:
1659:
1655:
1648:
1645:
1640:
1637:
1631:
1626:
1617:
1613:
1604:
1595:
1581:
1569:
1559:
1545:
1535:
1528:
1524:
1521:
1515:
1512:
1507:
1504:
1498:
1493:
1484:
1480:
1471:
1462:
1448:
1439:
1422:
1419:
1409:
1396:
1388:
1379:
1373:
1366:
1357:
1348:
1339:
1335:
1325:
1323:
1316:
1311:
1298:
1287:
1277:
1271:
1266:
1262:
1256:
1250:
1246:
1242:
1236:
1231:
1227:
1223:
1212:
1202:
1196:
1193:
1188:
1183:
1179:
1173:
1168:
1164:
1160:
1157:
1149:
1147:
1143:
1139:
1135:
1117:
1113:
1110:
1104:
1099:
1095:
1087:
1070:
1061:
1056:
1049:
1042:
1038:
1016:
1011:
1007:
1000:
997:
996:half-reaction
993:
986:
983:
976:
971: J K mol
955:
950:
943:
940:
927:
923:
920:
912:
908:
905:
903:
889:
885:
882:
874:
870:
869:
868:
865:
850:
846:
842:
839:
833:
830:
825:
822:
816:
811:
802:
798:
789:
768:
757:
747:
741:
738:
732:
729:
724:
721:
715:
710:
701:
697:
692:
688:
684:
681:
675:
672:
667:
664:
658:
653:
644:
640:
631:
622:
614:
606:
600:
594:
590:
585:
578:The constant
565:
562:
559:
556:
553:
550:
547:
532:
529:and R is the
528:
520:
501:
497:
493:
490:
487:
484:
481:
476:
472:
465:
462:
443:
438:
433:
428:
401:
391:
385:
382:
375:
374:
373:
371:
366:
359:
352:
348:
339:
314:
303:
294:
283:
273:
267:
262:
258:
250:
249:
248:
246:
242:
238:
234:
233:concentration
230:
226:
222:
211:
200:
196:
192:
188:
184:
175:
147:
139:
128:
127:
126:
120:
113:
94:
92:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
10927:. Retrieved
10925:. 2014-11-18
10922:
10864:
10860:
10854:
10835:
10826:
10816:
10810:
10791:
10784:
10765:
10758:
10742:
10738:
10725:
10713:
10702:. Retrieved
10700:. 2014-11-18
10697:
10688:
10676:
10670:
10666:
10662:gas constant
10656:
10650:
10646:
10641:
10622:
10612:
10601:. Retrieved
10597:
10587:
10577:
10576:
10564:
10560:
10554:
10543:. Retrieved
10539:
10515:. Retrieved
10511:
10502:
10491:. Retrieved
10464:(1): 29–46.
10461:
10457:
10447:
10436:. Retrieved
10432:
10422:
10413:
10395:
10391:
10385:
10358:
10352:
10264:
10246:
10216:
10208:
10183:
10171:
10155:
10029:
10022:
9844:
9841:
9832:
9825:
9813:
9800:
9789:
9774:
9771:
9690:
9611:
9608:
9461:
9362:
9279:
8934:
8931:
8763:
8753:
8747:
8743:
8739:
8733:
8727:
8713:
8707:
8701:
8697:
8690:
8679:
8669:
8658:
8650:
8636:
8622:
8612:
8603:
8590:
8391:
8119:
7980:
7971:
7968:
7796:
7641:
7630:
7608:
7597:
7589:
7585:
7569:
7562:
7496:
7483:
7479:
7470:
7466:
7456:
7447:
7444:gas constant
7438:
7429:
7419:
7219:
7214:Ox + e ⇌ Red
7203:
7195:
7183:
7175:
7164:
7039:
7036:
6948:
6706:
6700:
6696:Ox + e ⇌ Red
6690:
6250:
6247:
5913:
5902:
5875:(joules per
5834:
5811:
5805:
5410:
5399:
5377:
5225:
5219:
5216:
5178:
5154:
5141:
5119:
5115:
5085:
4956:
4834:
4827:
4761:
4749:
4731:
4718:
4635:between two
4629:electrolysis
4611:
4566:
4564:
4560:
4522:(SHE) whose
4424:
4348:
4161:as follows:
4087:
4006:is given by
3970:
3831:
3698:
3617:
3552:cell biology
3548:biochemistry
3508:
3493:
3342:
3338:voltammogram
3335:
3332:
3237:(1 mol/L):
3213:
3197:
3189:
3178:
3170:
3166:
3163:
3161:potential.
3158:
3154:
3126:
3011:
2815:
2812:
2783:
2717:
2518:
2478:
2426:
2174:
2059:
1931:
1738:
1596:
1463:
1440:
1386:
1377:
1371:
1364:
1355:
1346:
1337:
1331:
1318:
1314:
1312:
1150:
1137:
1083:
1068:
1059:
1040:
1014:
953:
925:
910:
901:
887:
872:
866:
604:
598:
592:
588:
518:
441:
431:
424:
367:
357:
350:
341:
340:, the ratio
335:
236:
194:
186:
177:
171:
118:
111:
105:
42:
36:
10745:(1): 5–16,
10230:heavy water
10219:cold fusion
10168:Limitations
9842:Therefore,
8648:reactions (
5928:(Na) + 1.5J
4712:+ 4 H + 4 e
3568:redox scale
3218:(M) or one
1033: C mol
223:(γ) by its
89:, a German
10941:Categories
10929:2021-12-06
10704:2021-12-06
10603:2021-12-15
10545:2021-12-06
10517:2021-12-06
10493:2021-12-02
10438:2021-11-24
10344:References
8586:activities
6682:Derivation
5879:per mole),
5185:physiology
5173:See also:
4637:electrodes
4351:activities
3693:See also:
3503:See also:
3171:vice versa
3147:activities
2712:See also:
2169:See also:
1134:logarithms
97:Expression
75:activities
10881:0013-4651
10573:0002-7863
10488:0034-6691
10480:1884-7692
10223:palladium
10104:⊖
10074:λ
10067:⊖
10047:
9992:⊖
9965:
9953:⊖
9935:
9902:
9876:−
9871:⊖
9752:
9721:⊖
9671:
9659:−
9651:⊖
9623:−
9592:⊖
9564:−
9556:⊖
9548:Δ
9523:⊖
9478:⊖
9470:Δ
9442:
9430:−
9422:⊖
9414:Δ
9382:⊖
9374:Δ
9325:⊖
9297:⊖
9249:
9223:−
9218:⊖
9161:
9135:−
9130:⊖
9073:
9047:−
9042:⊖
8905:
8879:−
8874:⊖
8830:
8813:⊖
8805:Δ
8796:Δ
8790:−
8784:Δ
8775:Δ
8489:≈
8475:ν
8455:∏
8441:ν
8421:∏
8295:
8286:−
8281:⊖
8260:Δ
8203:−
8128:Δ
8081:⊖
8042:
8033:−
8017:⊖
7928:
7919:−
7849:
7840:−
7824:−
7805:Δ
7774:×
7739:
7730:−
7718:×
7683:
7580:ideal gas
7546:Ω
7543:
7424:, and so
7355:
7334:−
7329:⊖
7272:
7251:−
7246:⊖
7109:
7092:⊖
7081:μ
7066:μ
6981:
6958:μ
6906:μ
6896:
6850:−
6842:
6807:−
6799:
6636:−
6614:−
6460:−
6438:−
6289:
5979:
5760:−
5736:−
5705:∑
5625:∑
5601:−
5577:−
5546:∑
5463:∑
5451:
5331:
5262:
5035:⊖
4992:−
4906:⊖
4863:−
4801:−
4796:⊖
4625:–pH plot)
4608:consumed.
4388:−
4312:−
4229:
4213:−
4208:⊖
4104:⊖
4096:Δ
4060:⊖
4052:Δ
4046:−
4027:⊖
3992:⊖
3931:⇀
3924:−
3913:−
3906:↽
3893:−
3828:half cell
3640:⊖
3589:⊖
3528:⊖
3473:⊖
3428:⊖
3388:γ
3355:γ
3106:⊖
3067:γ
3057:γ
3023:
2943:⊖
2847:⊖
2813:Indeed:
2737:⊖
2662:⊖
2578:⊖
2540:⊖
2498:⊖
2446:⊖
2388:
2362:−
2353:⊖
2301:γ
2291:γ
2285:
2259:−
2254:⊖
2232:⊖
2195:⊖
2126:
2100:−
2091:⊖
2039:⊖
1975:⊖
1944:γ
1894:
1868:−
1857:⊖
1840:⏟
1824:γ
1814:γ
1808:
1782:−
1777:⊖
1696:
1679:γ
1669:γ
1663:
1632:−
1627:⊖
1546:γ
1536:γ
1525:
1499:−
1494:⊖
1449:γ
1420:⊖
1272:
1243:λ
1237:−
1232:⊖
1197:
1174:−
1169:⊖
992:electrons
843:
817:−
812:⊖
742:
716:−
711:⊖
685:
659:−
654:⊖
554:−
545:Δ
494:
477:⊖
469:Δ
460:Δ
199:reductant
153:⟶
148:−
83:oxidation
59:full cell
55:half-cell
10834:(1993).
10540:PalmSens
10377:19124885
10272:See also
10160:and the
10124:at
9328:′
8759:enthalpy
8751:, where
8705:, where
7433:and the
5920:(Na) + J
5017:because
4961:into 2 H
4665:–pH plot
4641:hydrogen
4122:change,
3592:′
3531:′
3476:′
3431:′
3232:molarity
3190:de facto
3135:(mol/kg
3109:′
3012:because
2946:′
2740:′
2665:′
2581:′
2543:′
2501:′
2449:′
2356:′
2235:′
2198:′
2094:′
2042:′
1978:′
1860:′
1438:used.
1423:′
1384:, where
1055:activity
1006:coulombs
902:standard
621:electron
602:, where
10226:cathode
10115: V
10111:0.05916
8941:e → Red
8757:is the
8717:is the
8687:change
8674:
8655:
8640:is the
7649:
7627:
7616:
7594:
7578:for an
7492:entropy
7208:
7192:
7188:
7172:
7055:
7049:
6729:
6723:
5895:is the
5887:kelvins
5871:is the
5828:coulomb
5179:Beside
5159:⁄
5139:
5132:
5124:⁄
4995:0.05916
4866:0.05916
4804:0.05916
4747:
4740:
4729:
4722:
4708:O ⇌ O
4645:cathode
4391:0.05916
4318:0.05916
4218:0.05916
4130:is the
3685:(SHE).
3206:is one
2961:, when
2861:, when
2807:
2789:
2786:, when
2705:
2687:
1393:is the
982:kelvins
947:is the
937:is the
899:is the
867:where:
611:is the
525:is the
210:oxidant
116:
10879:
10842:
10799:
10773:
10680:; see
10660:; see
10629:
10571:
10486:
10478:
10375:
10365:
10255:, the
10137:
10134:298.15
10023:Or at
9792:) = 0
9783:, the
9284:(STP)
8068:where
7742:
7686:
7563:where
7534:
7507:
7490:. The
5877:kelvin
5824:joules
5806:where
5298:2.3026
4998:
4869:
4807:
4649:oxygen
4456:into H
4345:
4088:where
3635:red H+
3450:, and
3224:formal
3208:formal
3159:formal
3155:formal
1313:where
1008:) per
516:where
73:, and
41:, the
10578:Quote
10476:eISSN
10249:redox
9779:, or
9612:So,
8937:Ox +
8646:redox
5851:moles
5820:volts
5191:of a
4989:1.229
4752:with
4738:and 4
4734:for H
4653:anode
3766:plot)
3609:redox
3220:molal
3216:molar
3133:molal
3129:molar
958:8.314
582:(the
229:molal
225:molar
45:is a
10877:ISSN
10840:ISBN
10797:ISBN
10771:ISBN
10627:ISBN
10569:ISSN
10484:ISSN
10373:OCLC
10363:ISBN
9820:):
8761:and
8113:Y +
8109:B →
8105:A +
7477:and
7451:and
7422:mole
5938:pump
5936:= −J
5934:e.c.
5930:e.c.
5926:e.c.
5922:e.c.
5918:e.c.
5826:per
5116:i.e.
4567:i.e.
4036:volt
3832:i.e.
3726:and
3699:The
3550:and
3379:and
3343:The
3179:i.e.
3167:i.e.
2816:as,
2784:i.e.
2519:i.e.
1338:i.e.
1138:i.e.
1031:0184
1023:.332
1010:mole
932:cell
914:cell
807:cell
794:cell
615:and
172:The
10869:doi
10865:136
10747:doi
10466:doi
10038:log
9775:At
9537:):
8943:,
8702:zFE
8700:= −
8677:).
7592:ln(
7047:at
7045:≠ 0
7037:If
6893:exp
6839:exp
6796:exp
5846:out
5838:ion
5322:log
5197:ion
5099:red
5068:red
5030:red
4981:red
4939:red
4901:red
4855:red
4791:red
4778:red
4704:2 H
4601:SHE
4551:gas
4535:red
4477:red
4438:red
4366:red
4226:log
4203:red
4190:red
4022:red
3987:red
3808:red
3667:red
3583:red
3522:red
3467:red
3422:red
3289:red
3255:red
3230:in
3185:gas
3124:.
3100:red
3061:red
2976:red
2937:red
2924:red
2908:,
2876:red
2842:red
2829:red
2794:red
2768:red
2731:red
2708:= 1
2692:red
2656:red
2611:red
2572:red
2534:red
2492:red
2440:red
2398:Red
2347:red
2334:red
2295:Red
2249:red
2226:red
2189:red
2136:Red
2085:red
2072:red
2033:red
2006:red
1969:red
1904:Red
1851:red
1818:Red
1772:red
1751:red
1706:Red
1673:Red
1622:red
1609:red
1564:Red
1540:Red
1489:red
1476:red
1414:red
1282:Red
1263:log
1207:Red
1063:Red
1028:310
1025:123
1021:485
966:153
963:618
960:462
894:red
876:red
752:Red
706:red
649:red
636:red
396:Red
354:Red
336:At
304:Red
278:Red
205:Red
187:IAP
156:Red
123:Red
57:or
37:In
10943::
10921:.
10875:.
10863:.
10743:12
10696:.
10669:=
10649:=
10621:.
10596:.
10575:.
10565:71
10563:.
10538:.
10526:^
10510:.
10482:.
10474:.
10462:48
10460:.
10456:.
10431:.
10404:^
10396:96
10394:.
10371:.
10186:±∞
10042:10
10027:,
9962:ln
9932:ln
9899:ln
9836:eq
9831:=
9817:eq
9749:ln
9668:ln
9494:zF
9439:ln
9353:pH
9351:,
9246:ln
9158:ln
9070:ln
8902:ln
8827:ln
8748:TS
8746:−
8742:=
8653:=
8601:,
8588:,
8396::
8292:ln
8039:ln
7925:ln
7846:ln
7736:ln
7680:ln
7590:nR
7588:=
7540:ln
7484:eN
7482:=
7471:kN
7469:=
7464::
7352:ln
7269:ln
7217::
7190:=
7106:ln
6978:ln
6286:ln
5976:ln
5862:in
5855:SI
5830:),
5448:ln
5326:10
5259:ln
5203:.
4745:/4
4727:/2
4720:(2
4621:(E
4605:pH
4464:.
4332:pH
3768:.
3764:pH
3762:–
3728:pH
3560:pH
3454:,
3452:pH
3307:ox
3265:ox
3210:".
3071:ox
3020:ln
2986:ox
2886:ox
2803:ox
2701:ox
2621:ox
2476:.
2468:,
2466:pH
2408:Ox
2385:ln
2305:Ox
2282:ln
2146:Ox
2123:ln
1914:Ox
1891:ln
1828:Ox
1805:ln
1716:Ox
1693:ln
1683:Ox
1660:ln
1574:Ox
1550:Ox
1522:ln
1370:=
1344:,
1319:λV
1292:Ox
1267:10
1217:Ox
1194:ln
1140:,
1072:Ox
1019:96
1017:=
969:24
956:=
951::
840:ln
762:Ox
739:ln
682:ln
591:=
491:ln
406:Ox
361:Ox
315:Ox
288:Ox
216:Ox
212:,
201:,
144:ze
137:Ox
108:Ox
65:,
10932:.
10883:.
10871::
10848:.
10749::
10707:.
10677:e
10674:A
10671:N
10667:F
10657:k
10654:A
10651:N
10647:R
10635:.
10606:.
10548:.
10520:.
10496:.
10468::
10441:.
10379:.
10265:K
10141:K
10131:=
10128:T
10100:E
10096:z
10090:=
10082:T
10078:V
10063:E
10059:z
10053:=
10050:K
10002:T
9999:R
9988:E
9984:F
9981:z
9975:=
9968:K
9949:E
9945:=
9938:K
9926:F
9923:z
9918:T
9915:R
9905:K
9893:F
9890:z
9885:T
9882:R
9867:E
9863:=
9856:0
9833:K
9828:r
9826:Q
9814:K
9811:(
9803:r
9801:Q
9798:(
9790:E
9788:(
9756:K
9743:F
9740:z
9735:T
9732:R
9726:=
9716:l
9713:l
9710:e
9707:c
9703:E
9675:K
9665:T
9662:R
9656:=
9646:l
9643:l
9640:e
9637:c
9633:E
9629:F
9626:z
9587:l
9584:l
9581:e
9578:c
9574:E
9570:F
9567:z
9561:=
9552:G
9518:l
9515:l
9512:e
9509:c
9505:E
9474:G
9446:K
9436:T
9433:R
9427:=
9418:G
9401:K
9378:G
9320:E
9293:E
9262:.
9257:r
9253:Q
9240:F
9237:z
9232:T
9229:R
9214:E
9210:=
9197:]
9193:x
9190:O
9186:[
9181:]
9177:d
9174:e
9171:R
9167:[
9152:F
9149:z
9144:T
9141:R
9126:E
9122:=
9109:]
9105:x
9102:O
9098:[
9093:]
9089:d
9086:e
9083:R
9079:[
9064:e
9061:z
9056:T
9053:k
9038:E
9034:=
9027:E
9003:,
8997:]
8993:x
8990:O
8986:[
8981:]
8977:d
8974:e
8971:R
8967:[
8961:=
8956:r
8952:Q
8939:z
8918:.
8913:r
8909:Q
8896:e
8893:z
8888:T
8885:k
8870:E
8866:=
8863:E
8843:,
8838:r
8834:Q
8824:T
8821:k
8818:+
8809:G
8802:=
8799:S
8793:T
8787:H
8781:=
8778:G
8764:T
8754:H
8744:H
8740:G
8734:E
8728:G
8726:Δ
8714:F
8708:n
8698:G
8696:Δ
8691:G
8689:Δ
8680:E
8670:e
8666:/
8662:c
8659:μ
8651:E
8637:E
8628:j
8623:a
8613:t
8606:j
8604:ν
8593:j
8591:a
8572:,
8564:b
8560:]
8555:B
8551:[
8546:a
8542:]
8537:A
8533:[
8526:y
8522:]
8517:Y
8513:[
8508:z
8504:]
8499:Z
8495:[
8479:i
8469:i
8465:a
8459:i
8445:j
8435:j
8431:a
8425:j
8414:=
8409:r
8405:Q
8378:.
8370:b
8366:]
8361:B
8357:[
8352:a
8348:]
8343:A
8339:[
8332:z
8328:]
8323:Z
8319:[
8314:y
8310:]
8305:Y
8301:[
8289:k
8275:n
8272:x
8269:r
8264:S
8257:=
8252:)
8247:)
8243:B
8239:(
8236:S
8233:b
8230:+
8227:)
8223:A
8219:(
8216:S
8213:a
8208:(
8198:)
8193:)
8189:Z
8185:(
8182:S
8179:z
8176:+
8173:)
8169:Y
8165:(
8162:S
8159:y
8154:(
8149:=
8143:n
8140:x
8137:r
8132:S
8117:Z
8115:z
8111:y
8107:b
8103:a
8077:S
8056:,
8053:]
8049:A
8045:[
8036:k
8030:)
8026:A
8022:(
8013:S
8009:=
8006:)
8002:A
7998:(
7995:S
7984:2
7981:c
7975:1
7972:c
7955:.
7948:1
7944:c
7938:2
7934:c
7922:k
7914:1
7910:S
7906:=
7901:2
7897:S
7876:,
7869:1
7865:c
7859:2
7855:c
7843:k
7837:=
7832:1
7828:S
7819:2
7815:S
7811:=
7808:S
7783:.
7780:)
7777:c
7770:t
7767:n
7764:a
7761:t
7758:s
7755:n
7752:o
7749:c
7745:(
7733:k
7727:=
7724:)
7721:V
7714:t
7711:n
7708:a
7705:t
7702:s
7699:n
7696:o
7693:c
7689:(
7677:k
7674:=
7671:S
7661:c
7645:1
7642:V
7638:/
7634:2
7631:V
7622:n
7618:)
7612:1
7609:V
7605:/
7601:2
7598:V
7586:S
7584:Δ
7570:V
7565:Ω
7549:,
7537:k
7526:f
7523:e
7520:d
7514:=
7504:S
7487:A
7480:F
7474:A
7467:R
7457:F
7448:R
7439:e
7430:k
7397:.
7391:]
7387:x
7384:O
7380:[
7375:]
7371:d
7368:e
7365:R
7361:[
7347:F
7343:T
7340:R
7325:E
7321:=
7308:]
7304:x
7301:O
7297:[
7292:]
7288:d
7285:e
7282:R
7278:[
7264:e
7260:T
7257:k
7242:E
7238:=
7231:E
7204:F
7200:/
7196:R
7184:e
7180:/
7176:k
7167:e
7151:.
7145:]
7141:x
7138:O
7134:[
7129:]
7125:d
7122:e
7119:R
7115:[
7103:T
7100:k
7097:+
7086:c
7077:=
7071:c
7052:/
7043:c
7040:μ
7023:.
7017:]
7013:x
7010:O
7006:[
7001:]
6997:d
6994:e
6991:R
6987:[
6975:T
6972:k
6969:=
6963:c
6931:.
6927:)
6921:T
6918:k
6911:c
6900:(
6890:=
6876:)
6872:T
6869:k
6865:/
6861:]
6853:[
6846:(
6833:)
6829:T
6826:k
6822:/
6818:]
6810:[
6803:(
6790:=
6780:]
6776:x
6773:O
6769:[
6764:]
6760:d
6757:e
6754:R
6750:[
6726:/
6710:c
6707:μ
6667:.
6662:)
6653:t
6650:u
6647:o
6641:]
6631:l
6628:C
6623:[
6609:l
6606:C
6600:P
6596:+
6590:n
6587:i
6581:]
6576:+
6571:a
6568:N
6563:[
6554:+
6549:a
6546:N
6540:P
6536:+
6530:n
6527:i
6521:]
6516:+
6511:K
6506:[
6497:+
6492:K
6486:P
6482:r
6474:n
6471:i
6465:]
6455:l
6452:C
6447:[
6433:l
6430:C
6424:P
6420:+
6414:t
6411:u
6408:o
6402:]
6397:+
6392:a
6389:N
6384:[
6375:+
6370:a
6367:N
6361:P
6357:+
6351:t
6348:u
6345:o
6339:]
6334:+
6329:K
6324:[
6315:+
6310:K
6304:P
6300:r
6294:(
6281:F
6277:T
6274:R
6268:=
6263:m
6259:E
6234:.
6229:)
6220:n
6217:i
6211:]
6206:+
6201:a
6198:N
6193:[
6184:+
6179:a
6176:N
6170:P
6166:+
6160:n
6157:i
6151:]
6146:+
6141:K
6136:[
6127:+
6122:K
6116:P
6112:r
6104:t
6101:u
6098:o
6092:]
6087:+
6082:a
6079:N
6074:[
6065:+
6060:a
6057:N
6051:P
6047:+
6041:t
6038:u
6035:o
6029:]
6024:+
6019:K
6014:[
6005:+
6000:K
5994:P
5990:r
5984:(
5971:F
5967:T
5964:R
5958:=
5953:m
5949:E
5916:J
5906:r
5893:F
5889:,
5883:T
5869:R
5835:P
5815:m
5812:E
5792:,
5787:)
5777:t
5774:u
5771:o
5765:]
5755:j
5750:A
5745:[
5731:j
5726:A
5720:P
5714:M
5709:j
5700:+
5694:n
5691:i
5685:]
5680:+
5675:i
5670:M
5665:[
5656:+
5651:i
5646:M
5640:P
5634:N
5629:i
5615:n
5612:i
5606:]
5596:j
5591:A
5586:[
5572:j
5567:A
5561:P
5555:M
5550:j
5541:+
5535:t
5532:u
5529:o
5523:]
5518:+
5513:i
5508:M
5503:[
5494:+
5489:i
5484:M
5478:P
5472:N
5467:i
5456:(
5443:F
5439:T
5436:R
5430:=
5424:m
5419:E
5364:.
5358:]
5350:[
5345:]
5337:[
5315:F
5312:z
5307:T
5304:R
5295:=
5289:]
5281:[
5276:]
5268:[
5253:F
5250:z
5245:T
5242:R
5236:=
5233:E
5220:z
5161:z
5157:h
5151:h
5149:E
5142:e
5135:H
5126:z
5122:h
5095:E
5064:E
5026:E
5004:H
5001:p
4986:=
4977:E
4963:2
4959:2
4935:E
4897:E
4875:H
4872:p
4860:=
4851:E
4837:2
4813:H
4810:p
4787:E
4783:=
4774:E
4756:2
4754:O
4750:e
4743:H
4736:2
4732:e
4725:H
4710:2
4706:2
4697::
4695:h
4684:2
4675::
4673:h
4663:h
4661:E
4657:2
4623:h
4531:E
4504:h
4500:E
4473:E
4462:2
4458:2
4454:2
4434:E
4409:)
4404:z
4401:h
4396:(
4362:E
4326:z
4322:h
4308:)
4300:b
4296:}
4292:B
4289:{
4284:a
4280:}
4276:A
4273:{
4266:d
4262:}
4258:D
4255:{
4250:c
4246:}
4242:C
4239:{
4233:(
4221:z
4199:E
4195:=
4186:E
4182:=
4177:h
4173:E
4147:h
4143:E
4128:F
4124:z
4100:G
4070:F
4067:z
4056:G
4043:=
4040:)
4032:(
4018:E
3983:E
3956:D
3952:d
3949:+
3946:C
3942:c
3889:e
3884:z
3881:+
3875:+
3871:H
3865:h
3862:+
3859:B
3855:b
3852:+
3849:A
3845:a
3804:E
3781:h
3777:E
3748:h
3744:E
3735:(
3712:h
3708:E
3663:E
3631:E
3579:E
3518:E
3463:E
3418:E
3395:x
3392:o
3365:d
3362:e
3359:r
3318:1
3315:=
3302:M
3296:1
3284:M
3278:1
3272:=
3261:C
3251:C
3235:M
3228:C
3183:P
3177:(
3142:O
3140:2
3138:H
3096:E
3034:0
3031:=
3027:1
3008:,
2996:1
2993:=
2982:C
2972:C
2933:E
2929:=
2920:E
2896:1
2893:=
2882:a
2872:a
2838:E
2834:=
2825:E
2801:C
2798:/
2792:C
2764:E
2727:E
2699:C
2696:/
2690:C
2652:E
2631:1
2628:=
2617:C
2607:C
2568:E
2530:E
2488:E
2436:E
2404:C
2394:C
2379:F
2376:z
2371:T
2368:R
2343:E
2339:=
2330:E
2276:F
2273:z
2268:T
2265:R
2245:E
2241:=
2222:E
2185:E
2176:(
2142:C
2132:C
2117:F
2114:z
2109:T
2106:R
2081:E
2077:=
2068:E
2029:E
2002:E
1965:E
1936:(
1910:C
1900:C
1885:F
1882:z
1877:T
1874:R
1847:E
1836:)
1799:F
1796:z
1791:T
1788:R
1768:E
1763:(
1756:=
1747:E
1724:)
1712:C
1702:C
1690:+
1656:(
1649:F
1646:z
1641:T
1638:R
1618:E
1614:=
1605:E
1582:)
1570:C
1560:C
1529:(
1516:F
1513:z
1508:T
1505:R
1485:E
1481:=
1472:E
1410:E
1399:i
1390:i
1387:γ
1381:i
1378:C
1375:i
1372:γ
1368:i
1365:a
1359:i
1356:C
1350:i
1347:a
1342:i
1321:T
1315:λ
1299:.
1288:a
1278:a
1257:z
1251:T
1247:V
1228:E
1224:=
1213:a
1203:a
1189:z
1184:T
1180:V
1165:E
1161:=
1158:E
1136:(
1118:F
1114:T
1111:R
1105:=
1100:T
1096:V
1069:a
1060:a
1051:a
1044:r
1041:Q
1036:,
1015:F
1002:F
998:,
988:z
984:,
978:T
974:,
954:R
945:R
941:,
926:E
911:E
906:,
888:E
873:E
851:r
847:Q
834:F
831:z
826:T
823:R
803:E
799:=
790:E
769:.
758:a
748:a
733:F
730:z
725:T
722:R
702:E
698:=
693:r
689:Q
676:F
673:z
668:T
665:R
645:E
641:=
632:E
617:q
608:A
605:N
599:q
596:A
593:N
589:F
580:F
566:.
563:E
560:F
557:z
551:=
548:G
535:E
522:r
519:Q
502:r
498:Q
488:T
485:R
482:+
473:G
466:=
463:G
442:G
440:Δ
432:G
430:Δ
402:a
392:a
386:=
383:K
369:K
358:a
351:a
345:r
343:Q
318:]
312:[
307:]
301:[
295:=
284:a
274:a
268:=
263:r
259:Q
237:C
214:a
203:a
195:a
193:(
181:r
179:Q
176:(
140:+
119:e
112:z
34:.
20:)
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