Nernst equation - Knowledge

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

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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

17: 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. 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

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to convert from chemical potentials to electrode potentials, and remembering that

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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:

Fundamentals of Biochemistry: Life at the Molecular Level

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: 18:Formal standard reduction potential 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: 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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Index