Nernst equation - Knowledge

5791: 4551:

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.

6666: 5402: 6242: 1917: 4578: 6233: 5786:{\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)},} 8377: 9265: 1730: 6661:{\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)}.} 1724: 5932: 4332: 1298: 6934: 1582: 10008: 768: 10417: 7562:

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

5892:

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

4550:

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

8112: 3483:

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

2164:

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

4562:

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

5102:

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,

4708:

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

4558:, 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 8571: 10161:

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

7400: 208:). 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 10141: 2308: 9007: 1390:. 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 1588: 3317: 1142: 6727: 1455: 2411: 2149: 5137:

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

10181:

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

3153:

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,

9836: 615: 4156: 1912:{\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}}}}} 2547:

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

6228:{\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)}.} 10582: 5363: 2505:

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,

8388: 4596:

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

7782: 7211: 4072: 10021: 5893:

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

7150: 3955: 852: 2205: 10162:

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

8842: 10326: 5169: 5163: 3493: 2702: 320: 8372:{\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}}}.} 5929:), 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. 4812: 10907: 10682: 3074: 7875: 7548: 8055: 2948: 2313: 2051: 9756: 6732: 9593: 8917: 2995: 2895: 2630: 409: 7954: 3322:

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.

2848: 503: 9260:{\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}}} 7022: 4409: 3232: 9841: 9012: 7216: 9675: 5003: 3594: 3533: 3478: 3433: 3111: 2742: 2667: 2583: 2545: 2503: 2451: 2200: 2044: 1980: 1425: 9446: 3641: 4874: 1719:{\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)} 156: 5036: 4907: 4656:

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:

4327:{\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}}} 3993: 10569:: 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. 5217: 1293:{\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}}}}.} 6929:{\displaystyle {\begin{aligned}{\frac {}{}}&={\frac {\exp \left(-/kT\right)}{\exp \left(-/kT\right)}}\\&=\exp \left({\frac {\mu _{\mathrm {c} }}{kT}}\right).\end{aligned}}} 1577:{\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)} 1119: 7655: 9524: 9479: 9383: 9002: 4105: 9330: 5100: 5069: 4940: 4536: 4478: 4439: 4367: 3809: 3668: 2769: 2007: 565: 7049: 3366: 9298: 8082: 3396: 773: 10003:{\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}}} 763:{\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}}}}.} 3033: 1943: 1448: 6720:, 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 4505: 4148: 3782: 3749: 3713: 8759: 4001: 526:

associated with the electrochemical reaction is defined as the decrease in Gibbs free energy per coulomb of charge transferred, which leads to the relationship

10719: 4644:(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 3829: 6690:

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

7789: 8566:{\displaystyle Q_{r}={\frac {\displaystyle \prod _{j}a_{j}^{\nu _{j}}}{\displaystyle \prod _{i}a_{i}^{\nu _{i}}}}\approx {\frac {^{z}^{y}}{^{a}^{b}}},} 7488: 7979: 7395:{\displaystyle {\begin{aligned}E&=E^{\ominus }-{\frac {kT}{e}}\ln {\frac {}{}}\\&=E^{\ominus }-{\frac {RT}{F}}\ln {\frac {}{}}.\end{aligned}}} 5901:

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

10136:{\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}}} 3480:

cannot be referred as an immutable standard potential but needs to be systematically determined for each specific set of experimental conditions.

242: 8847: 7880: 444: 6941: 2303:{\displaystyle E_{\text{red}}^{\ominus '}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {\gamma _{\text{Red}}}{\gamma _{\text{Ox}}}}} 7641:. In this sense there is no difference in statistical properties of ideal gas atoms compared with the dissolved species of a solution with 4757: 10548:

Brown, Raymond A.; Swift, Ernest H. (1949). "The formal potential of the antimonous-antimonic half cell in hydrochloric acid solutions".

4817:

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

3038: 3329:, where at this point the concentration of Ox (the oxidized species) and Red (the reduced species) at the electrode surface are equal. 4821:. As the slopes are negative, at high pH, both hydrogen and oxygen evolution requires a much lower reduction potential than at low pH. 10233:

claimed their original calculation was affected by a misinterpretation of the Nernst equation. He cited a paper about Pd–Zr alloys.

10321: 10945: 9686: 9532: 10401:

Bard, Allen J.; Faulkner, Larry R. (2001). "Chapter 2. Potentials and Thermodynamics of Cells – See: 2.1.6 Formal Potentials".

2953: 2903: 2853: 2588: 367: 10886: 2808: 228:, also denoted here below with square brackets ) of all the dissolved species of interest are sufficiently low and that their 10832: 10619: 10355: 3312:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}={\frac {1\,\mathrm {M} _{\text{red}}}{1\,\mathrm {M} _{\text{ox}}}}=1} 3162:, the system is close to equilibrium, reversible and is at its formal potential. When the formal potential is measured under 10173:

At very low concentrations of the potential-determining ions, the potential predicted by Nernst equation approaches toward

4372: 7609:

takes place. It follows from the definition of entropy and from the condition of constant temperature and quantity of gas

8935: 6702:

of this solution is the difference between the energy barriers for taking electrons from and for giving electrons to the

10524: 2310:

So that the Nernst equation for the half-cell reaction can be correctly formally written in terms of concentrations as:

10940: 9607: 5103:

commonly referred for biochemical reactions, also depends on the slope of the corresponding line in a Pourbaix diagram

6680:

For simplicity, we will consider a solution of redox-active molecules that undergo a one-electron reversible reaction

4960: 10789: 10763: 9270: 8085: 5212:

across a membrane. This potential is determined using the concentration of the ion both inside and outside the cell:

4585: 2406:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}-{\frac {RT}{zF}}\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}} 2144:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}-{\frac {RT}{zF}}\ln {\frac {C_{\text{Red}}}{C_{\text{Ox}}}}} 9398: 3203:

In this case, as for the standard reduction potentials, the concentrations of dissolved species remain equal to one

529: 2510:, that it depends on the experimental conditions and because the ionic strength affects the activity coefficients, 7645:

equaling one: particles freely "hang around" filling the provided volume), which is inversely proportional to the

7449:. To convert to the molar quantities given in most chemistry textbooks, it is simply necessary to multiply by the 3614: 4834: 10442: 3562: 3501: 3446: 3401: 3079: 2710: 2635: 2551: 2513: 2471: 2419: 2168: 2012: 1948: 1393: 10240:

systems and can be used, for example, to assess whether a particular reaction will go to completion or not. At

5897:(the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See: 5009: 4880: 3966: 120: 3643:

fixed arbitrarily to zero by convention, it is no longer the case at a pH of 7. Then, the reduction potential

2453:

is the reduction potential that applies to a half reaction under a set of specified conditions such as, e.g.,

5206:

The Nernst equation has a physiological application when used to calculate the potential of an ion of charge

10891: 5846:

units, though the units strictly don't matter, as the ion concentration terms become a dimensionless ratio),

10316: 10146: 8756:

is the temperature of the system. Using these relations, we can now write the change in Gibbs free energy,

7556:

is the number of states available to the molecule. The number of states must vary linearly with the volume

4559: 4342:, and exponents are shown in the conventional manner. This equation is the equation of a straight line for 3961: 3544: 2159: 1079: 889: 51: 2669:

is also determined at pH 7, as e.g. for redox reactions important in biochemistry or biological systems.

10271: 9488: 9454: 9358: 5039: 4910: 4589: 4508: 4080: 3812: 3671: 3608: 3188: 4554:

Problems may occur when mixing different sources of data using different conventions or approximations (

10296: 9761:

Starting from the Nernst equation, one can also demonstrate the same relationship in the reverse way.

8587: 5189: 3559:

better corresponding to real conditions than the standard state. Formal standard reduction potentials (

35: 10443:"Redox potentials of proteins and other compounds of bioelectrochemical interest in aqueous solutions" 9773: 9769: 6707: 5368: 55: 9344:, and complexing agents) and is the potential that is actually measured in an electrochemical cell. 5078: 5047: 4918: 4514: 4456: 4417: 4345: 3787: 3646: 2747: 1985: 10178: 10163: 9303: 3338: 9276: 8599:, and the denominator is a similar product of reactant activities. All activities refer to a time 8060: 5921:(K) = 0 (as for both ions flux by electrochemical force is compensated by that by the pump, i.e. J 3371: 10935: 9598:

The sign is negative, because the considered system performs the work and thus releases energy.

4748:

respectively), so it simplifies when solving the Nernst equation expressed as a function of pH.

1121:

is approximately 25.693 mV. The Nernst equation is frequently expressed in terms of base-10

927: 612:

charge. This immediately leads to the Nernst equation, which for an electrochemical half-cell is

5358:{\displaystyle E={\frac {RT}{zF}}\ln {\frac {}{}}=2.3026{\frac {RT}{zF}}\log _{10}{\frac {}{}}.} 10496: 8574: 4601:

To illustrate the dependency of the reduction potential on pH, one can simply consider the two

3004: 2672: 63: 10804: 10779: 10753: 10607: 7613:

that the change in the number of states must be proportional to the relative change in volume

10706: 7777:{\displaystyle S=k\ln \ (\mathrm {constant} \times V)=-k\ln \ (\mathrm {constant} \times c).} 5898: 4617: 4120: 1928: 1433: 4682:

Higher stability line with oxygen gas evolution due to water oxygen oxidation at very high E

10752:

Bard, Allen J.; Inzelt, György; Scholz, Fritz, eds. (2012-10-02), "Karaoglanoff equation",

10726:[On Oxidation and Reduction Processes in the Electrolysis of Iron Salt Solutions], 10249: 10241: 10150: 9797: 9765: 9386: 9333: 8606: 7642: 4483: 4339: 4126: 4067:{\displaystyle E_{\text{red}}^{\ominus }({\text{volt}})=-{\frac {\Delta G^{\ominus }}{zF}}} 3760: 3727: 3691: 3333: 3212: 3196: 3139: 1922: 1383: 1043: 353: 326: 229: 209: 47: 5397:

under the constraints that total current density driven by electrochemical force is zero:

4660:

Lower stability line with hydrogen gas evolution due to the proton reduction at very low E

8: 10306: 10276: 10245: 8623:

may be replaced by a concentration term, .In an electrochemical cell, the cell potential

7646: 3220: 3204: 3163: 3117: 907: 869: 213: 39: 10608:"Table 14-4 Standard Reduction Potentials for Some Biochemically Import Half-Reactions" 10464: 10291: 10266: 8630: 7564: 7414: 6691: 5861: 5372: 5201: 5177: 5123: 4731: 4713: 2771:

of the half-reaction at unity concentration ratio of the oxidized and reduced species (

1321:

Similarly to equilibrium constants, activities are always measured with respect to the

1134: 10901: 7145:{\displaystyle \mu _{\mathrm {c} }=\mu _{\mathrm {c} }^{\ominus }+kT\ln {\frac {}{}}.} 3950:{\displaystyle a\,A+b\,B+h\,{\ce {H+}}+z\,e^{-}\quad {\ce {<=>}}\quad c\,C+d\,D} 10865: 10828: 10785: 10759: 10615: 10557: 10472: 10361: 10351: 10311: 10187: 10183: 9784: 9353: 8711: 8673: 8382: 7450: 7423: 6703: 5394: 5390: 4108: 3601: 3187:"A formal potential is defined as the potential of a half-cell, measured against the 3135: 601: 515: 415: 236:

as commonly done when simplifying, or idealizing, a reaction for didactic purposes:

179: 162: 10848:

Huot, J. Y. (1989). "Electrolytic Hydrogenation and Amorphization of Pd-Zr Alloys".

10724:"Über Oxydations- und Reduktionsvorgänge bei der Elektrolyse von Eisensaltzlösungen" 5389:

When the membrane is permeable to more than one ion, as is inevitably the case, the

5371:(i.e., no net flux of ions), and if the cell is permeable to only one ion, then the 847:{\displaystyle E_{\text{cell}}=E_{\text{cell}}^{\ominus }-{\frac {RT}{zF}}\ln Q_{r}} 770:

For a complete electrochemical reaction (full cell), the equation can be written as

10902:

DoITPoMS Teaching and Learning Package- "The Nernst Equation and Pourbaix Diagrams"

10857: 10820: 10735: 10670: 10454: 10301: 10286: 10230: 10229:. In reality, only 10,000–20,000 atmospheres were achieved. The American physicist 8707: 7441: 6721: 5885: 5384: 5164:

Table of standard reduction potentials for half-reactions important in biochemistry

4818: 4606: 4581: 4572: 3720: 3683: 3494:

Table of standard reduction potentials for half-reactions important in biochemistry

2703:

Table of standard reduction potentials for half-reactions important in biochemistry

2462: 1130: 572: 79: 67: 27: 10459: 7158:

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

4545: 10236:

The Nernst equation allows the calculation of the extent of reaction between two

10222: 10210:. Fleischmann and Pons, claiming that cold fusion could exist, calculated that a 3192: 3170:

the activity of each dissolved species is 1 mol/L, T = 298.15 K = 25 °C = 77 °F,

1074: 4563:

without paying attention to the different conventions on which they are based).

10226: 10013: 9337: 3552: 3436: 2458: 1322: 425: 75: 20: 4588:(STP). The vertical scale (ordinate) is the electrode potential relative to a 3719:

of a solution are related by the Nernst equation as commonly represented by a

10929: 10869: 10827:(2 ed.). Oxford and New York: Oxford University Press. pp. 33, 47. 10739: 10561: 10476: 10468: 10281: 10167: 5181: 5134: 4621: 3325:

The formal potential is also found halfway between the two peaks in a cyclic

984: 233: 221: 10365: 10221:

electrolysis cell could achieve up to 10 atmospheres of pressure inside the

8837:{\displaystyle \Delta G=\Delta H-T\Delta S=\Delta G^{\ominus }+kT\ln Q_{r},} 7967:

is unity (e.g., 1 atm or 1 M), it will merely cancel the units of

10896: 10650: 7432: 4538:= 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P 3540: 3536: 937: 519: 232:

are close to unity, their chemical activities can be approximated by their

10327:

Standard apparent reduction potentials in biochemistry at pH 7 (data page)

10206:

The Nernst equation has been involved in the scientific controversy about

8088:

and denotes the concentration of A. The change in entropy for a reaction

5854:

is the intracellular concentration of that ion (in moles per cubic meter),

3670:

of a hydrogen electrode operating at pH 7 is -0.413 V with respect to the

3435:, and because they depend on experimental conditions such as temperature, 315:{\displaystyle Q_{r}={\frac {a_{\text{Red}}}{a_{\text{Ox}}}}={\frac {}{}}} 10218: 10207: 8710:. There is a negative sign because a spontaneous reaction has a negative 7410: 5839: 4584:

for water, including stability regions for water, oxygen and hydrogen at

3604:

or to fuel microbial activity under some conditions is feasible or not.

3326: 998: 10198:

The expression of time dependence has been established by Karaoglanoff.

7786:

The change in entropy from some state 1 to another state 2 is therefore

3677: 10257:

of the reaction to be calculated and hence the extent of the reaction.

5173: 3116:

The formal reduction potential makes possible to more simply work with

1122: 10861: 10170:

and resistive loss terms which contribute to the measured potential.

10211: 10177:. This is physically meaningless because, under such conditions, the 7976:. We can, therefore, write the entropy of an arbitrary molecule A as 7568: 4625: 3816: 1316: 187: 71: 43: 10723: 9336:

of the dissolved species under given experimental conditions (T, P,

5393:

can be determined from the Goldman equation, which is a solution of

4807:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-0.05916\ pH} 2046:

and the concentrations in the simplest form of the Nernst equation:

8747: 4629: 3208: 3121: 3069:{\displaystyle {\frac {\gamma _{\text{red}}}{\gamma _{\text{ox}}}}} 2202:) which is related to the standard reduction potential as follows: 1325:(1 mol/L for solutes, 1 atm for gases, and T = 298.15 K, 980: 609: 217: 10225:

of the metal of the cathode, enough pressure to cause spontaneous

7870:{\displaystyle \Delta S=S_{2}-S_{1}=-k\ln {\frac {c_{2}}{c_{1}}},} 10214: 10186:

in electricity transfer and electrode equilibria, as analyzed by

7543:{\displaystyle S\ {\stackrel {\mathrm {def} }{=}}\ k\ln \Omega ,} 7480: 5816: 4633: 994: 198: 8050:{\displaystyle S(\mathrm {A} )=S^{\ominus }(\mathrm {A} )-k\ln,} 4577: 5875: 5865: 4742: 4637: 4546:

Main factors affecting the formal standard reduction potentials

3138:. Because molar and molal concentrations were once referred as 970: 3487: 2673:

Determination of the formal standard reduction potential when

10237: 8634: 7200:, we obtain the Nernst equation for the one-electron process 5812: 4641: 4602: 4542:= 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0). 3597: 3556: 3126: 59: 7404: 7046: = 1, we need to add in this additional constant: 4441:

at higher pH values. This is observed for the reduction of O

1982:

and called the formal standard reduction potential, so that

10606:

Voet, Donald; Voet, Judith G.; Pratt, Charlotte W. (2016).

9751:{\displaystyle E_{cell}^{\ominus }={\frac {RT}{zF}}\ln {K}} 5808: 10405:(2 ed.). New York: John Wiley & Sons. p. 52. 10201: 9588:{\displaystyle \Delta G^{\ominus }=-zFE_{cell}^{\ominus }} 9485:) transferred during the reaction and the cell potential ( 5170:

important redox reactions in biochemistry and microbiology

4648:) enters in contact with water and reacts with it. In the 3819:

equation, conventionally written as a reduction reaction (

10612:

Fundamentals of Biochemistry: Life at the Molecular Level

8912:{\displaystyle E=E^{\ominus }-{\frac {kT}{ze}}\ln Q_{r}.} 5185: 3607:

While, standard reduction potentials always refer to the

3555:

pH of 0. The advantage is to defining a more appropriate

2990:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}=1} 2943:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus '}} 2890:{\displaystyle {\frac {a_{\text{red}}}{a_{\text{ox}}}}=1} 2625:{\displaystyle {\frac {C_{\text{red}}}{C_{\text{ox}}}}=1} 2416:

According to Wenzel (2020), a formal reduction potential

404:{\displaystyle K={\frac {a_{\text{Red}}}{a_{\text{Ox}}}}} 7949:{\displaystyle S_{2}=S_{1}-k\ln {\frac {c_{2}}{c_{1}}}.} 5830:

is the permeability for that ion (in meters per second),

3551:

of most physiological and intracellular fluids than the

2843:{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }} 498:{\displaystyle \Delta G=\Delta G^{\ominus }+RT\ln Q_{r}} 90: 10418:"4. Table of Standard State Electrochemical Potentials" 10248:(emf) of the two half cells are equal. This allows the 9347: 9341: 8921:

This is the more general form of the Nernst equation.

7017:{\displaystyle \mu _{\mathrm {c} }=kT\ln {\frac {}{}}.} 5843: 4593: 3752: 3716: 3548: 3440: 2454: 10403:

Electrochemical methods: Fundamentals and applications

3909: 3823:, electrons accepted by an oxidant on the left side): 2153: 1329:, 25 °C or 77 °F). The chemical activity of a species 414:

The standard thermodynamics also says that the actual

10024: 9839: 9689: 9610: 9535: 9491: 9457: 9401: 9361: 9306: 9279: 9010: 8938: 8850: 8762: 8726:. The Gibbs free energy is related to the entropy by 8573:

where the numerator is a product of reaction product

8441: 8407: 8391: 8115: 8063: 7982: 7883: 7792: 7658: 7491: 7214: 7052: 6944: 6730: 6245: 5935: 5691: 5611: 5532: 5449: 5405: 5220: 5081: 5050: 5012: 4963: 4921: 4883: 4837: 4760: 4751:

The result can be numerically expressed as follows:

4517: 4486: 4459: 4420: 4404:{\displaystyle -0.05916\,\left({\frac {h}{z}}\right)} 4375: 4348: 4159: 4129: 4083: 4004: 3969: 3832: 3790: 3763: 3730: 3694: 3678:

Expression of the Nernst equation as a function of pH

3649: 3617: 3565: 3504: 3449: 3404: 3374: 3341: 3235: 3082: 3041: 3007: 2956: 2906: 2856: 2811: 2750: 2713: 2638: 2591: 2554: 2516: 2474: 2422: 2316: 2208: 2171: 2054: 2015: 1988: 1951: 1931: 1733: 1591: 1458: 1436: 1396: 1145: 1082: 993:

is the Faraday constant, the magnitude of charge (in

776: 618: 532: 447: 370: 245: 123: 10379:

Wahl (2005). "A Short History of Electrochemistry".

5375:

must be equal to the Nernst potential for that ion.

5133:

involved in the reduction reaction, and thus on the

10193: 9481:

is also equal to the product of the total charge (

5838:is the extracellular concentration of that ion (in 4566: 2744:can be defined as the measured reduction potential 1036:

is the reaction quotient of the cell reaction, and,

10781:Introduction to Polarography and Allied Techniques 10525:"Origins of electrochemical potentials — PalmSens" 10135: 10002: 9750: 9669: 9587: 9518: 9473: 9440: 9377: 9324: 9292: 9259: 8996: 8911: 8836: 8565: 8371: 8076: 8049: 7948: 7869: 7776: 7542: 7394: 7144: 7016: 6928: 6660: 6227: 5785: 5357: 5094: 5063: 5030: 4997: 4954:O the here above mentioned relationship becomes: 4934: 4901: 4868: 4806: 4592:electrode. The horizontal scale (abscissa) is the 4530: 4499: 4472: 4433: 4403: 4361: 4326: 4142: 4099: 4066: 3987: 3949: 3803: 3776: 3743: 3707: 3662: 3635: 3588: 3527: 3472: 3427: 3390: 3360: 3311: 3105: 3068: 3027: 2989: 2942: 2889: 2842: 2763: 2736: 2661: 2624: 2577: 2539: 2497: 2445: 2405: 2302: 2194: 2143: 2038: 2001: 1974: 1937: 1911: 1718: 1576: 1442: 1419: 1317:Form with activity coefficients and concentrations 1292: 1113: 846: 762: 559: 497: 403: 314: 150: 10825:Cold Fusion: The Scientific Fiasco of the Century 9670:{\displaystyle -zFE_{cell}^{\ominus }=-RT\ln {K}} 6938:Taking the natural logarithm of both sides gives 3917: 3916: 3899: 3898: 3484:confuse them with standard reduction potentials. 38:relationship that permits the calculation of the 10927: 10751: 10675: 10339: 7409:Quantities here are given per molecule, not per 4998:{\displaystyle E_{\text{red}}=1.229-0.05916\ pH} 4828:the here above mentioned relationship becomes: 3611:(SHE), with = 1 M corresponding to a pH 0, and 10396: 10394: 7958:If state 1 is at standard conditions, in which 3142:, it could explain the origin of the adjective 1430:Taking into account the activity coefficients ( 174:), also often called the ion activity product ( 9441:{\displaystyle \Delta G^{\ominus }=-RT\ln {K}} 6710:. The ratio of oxidized to reduced molecules, 66:(often approximated by concentrations) of the 10605: 10489: 8240: 8196: 8186: 8142: 10718: 10400: 10391: 8381:We define the ratio in the last term as the 4605:determining the water stability domain in a 4284: 4277: 4268: 4261: 4250: 4243: 4234: 4227: 3636:{\displaystyle E_{\text{red H+}}^{\ominus }} 10350:. Columbus, OH: American Chemical Society. 8700:is the number of electrons transferred and 6237:When chloride (Cl) is taken into account, 4869:{\displaystyle E_{\text{red}}=-0.05916\ pH} 4449:O, or OH, and for the reduction of H into H 3488:Formal standard reduction potential at pH 7 2413:and likewise for the full cell expression. 2009:can be directly expressed as a function of 1342:, is related to the measured concentration 424:is related to the free energy change under 10574: 10547: 10518: 10516: 10409: 9300:is often replaced by the formal potential 5157: 3589:{\displaystyle E_{\text{red}}^{\ominus '}} 3528:{\displaystyle E_{\text{red}}^{\ominus '}} 3473:{\displaystyle E_{\text{red}}^{\ominus '}} 3428:{\displaystyle E_{\text{red}}^{\ominus '}} 3106:{\displaystyle E_{\text{red}}^{\ominus '}} 2737:{\displaystyle E_{\text{red}}^{\ominus '}} 2662:{\displaystyle E_{\text{red}}^{\ominus '}} 2578:{\displaystyle E_{\text{red}}^{\ominus '}} 2540:{\displaystyle E_{\text{red}}^{\ominus '}} 2498:{\displaystyle E_{\text{red}}^{\ominus '}} 2446:{\displaystyle E_{\text{red}}^{\ominus '}} 2195:{\displaystyle E_{\text{red}}^{\ominus '}} 2039:{\displaystyle E_{\text{red}}^{\ominus '}} 1975:{\displaystyle E_{\text{red}}^{\ominus '}} 1420:{\displaystyle E_{\text{red}}^{\ominus '}} 151:{\displaystyle {\ce {Ox + ze- -> Red}}} 58:, the number of electrons involved in the 10599: 10541: 10458: 10346:Orna, Mary Virginia; Stock, John (1989). 10345: 9796:) attains the special value known as the 7405:Using thermodynamics (chemical potential) 6675: 5031:{\displaystyle E_{\text{red}}^{\ominus }} 4902:{\displaystyle E_{\text{red}}^{\ominus }} 4382: 4309: 4115:is the number of electrons involved, and 3988:{\displaystyle E_{\text{red}}^{\ominus }} 3943: 3933: 3875: 3856: 3846: 3836: 3287: 3269: 338:of the activity of the reaction product ( 10908:"20.5: Gibbs energy and redox reactions" 10841: 10819: 10683:"20.5: Gibbs energy and redox reactions" 10550:Journal of the American Chemical Society 10522: 10434: 10322:Standard electrode potential (data page) 4942:= -0.414 V for the reduction of protons. 4576: 3547:measured at pH 7, a value closer to the 2707:The formal standard reduction potential 1055:is the activity of the reduced form and 224:(C): a = γ C. So, if the concentration ( 110:) to be converted in its reduced form ( 10513: 10372: 10272:Dependency of reduction potential on pH 10202:Significance in other scientific fields 10190:and B. Damaskin, Sergio Trasatti, etc. 5071:= +0.815 V for the reduction of oxygen. 4620:by applying a sufficient difference of 3892: 3191:, when the total concentration of each 114:), the half-reaction is expressed as: 10928: 10897:Interactive Nernst/Goldman Java Applet 10850:Journal of the Electrochemical Society 10777: 10580: 10415: 7652:, so we can also write the entropy as 5172:, the Nernst equation is also used in 3498:Formal standard reduction potentials ( 3215:(F). So, expressing the concentration 3183:According to Brown and Swift (1949): 1073:At room temperature (25 °C), the 4123:. The Nernst equation relates pH and 3596:) allow to more easily estimate if a 3398:are included in the formal potential 1114:{\displaystyle V_{T}={\frac {RT}{F}}} 1064:is the activity of the oxidized form. 91:General form with chemical activities 10847: 10614:(5th ed.). Wiley. p. 466. 10440: 10378: 9348:Relation to the chemical equilibrium 5842:per cubic meter, to match the other 4369:as a function of pH with a slope of 2585:refers to its value determined when 983:transferred in the cell reaction or 9519:{\displaystyle E_{cell}^{\ominus }} 9474:{\displaystyle \Delta G^{\ominus }} 9378:{\displaystyle \Delta G^{\ominus }} 8997:{\displaystyle Q_{r}={\frac {}{}},} 8605:. Under certain circumstances (see 5913:(K) is no longer zero, but rather J 5378: 5195: 4636:(reduction of water protons) while 4100:{\displaystyle \Delta G^{\ominus }} 2154:Formal standard reduction potential 1921:Where the first term including the 13: 10348:Electrochemistry, past and present 9536: 9458: 9402: 9362: 9181: 9178: 9165: 9162: 9159: 9093: 9090: 9077: 9074: 9071: 8981: 8978: 8965: 8962: 8959: 8793: 8784: 8772: 8763: 8543: 8525: 8505: 8487: 8349: 8331: 8311: 8293: 8263: 8260: 8257: 8248: 8231: 8211: 8177: 8157: 8131: 8128: 8125: 8116: 8037: 8014: 7990: 7877:so that the entropy of state 2 is 7793: 7758: 7755: 7752: 7749: 7746: 7743: 7740: 7737: 7702: 7699: 7696: 7693: 7690: 7687: 7684: 7681: 7534: 7514: 7511: 7508: 7375: 7372: 7359: 7356: 7353: 7292: 7289: 7276: 7273: 7270: 7129: 7126: 7113: 7110: 7107: 7074: 7059: 7001: 6998: 6985: 6982: 6979: 6951: 6899: 6764: 6761: 6748: 6745: 6742: 6641: 6638: 6635: 6619: 6616: 6597: 6594: 6578: 6575: 6559: 6556: 6537: 6534: 6518: 6515: 6499: 6480: 6462: 6459: 6443: 6440: 6421: 6418: 6402: 6399: 6396: 6380: 6377: 6358: 6355: 6339: 6336: 6333: 6317: 6298: 6208: 6205: 6189: 6186: 6167: 6164: 6148: 6145: 6129: 6110: 6092: 6089: 6086: 6070: 6067: 6048: 6045: 6029: 6026: 6023: 6007: 5988: 5765: 5762: 5759: 5738: 5714: 5682: 5679: 5658: 5634: 5603: 5600: 5579: 5555: 5523: 5520: 5517: 5496: 5472: 5412: 4507:to indicate that it refers to the 4084: 4040: 3290: 3272: 1068: 533: 457: 448: 74:respectively. It was named after 14: 10957: 10887:Nernst/Goldman Equation Simulator 10880: 10806:The Journal of Physical Chemistry 9271:standard temperature and pressure 4586:standard temperature and pressure 2632:. A more particular case is when 910:) at the temperature of interest, 10194:Time dependence of the potential 8586:, each raised to the power of a 4567:Examples with a Pourbaix diagram 3600:reaction supposed to occur in a 3134:, m) concentrations in place of 1450:) the Nernst equation becomes: 1046:for the relevant species, where 16:Physical law in electrochemistry 10813: 10797: 10771: 10745: 10712: 10700: 10628: 10110: 6803:barrier for gaining an electron 6706:that is setting the solution's 5038:= +1.229 V with respect to the 3929: 3886: 3211:(m), and so are said to be one 3158:from reduction to oxidation or 2468:The formal reduction potential 1137:, in which case it is written: 872:at the temperature of interest, 10946:Eponymous equations of physics 10758:, Springer, pp. 527–528, 10156: 9185: 9174: 9169: 9155: 9097: 9086: 9081: 9067: 8985: 8974: 8969: 8955: 8548: 8539: 8530: 8521: 8510: 8501: 8492: 8483: 8354: 8345: 8336: 8327: 8316: 8307: 8298: 8289: 8235: 8227: 8215: 8207: 8181: 8173: 8161: 8153: 8041: 8033: 8018: 8010: 7994: 7986: 7768: 7733: 7712: 7677: 7379: 7368: 7363: 7349: 7296: 7285: 7280: 7266: 7133: 7122: 7117: 7103: 7005: 6994: 6989: 6975: 6849: 6846:barrier for losing an electron 6841: 6806: 6798: 6768: 6757: 6752: 6738: 5807:is the membrane potential (in 5346: 5338: 5333: 5325: 5277: 5269: 5264: 5256: 5095:{\displaystyle E_{\text{red}}} 5064:{\displaystyle E_{\text{red}}} 4935:{\displaystyle E_{\text{red}}} 4531:{\displaystyle E_{\text{red}}} 4473:{\displaystyle E_{\text{red}}} 4434:{\displaystyle E_{\text{red}}} 4362:{\displaystyle E_{\text{red}}} 4338:where curly brackets indicate 4028: 4020: 3919: 3894: 3804:{\displaystyle E_{\text{red}}} 3663:{\displaystyle E_{\text{red}}} 2799:= 1) under given conditions. 2764:{\displaystyle E_{\text{red}}} 2002:{\displaystyle E_{\text{red}}} 575:) is a unit conversion factor 560:{\displaystyle \Delta G=-zFE.} 306: 300: 295: 289: 141: 1: 10728:Zeitschrift für Elektrochemie 10460:10.5189/revpolarography.48.29 10416:Wenzel, Thomas (2020-06-09). 10332: 9325:{\displaystyle E^{\ominus '}} 8609:) each activity term such as 6670: 4824:For the reduction of H into H 4616:. When water is submitted to 4560:standard reduction potentials 4414:This equation predicts lower 3545:standard reduction potentials 3361:{\displaystyle \gamma _{red}} 893:half-cell reduction potential 197:) and the oxidized form (the 85: 82:who formulated the equation. 10581:Harvey, David (2020-06-15). 10317:Standard electrode potential 10147:standard electrode potential 9293:{\displaystyle E^{\ominus }} 8077:{\displaystyle S^{\ominus }} 7571:where the change of entropy 7483:of a molecule is defined as 5184:with respect to one type of 3962:standard reduction potential 3535:) are also commonly used in 3391:{\displaystyle \gamma _{ox}} 2160:Standard electrode potential 938:universal ideal gas constant 520:universal ideal gas constant 178:), is the ratio between the 52:standard electrode potential 7: 10809:. Cornell University. 1906. 10260: 10166:, and there are additional 5142:value (SHE) when the ratio 5040:standard hydrogen electrode 4911:standard hydrogen electrode 4509:standard hydrogen electrode 3813:standard hydrogen electrode 3672:standard hydrogen electrode 3609:standard hydrogen electrode 3189:standard hydrogen electrode 345:) by the reagent activity ( 186:) of the reduced form (the 10: 10962: 10892:Nernst Equation Calculator 10755:Electrochemical Dictionary 10164:when there is current flow 8588:stoichiometric coefficient 5382: 5199: 5190:acid dissociation constant 5188:. It can be linked to the 5161: 4603:oxido-reduction equilibria 4570: 3681: 3491: 2700: 2461:, or the concentration of 2157: 18: 10941:Electrochemical equations 10145:We have thus related the 9774:electrochemical potential 9770:thermodynamic equilibrium 8720:and a positive potential 7154:Dividing the equation by 6708:electrochemical potential 5369:thermodynamic equilibrium 5075:The offset of -414 mV in 4411:volt (pH has no units). 3028:{\displaystyle \ln {1}=0} 70:undergoing reduction and 10740:10.1002/bbpc.19060120105 10179:exchange current density 8844:and the cell potential, 7431:are used instead of the 5903:by electrochemical force 5367:When the membrane is in 36:chemical thermodynamical 19:Not to be confused with 10778:Zutshi, Kamala (2008), 8924:For the redox reaction 5158:Applications in biology 4480:is then often noted as 1938:{\displaystyle \gamma } 1443:{\displaystyle \gamma } 928:standard cell potential 906:is the cell potential ( 361:of the half-reaction: 10447:Review of Polarography 10297:Nernst–Planck equation 10137: 10004: 9752: 9671: 9589: 9520: 9475: 9442: 9379: 9326: 9294: 9269:The cell potential at 9261: 8998: 8913: 8838: 8567: 8373: 8078: 8051: 7950: 7871: 7778: 7544: 7396: 7146: 7018: 6930: 6676:Using Boltzmann factor 6662: 6229: 5874:is the temperature in 5787: 5706: 5626: 5547: 5464: 5359: 5096: 5065: 5032: 4999: 4946:For the reduction of O 4936: 4903: 4877:because by convention 4870: 4808: 4598: 4532: 4501: 4474: 4435: 4405: 4363: 4328: 4144: 4101: 4068: 3989: 3951: 3805: 3778: 3745: 3709: 3664: 3637: 3590: 3529: 3474: 3429: 3392: 3362: 3313: 3201: 3181:a standard potential. 3107: 3070: 3029: 2991: 2944: 2891: 2844: 2765: 2738: 2663: 2626: 2579: 2541: 2499: 2447: 2407: 2304: 2196: 2145: 2040: 2003: 1976: 1939: 1913: 1720: 1578: 1444: 1421: 1306:= ln(10) ≈ 2.3026 and 1294: 1115: 969:is the temperature in 848: 764: 561: 499: 405: 316: 152: 10707:J. Electroanal. Chem. 10501:TheFreeDictionary.com 10153:of a redox reaction. 10138: 10005: 9753: 9672: 9590: 9521: 9476: 9443: 9380: 9334:activity coefficients 9332:, which includes the 9327: 9295: 9262: 8999: 8914: 8839: 8683:only by a constant: 8568: 8374: 8079: 8052: 7951: 7872: 7779: 7643:activity coefficients 7545: 7397: 7147: 7019: 6931: 6724:for these processes: 6663: 6230: 5899:sodium-potassium pump 5788: 5692: 5612: 5533: 5450: 5395:G-H-K influx equation 5360: 5097: 5066: 5033: 5000: 4937: 4904: 4871: 4809: 4580: 4533: 4502: 4500:{\displaystyle E_{h}} 4475: 4436: 4406: 4364: 4329: 4145: 4143:{\displaystyle E_{h}} 4102: 4069: 3990: 3952: 3811:expressed versus the 3806: 3779: 3777:{\displaystyle E_{h}} 3746: 3744:{\displaystyle E_{h}} 3710: 3708:{\displaystyle E_{h}} 3665: 3638: 3591: 3530: 3475: 3430: 3393: 3363: 3334:activity coefficients 3314: 3185: 3140:formal concentrations 3108: 3071: 3030: 2992: 2945: 2892: 2845: 2766: 2739: 2664: 2627: 2580: 2542: 2500: 2448: 2408: 2305: 2197: 2146: 2041: 2004: 1977: 1940: 1923:activity coefficients 1914: 1721: 1579: 1445: 1422: 1351:via the relationship 1295: 1116: 849: 765: 562: 522:. The cell potential 500: 441:by the relationship: 406: 317: 230:activity coefficients 216:(mol/L solution), or 153: 10912:Chemistry LibreTexts 10784:, pp. 127–128, 10709:, 79 (1977), 259-266 10687:Chemistry LibreTexts 10587:Chemistry LibreTexts 10583:"2.2: Concentration" 10441:Kano, Kenji (2002). 10422:Chemistry LibreTexts 10250:equilibrium constant 10246:electromotive forces 10242:chemical equilibrium 10151:equilibrium constant 10022: 9837: 9798:equilibrium constant 9766:chemical equilibrium 9687: 9608: 9533: 9489: 9455: 9399: 9387:equilibrium constant 9359: 9304: 9277: 9008: 8936: 8848: 8760: 8607:chemical equilibrium 8389: 8113: 8061: 7980: 7881: 7790: 7656: 7489: 7212: 7050: 6942: 6728: 6243: 5933: 5888:(coulombs per mole). 5403: 5218: 5176:for calculating the 5079: 5048: 5010: 4961: 4919: 4881: 4835: 4758: 4677:(cathode: reduction) 4622:electrical potential 4515: 4484: 4457: 4418: 4373: 4346: 4157: 4127: 4081: 4002: 3967: 3830: 3788: 3761: 3728: 3692: 3647: 3615: 3563: 3502: 3447: 3402: 3372: 3339: 3233: 3177:= 1 bar) it becomes 3080: 3039: 3035:, and that the term 3005: 2954: 2904: 2854: 2809: 2748: 2711: 2636: 2589: 2552: 2514: 2472: 2420: 2314: 2206: 2169: 2052: 2013: 1986: 1949: 1929: 1731: 1589: 1456: 1434: 1394: 1384:activity coefficient 1143: 1080: 774: 616: 530: 445: 368: 354:equilibrium constant 327:chemical equilibrium 243: 210:activity coefficient 121: 56:absolute temperature 10307:Reduction potential 10277:Electrode potential 9713: 9643: 9584: 9515: 8473: 8439: 8273: 8086:standard conditions 7084: 5752: 5728: 5672: 5648: 5593: 5569: 5510: 5486: 5027: 4898: 4788: 4632:is produced at the 4628:immersed in water, 4200: 4019: 3984: 3905: 3784:explicitly denotes 3632: 3585: 3524: 3469: 3424: 3164:standard conditions 3102: 2939: 2839: 2733: 2658: 2574: 2536: 2494: 2442: 2349: 2246: 2228: 2191: 2087: 2035: 1971: 1853: 1769: 1619: 1486: 1416: 908:electromotive force 870:reduction potential 804: 703: 646: 608:is the fundamental 180:chemical activities 99:) accepts a number 50:reaction) from the 40:reduction potential 10497:"Formal potential" 10292:Membrane potential 10267:Concentration cell 10133: 10000: 9998: 9783:and therefore the 9748: 9690: 9667: 9620: 9585: 9561: 9516: 9492: 9471: 9451:At the same time, 9438: 9385:is related to the 9375: 9322: 9290: 9257: 9255: 8994: 8909: 8834: 8672:is related to the 8631:chemical potential 8563: 8474: 8452: 8451: 8440: 8418: 8417: 8369: 8251: 8084:is the entropy at 8074: 8047: 7946: 7867: 7774: 7565:isothermal process 7540: 7442:Faraday's constant 7415:Boltzmann constant 7392: 7390: 7142: 7068: 7014: 6926: 6924: 6692:chemical potential 6658: 6225: 5886:Faraday's constant 5862:ideal gas constant 5783: 5772: 5771: 5736: 5712: 5656: 5632: 5610: 5609: 5577: 5553: 5494: 5470: 5373:membrane potential 5355: 5202:Reversal potential 5178:electric potential 5092: 5061: 5028: 5013: 4995: 4932: 4899: 4884: 4866: 4804: 4774: 4704:(anode: oxidation) 4599: 4528: 4497: 4470: 4431: 4401: 4359: 4324: 4186: 4140: 4121:Faraday's constant 4097: 4064: 4005: 3985: 3970: 3947: 3924: 3801: 3774: 3741: 3705: 3660: 3633: 3618: 3586: 3566: 3525: 3505: 3470: 3450: 3425: 3405: 3388: 3358: 3309: 3146:in the expression 3103: 3083: 3066: 3025: 2987: 2940: 2920: 2887: 2840: 2825: 2761: 2734: 2714: 2659: 2639: 2622: 2575: 2555: 2537: 2517: 2495: 2475: 2443: 2423: 2403: 2330: 2300: 2232: 2209: 2192: 2172: 2141: 2068: 2036: 2016: 1999: 1972: 1952: 1935: 1909: 1855: 1834: 1831: 1755: 1716: 1605: 1574: 1472: 1440: 1417: 1397: 1290: 1135:natural logarithms 1111: 844: 790: 760: 689: 632: 557: 495: 401: 352:) is equal to the 312: 148: 95:When an oxidizer ( 10862:10.1149/1.2096700 10834:978-0-19-855817-0 10821:Huizenga, John R. 10621:978-1-118-91840-1 10523:PalmSens (2021). 10357:978-0-8412-1572-6 10312:Solvated electron 10188:Alexander Frumkin 10184:solvated electron 10131: 10127: 10114: 10108: 10105: 10076: 9994: 9918: 9885: 9785:reaction quotient 9735: 9354:Gibbs free energy 9232: 9189: 9144: 9101: 9056: 8989: 8888: 8712:Gibbs free energy 8674:Gibbs free energy 8558: 8475: 8442: 8408: 8383:reaction quotient 8364: 8109:is then given by 7941: 7862: 7732: 7676: 7524: 7519: 7497: 7451:Avogadro constant 7383: 7338: 7300: 7255: 7137: 7009: 6913: 6869: 6847: 6804: 6772: 6704:working electrode 6648: 6272: 6215: 5962: 5773: 5434: 5391:resting potential 5350: 5344: 5331: 5307: 5281: 5275: 5262: 5245: 5126:to the number of 5119:of the number of 5089: 5058: 5020: 4988: 4971: 4929: 4891: 4859: 4845: 4797: 4781: 4768: 4640:is formed at the 4525: 4467: 4428: 4395: 4356: 4322: 4317: 4294: 4212: 4193: 4180: 4109:Gibbs free energy 4062: 4026: 4012: 3977: 3926: 3861: 3798: 3657: 3625: 3602:metabolic process 3573: 3543:for referring to 3512: 3457: 3412: 3301: 3297: 3279: 3258: 3255: 3245: 3090: 3064: 3061: 3051: 2979: 2976: 2966: 2927: 2914: 2879: 2876: 2866: 2832: 2819: 2758: 2721: 2646: 2614: 2611: 2601: 2562: 2524: 2482: 2463:complexing agents 2430: 2401: 2398: 2388: 2371: 2337: 2324: 2298: 2295: 2285: 2268: 2239: 2216: 2179: 2139: 2136: 2126: 2109: 2075: 2062: 2023: 1996: 1959: 1907: 1904: 1894: 1877: 1841: 1821: 1818: 1808: 1791: 1762: 1749: 1747: 1741: 1709: 1706: 1696: 1676: 1673: 1663: 1641: 1612: 1599: 1567: 1564: 1554: 1543: 1540: 1530: 1508: 1479: 1466: 1404: 1285: 1282: 1272: 1248: 1210: 1207: 1197: 1180: 1131:common logarithms 1109: 979:is the number of 868:is the half-cell 826: 797: 784: 755: 752: 742: 725: 696: 668: 639: 626: 602:Avogadro constant 516:reaction quotient 416:Gibbs free energy 399: 396: 386: 310: 281: 278: 268: 163:reaction quotient 146: 134: 127: 10953: 10922: 10920: 10919: 10874: 10873: 10845: 10839: 10838: 10817: 10811: 10810: 10801: 10795: 10794: 10775: 10769: 10768: 10749: 10743: 10742: 10722:(January 1906), 10720:Karaoglanoff, Z. 10716: 10710: 10704: 10698: 10697: 10695: 10694: 10679: 10673: 10671:Faraday constant 10668: 10648: 10632: 10626: 10625: 10603: 10597: 10596: 10594: 10593: 10578: 10572: 10571: 10556:(8): 2719–2723. 10545: 10539: 10538: 10536: 10535: 10520: 10511: 10510: 10508: 10507: 10493: 10487: 10486: 10484: 10483: 10462: 10438: 10432: 10431: 10429: 10428: 10413: 10407: 10406: 10398: 10389: 10388: 10376: 10370: 10369: 10343: 10302:Pourbaix diagram 10287:Goldman equation 10256: 10231:John R. Huizenga 10176: 10142: 10140: 10139: 10134: 10132: 10129: 10125: 10115: 10112: 10109: 10107: 10106: 10103: 10097: 10096: 10095: 10082: 10077: 10075: 10074: 10073: 10060: 10059: 10058: 10045: 10034: 10033: 10009: 10007: 10006: 10001: 9999: 9995: 9993: 9985: 9984: 9983: 9967: 9945: 9944: 9919: 9917: 9909: 9901: 9886: 9884: 9876: 9868: 9863: 9862: 9827: 9808: 9795: 9782: 9757: 9755: 9754: 9749: 9747: 9736: 9734: 9726: 9718: 9712: 9707: 9680:And therefore: 9676: 9674: 9673: 9668: 9666: 9642: 9637: 9594: 9592: 9591: 9586: 9583: 9578: 9548: 9547: 9525: 9523: 9522: 9517: 9514: 9509: 9484: 9480: 9478: 9477: 9472: 9470: 9469: 9447: 9445: 9444: 9439: 9437: 9414: 9413: 9391: 9384: 9382: 9381: 9376: 9374: 9373: 9331: 9329: 9328: 9323: 9321: 9320: 9319: 9299: 9297: 9296: 9291: 9289: 9288: 9266: 9264: 9263: 9258: 9256: 9249: 9248: 9233: 9231: 9223: 9215: 9210: 9209: 9194: 9190: 9188: 9184: 9172: 9168: 9153: 9145: 9143: 9135: 9127: 9122: 9121: 9106: 9102: 9100: 9096: 9084: 9080: 9065: 9057: 9055: 9047: 9039: 9034: 9033: 9003: 9001: 9000: 8995: 8990: 8988: 8984: 8972: 8968: 8953: 8948: 8947: 8931: 8929: 8918: 8916: 8915: 8910: 8905: 8904: 8889: 8887: 8879: 8871: 8866: 8865: 8843: 8841: 8840: 8835: 8830: 8829: 8805: 8804: 8755: 8745: 8739: 8725: 8719: 8708:Faraday constant 8705: 8699: 8693: 8682: 8671: 8665: 8664: 8662: 8661: 8656: 8653: 8628: 8622: 8620: 8619: 8604: 8598: 8585: 8572: 8570: 8569: 8564: 8559: 8557: 8556: 8555: 8546: 8538: 8537: 8528: 8519: 8518: 8517: 8508: 8500: 8499: 8490: 8481: 8476: 8472: 8471: 8470: 8460: 8450: 8438: 8437: 8436: 8426: 8416: 8406: 8401: 8400: 8378: 8376: 8375: 8370: 8365: 8363: 8362: 8361: 8352: 8344: 8343: 8334: 8325: 8324: 8323: 8314: 8306: 8305: 8296: 8287: 8272: 8267: 8266: 8244: 8243: 8234: 8214: 8200: 8199: 8190: 8189: 8180: 8160: 8146: 8145: 8136: 8135: 8134: 8105: 8101: 8097: 8093: 8083: 8081: 8080: 8075: 8073: 8072: 8056: 8054: 8053: 8048: 8040: 8017: 8009: 8008: 7993: 7975: 7966: 7955: 7953: 7952: 7947: 7942: 7940: 7939: 7930: 7929: 7920: 7906: 7905: 7893: 7892: 7876: 7874: 7873: 7868: 7863: 7861: 7860: 7851: 7850: 7841: 7824: 7823: 7811: 7810: 7783: 7781: 7780: 7775: 7761: 7730: 7705: 7674: 7651: 7640: 7639: 7637: 7636: 7628: 7625: 7612: 7608: 7606: 7604: 7603: 7595: 7592: 7561: 7555: 7549: 7547: 7546: 7541: 7522: 7521: 7520: 7518: 7517: 7505: 7500: 7495: 7478: 7465: 7448: 7439: 7430: 7421: 7401: 7399: 7398: 7393: 7391: 7384: 7382: 7378: 7366: 7362: 7347: 7339: 7334: 7326: 7321: 7320: 7305: 7301: 7299: 7295: 7283: 7279: 7264: 7256: 7251: 7243: 7238: 7237: 7205: 7204: 7199: 7198: 7196: 7195: 7190: 7187: 7178: 7176: 7175: 7170: 7167: 7157: 7151: 7149: 7148: 7143: 7138: 7136: 7132: 7120: 7116: 7101: 7083: 7078: 7077: 7064: 7063: 7062: 7045: 7043: 7042: 7035: 7023: 7021: 7020: 7015: 7010: 7008: 7004: 6992: 6988: 6973: 6956: 6955: 6954: 6935: 6933: 6932: 6927: 6925: 6918: 6914: 6912: 6904: 6903: 6902: 6892: 6874: 6870: 6868: 6867: 6863: 6856: 6848: 6845: 6825: 6824: 6820: 6813: 6805: 6802: 6782: 6773: 6771: 6767: 6755: 6751: 6736: 6722:Boltzmann factor 6719: 6717: 6716: 6701: 6686: 6667: 6665: 6664: 6659: 6654: 6653: 6649: 6647: 6646: 6645: 6644: 6632: 6628: 6627: 6622: 6608: 6607: 6606: 6605: 6600: 6583: 6582: 6581: 6572: 6568: 6567: 6562: 6548: 6547: 6546: 6545: 6540: 6523: 6522: 6521: 6512: 6508: 6507: 6502: 6491: 6490: 6489: 6488: 6483: 6468: 6467: 6466: 6465: 6456: 6452: 6451: 6446: 6432: 6431: 6430: 6429: 6424: 6407: 6406: 6405: 6393: 6389: 6388: 6383: 6369: 6368: 6367: 6366: 6361: 6344: 6343: 6342: 6330: 6326: 6325: 6320: 6309: 6308: 6307: 6306: 6301: 6286: 6273: 6268: 6260: 6255: 6254: 6234: 6232: 6231: 6226: 6221: 6220: 6216: 6214: 6213: 6212: 6211: 6202: 6198: 6197: 6192: 6178: 6177: 6176: 6175: 6170: 6153: 6152: 6151: 6142: 6138: 6137: 6132: 6121: 6120: 6119: 6118: 6113: 6098: 6097: 6096: 6095: 6083: 6079: 6078: 6073: 6059: 6058: 6057: 6056: 6051: 6034: 6033: 6032: 6020: 6016: 6015: 6010: 5999: 5998: 5997: 5996: 5991: 5976: 5963: 5958: 5950: 5945: 5944: 5896: 5883: 5873: 5859: 5853: 5837: 5829: 5811:, equivalent to 5806: 5792: 5790: 5789: 5784: 5779: 5778: 5774: 5770: 5769: 5768: 5756: 5751: 5746: 5741: 5730: 5729: 5727: 5722: 5717: 5705: 5700: 5687: 5686: 5685: 5676: 5671: 5666: 5661: 5650: 5649: 5647: 5642: 5637: 5625: 5620: 5608: 5607: 5606: 5597: 5592: 5587: 5582: 5571: 5570: 5568: 5563: 5558: 5546: 5541: 5528: 5527: 5526: 5514: 5509: 5504: 5499: 5488: 5487: 5485: 5480: 5475: 5463: 5458: 5448: 5435: 5430: 5422: 5417: 5416: 5415: 5385:Goldman equation 5379:Goldman equation 5364: 5362: 5361: 5356: 5351: 5349: 5345: 5342: 5336: 5332: 5330:ion outside cell 5329: 5323: 5318: 5317: 5308: 5306: 5298: 5290: 5282: 5280: 5276: 5273: 5267: 5263: 5261:ion outside cell 5260: 5254: 5246: 5244: 5236: 5228: 5211: 5196:Nernst potential 5154:differs from 1. 5152: 5151: 5147: 5129: 5122: 5117: 5116: 5112: 5101: 5099: 5098: 5093: 5091: 5090: 5087: 5070: 5068: 5067: 5062: 5060: 5059: 5056: 5037: 5035: 5034: 5029: 5026: 5021: 5018: 5004: 5002: 5001: 4996: 4986: 4973: 4972: 4969: 4941: 4939: 4938: 4933: 4931: 4930: 4927: 4908: 4906: 4905: 4900: 4897: 4892: 4889: 4875: 4873: 4872: 4867: 4857: 4847: 4846: 4843: 4819:Pourbaix diagram 4813: 4811: 4810: 4805: 4795: 4787: 4782: 4779: 4770: 4769: 4766: 4737: 4730: 4719: 4712: 4703: 4702: 4676: 4675: 4655: 4615: 4607:Pourbaix diagram 4582:Pourbaix diagram 4573:Pourbaix diagram 4537: 4535: 4534: 4529: 4527: 4526: 4523: 4506: 4504: 4503: 4498: 4496: 4495: 4479: 4477: 4476: 4471: 4469: 4468: 4465: 4440: 4438: 4437: 4432: 4430: 4429: 4426: 4410: 4408: 4407: 4402: 4400: 4396: 4388: 4368: 4366: 4365: 4360: 4358: 4357: 4354: 4333: 4331: 4330: 4325: 4323: 4320: 4318: 4313: 4304: 4299: 4295: 4293: 4292: 4291: 4276: 4275: 4259: 4258: 4257: 4242: 4241: 4225: 4213: 4205: 4199: 4194: 4191: 4182: 4181: 4178: 4169: 4168: 4149: 4147: 4146: 4141: 4139: 4138: 4118: 4114: 4107:is the standard 4106: 4104: 4103: 4098: 4096: 4095: 4073: 4071: 4070: 4065: 4063: 4061: 4053: 4052: 4051: 4038: 4027: 4024: 4018: 4013: 4010: 3994: 3992: 3991: 3986: 3983: 3978: 3975: 3956: 3954: 3953: 3948: 3928: 3927: 3925: 3923: 3922: 3915: 3907: 3906: 3904: 3897: 3889: 3885: 3884: 3868: 3867: 3866: 3859: 3810: 3808: 3807: 3802: 3800: 3799: 3796: 3783: 3781: 3780: 3775: 3773: 3772: 3756: 3750: 3748: 3747: 3742: 3740: 3739: 3721:Pourbaix diagram 3714: 3712: 3711: 3706: 3704: 3703: 3684:Pourbaix diagram 3669: 3667: 3666: 3661: 3659: 3658: 3655: 3642: 3640: 3639: 3634: 3631: 3626: 3623: 3595: 3593: 3592: 3587: 3584: 3583: 3574: 3571: 3534: 3532: 3531: 3526: 3523: 3522: 3513: 3510: 3479: 3477: 3476: 3471: 3468: 3467: 3458: 3455: 3434: 3432: 3431: 3426: 3423: 3422: 3413: 3410: 3397: 3395: 3394: 3389: 3387: 3386: 3367: 3365: 3364: 3359: 3357: 3356: 3318: 3316: 3315: 3310: 3302: 3300: 3299: 3298: 3295: 3293: 3282: 3281: 3280: 3277: 3275: 3264: 3259: 3257: 3256: 3253: 3247: 3246: 3243: 3237: 3225: 3218: 3176: 3133: 3112: 3110: 3109: 3104: 3101: 3100: 3091: 3088: 3075: 3073: 3072: 3067: 3065: 3063: 3062: 3059: 3053: 3052: 3049: 3043: 3034: 3032: 3031: 3026: 3018: 2996: 2994: 2993: 2988: 2980: 2978: 2977: 2974: 2968: 2967: 2964: 2958: 2949: 2947: 2946: 2941: 2938: 2937: 2928: 2925: 2916: 2915: 2912: 2896: 2894: 2893: 2888: 2880: 2878: 2877: 2874: 2868: 2867: 2864: 2858: 2849: 2847: 2846: 2841: 2838: 2833: 2830: 2821: 2820: 2817: 2798: 2797: 2795: 2794: 2788: 2785: 2770: 2768: 2767: 2762: 2760: 2759: 2756: 2743: 2741: 2740: 2735: 2732: 2731: 2722: 2719: 2696: 2695: 2693: 2692: 2686: 2683: 2668: 2666: 2665: 2660: 2657: 2656: 2647: 2644: 2631: 2629: 2628: 2623: 2615: 2613: 2612: 2609: 2603: 2602: 2599: 2593: 2584: 2582: 2581: 2576: 2573: 2572: 2563: 2560: 2546: 2544: 2543: 2538: 2535: 2534: 2525: 2522: 2504: 2502: 2501: 2496: 2493: 2492: 2483: 2480: 2452: 2450: 2449: 2444: 2441: 2440: 2431: 2428: 2412: 2410: 2409: 2404: 2402: 2400: 2399: 2396: 2390: 2389: 2386: 2380: 2372: 2370: 2362: 2354: 2348: 2347: 2338: 2335: 2326: 2325: 2322: 2309: 2307: 2306: 2301: 2299: 2297: 2296: 2293: 2287: 2286: 2283: 2277: 2269: 2267: 2259: 2251: 2245: 2240: 2237: 2227: 2226: 2217: 2214: 2201: 2199: 2198: 2193: 2190: 2189: 2180: 2177: 2150: 2148: 2147: 2142: 2140: 2138: 2137: 2134: 2128: 2127: 2124: 2118: 2110: 2108: 2100: 2092: 2086: 2085: 2076: 2073: 2064: 2063: 2060: 2045: 2043: 2042: 2037: 2034: 2033: 2024: 2021: 2008: 2006: 2005: 2000: 1998: 1997: 1994: 1981: 1979: 1978: 1973: 1970: 1969: 1960: 1957: 1944: 1942: 1941: 1936: 1918: 1916: 1915: 1910: 1908: 1906: 1905: 1902: 1896: 1895: 1892: 1886: 1878: 1876: 1868: 1860: 1854: 1852: 1851: 1842: 1839: 1832: 1827: 1823: 1822: 1820: 1819: 1816: 1810: 1809: 1806: 1800: 1792: 1790: 1782: 1774: 1768: 1763: 1760: 1743: 1742: 1739: 1725: 1723: 1722: 1717: 1715: 1711: 1710: 1708: 1707: 1704: 1698: 1697: 1694: 1688: 1677: 1675: 1674: 1671: 1665: 1664: 1661: 1655: 1642: 1640: 1632: 1624: 1618: 1613: 1610: 1601: 1600: 1597: 1583: 1581: 1580: 1575: 1573: 1569: 1568: 1566: 1565: 1562: 1556: 1555: 1552: 1546: 1544: 1542: 1541: 1538: 1532: 1531: 1528: 1522: 1509: 1507: 1499: 1491: 1485: 1480: 1477: 1468: 1467: 1464: 1449: 1447: 1446: 1441: 1426: 1424: 1423: 1418: 1415: 1414: 1405: 1402: 1389: 1381: 1372: 1350: 1341: 1332: 1313:≈ 0.05916 Volt. 1299: 1297: 1296: 1291: 1286: 1284: 1283: 1280: 1274: 1273: 1270: 1264: 1259: 1258: 1249: 1244: 1243: 1242: 1229: 1224: 1223: 1211: 1209: 1208: 1205: 1199: 1198: 1195: 1189: 1181: 1176: 1175: 1166: 1161: 1160: 1120: 1118: 1117: 1112: 1110: 1105: 1097: 1092: 1091: 1063: 1054: 1042:is the chemical 1041: 1035: 1024: 1023: 1021: 1018: 1015: 1011: 992: 978: 968: 962: 961: 959: 956: 953: 950: 935: 925: 924: 923: 905: 887: 886: 885: 867: 853: 851: 850: 845: 843: 842: 827: 825: 817: 809: 803: 798: 795: 786: 785: 782: 769: 767: 766: 761: 756: 754: 753: 750: 744: 743: 740: 734: 726: 724: 716: 708: 702: 697: 694: 685: 684: 669: 667: 659: 651: 645: 640: 637: 628: 627: 624: 607: 599: 590: 573:Faraday constant 570: 566: 564: 563: 558: 525: 513: 504: 502: 501: 496: 494: 493: 469: 468: 440: 439: 438: 423: 410: 408: 407: 402: 400: 398: 397: 394: 388: 387: 384: 378: 359: 336: 321: 319: 318: 313: 311: 309: 298: 287: 282: 280: 279: 276: 270: 269: 266: 260: 255: 254: 220:(mol/kg water), 207: 196: 172: 157: 155: 154: 149: 147: 144: 140: 139: 132: 125: 113: 106: 98: 80:physical chemist 68:chemical species 28:electrochemistry 10961: 10960: 10956: 10955: 10954: 10952: 10951: 10950: 10926: 10925: 10917: 10915: 10906: 10883: 10878: 10877: 10846: 10842: 10835: 10818: 10814: 10803: 10802: 10798: 10792: 10776: 10772: 10766: 10750: 10746: 10717: 10713: 10705: 10701: 10692: 10690: 10681: 10680: 10676: 10664: 10654: 10653: 10644: 10634: 10633: 10629: 10622: 10604: 10600: 10591: 10589: 10579: 10575: 10546: 10542: 10533: 10531: 10521: 10514: 10505: 10503: 10495: 10494: 10490: 10481: 10479: 10439: 10435: 10426: 10424: 10414: 10410: 10399: 10392: 10387:(8): 1820–1828. 10381:Galvanotechtnik 10377: 10373: 10358: 10344: 10340: 10335: 10263: 10252: 10223:crystal lattice 10204: 10196: 10174: 10159: 10128: 10111: 10102: 10098: 10091: 10087: 10083: 10081: 10069: 10065: 10061: 10054: 10050: 10046: 10044: 10029: 10025: 10023: 10020: 10019: 9997: 9996: 9986: 9979: 9975: 9968: 9966: 9959: 9947: 9946: 9940: 9936: 9929: 9910: 9902: 9900: 9897: 9896: 9877: 9869: 9867: 9858: 9854: 9847: 9840: 9838: 9835: 9834: 9826: 9818: 9813: 9807: 9801: 9793: 9788: 9776: 9743: 9727: 9719: 9717: 9708: 9694: 9688: 9685: 9684: 9662: 9638: 9624: 9609: 9606: 9605: 9579: 9565: 9543: 9539: 9534: 9531: 9530: 9510: 9496: 9490: 9487: 9486: 9482: 9465: 9461: 9456: 9453: 9452: 9433: 9409: 9405: 9400: 9397: 9396: 9389: 9369: 9365: 9360: 9357: 9356: 9350: 9312: 9311: 9307: 9305: 9302: 9301: 9284: 9280: 9278: 9275: 9274: 9254: 9253: 9244: 9240: 9224: 9216: 9214: 9205: 9201: 9192: 9191: 9177: 9173: 9158: 9154: 9152: 9136: 9128: 9126: 9117: 9113: 9104: 9103: 9089: 9085: 9070: 9066: 9064: 9048: 9040: 9038: 9029: 9025: 9018: 9011: 9009: 9006: 9005: 8977: 8973: 8958: 8954: 8952: 8943: 8939: 8937: 8934: 8933: 8927: 8925: 8900: 8896: 8880: 8872: 8870: 8861: 8857: 8849: 8846: 8845: 8825: 8821: 8800: 8796: 8761: 8758: 8757: 8751: 8741: 8727: 8721: 8714: 8701: 8695: 8684: 8677: 8667: 8657: 8654: 8652: 8646: 8645: 8643: 8638: 8633:available from 8624: 8618: 8615: 8614: 8613: 8610: 8600: 8596: 8591: 8583: 8578: 8551: 8547: 8542: 8533: 8529: 8524: 8520: 8513: 8509: 8504: 8495: 8491: 8486: 8482: 8480: 8466: 8462: 8461: 8456: 8446: 8432: 8428: 8427: 8422: 8412: 8405: 8396: 8392: 8390: 8387: 8386: 8357: 8353: 8348: 8339: 8335: 8330: 8326: 8319: 8315: 8310: 8301: 8297: 8292: 8288: 8286: 8268: 8256: 8255: 8239: 8238: 8230: 8210: 8195: 8194: 8185: 8184: 8176: 8156: 8141: 8140: 8124: 8123: 8119: 8114: 8111: 8110: 8107: 8103: 8099: 8095: 8091: 8068: 8064: 8062: 8059: 8058: 8036: 8013: 8004: 8000: 7989: 7981: 7978: 7977: 7974: 7968: 7965: 7959: 7935: 7931: 7925: 7921: 7919: 7901: 7897: 7888: 7884: 7882: 7879: 7878: 7856: 7852: 7846: 7842: 7840: 7819: 7815: 7806: 7802: 7791: 7788: 7787: 7736: 7680: 7657: 7654: 7653: 7649: 7635: 7629: 7626: 7624: 7618: 7617: 7615: 7614: 7610: 7602: 7596: 7593: 7591: 7585: 7584: 7582: 7572: 7557: 7553: 7507: 7506: 7501: 7499: 7498: 7490: 7487: 7486: 7477: 7467: 7464: 7454: 7444: 7435: 7426: 7424:electron charge 7417: 7407: 7389: 7388: 7371: 7367: 7352: 7348: 7346: 7327: 7325: 7316: 7312: 7303: 7302: 7288: 7284: 7269: 7265: 7263: 7244: 7242: 7233: 7229: 7222: 7215: 7213: 7210: 7209: 7202: 7201: 7191: 7188: 7183: 7182: 7180: 7171: 7168: 7163: 7162: 7160: 7159: 7155: 7125: 7121: 7106: 7102: 7100: 7079: 7073: 7072: 7058: 7057: 7053: 7051: 7048: 7047: 7040: 7039: 7037: 7033: 7027: 6997: 6993: 6978: 6974: 6972: 6950: 6949: 6945: 6943: 6940: 6939: 6923: 6922: 6905: 6898: 6897: 6893: 6891: 6887: 6872: 6871: 6852: 6844: 6837: 6833: 6826: 6809: 6801: 6794: 6790: 6783: 6781: 6774: 6760: 6756: 6741: 6737: 6735: 6731: 6729: 6726: 6725: 6714: 6713: 6711: 6700: 6694: 6684: 6678: 6673: 6634: 6633: 6623: 6615: 6614: 6610: 6609: 6601: 6593: 6592: 6591: 6587: 6574: 6573: 6563: 6555: 6554: 6550: 6549: 6541: 6533: 6532: 6531: 6527: 6514: 6513: 6503: 6498: 6497: 6493: 6492: 6484: 6479: 6478: 6477: 6473: 6469: 6458: 6457: 6447: 6439: 6438: 6434: 6433: 6425: 6417: 6416: 6415: 6411: 6395: 6394: 6384: 6376: 6375: 6371: 6370: 6362: 6354: 6353: 6352: 6348: 6332: 6331: 6321: 6316: 6315: 6311: 6310: 6302: 6297: 6296: 6295: 6291: 6287: 6285: 6281: 6280: 6261: 6259: 6250: 6246: 6244: 6241: 6240: 6204: 6203: 6193: 6185: 6184: 6180: 6179: 6171: 6163: 6162: 6161: 6157: 6144: 6143: 6133: 6128: 6127: 6123: 6122: 6114: 6109: 6108: 6107: 6103: 6099: 6085: 6084: 6074: 6066: 6065: 6061: 6060: 6052: 6044: 6043: 6042: 6038: 6022: 6021: 6011: 6006: 6005: 6001: 6000: 5992: 5987: 5986: 5985: 5981: 5977: 5975: 5971: 5970: 5951: 5949: 5940: 5936: 5934: 5931: 5930: 5928: 5924: 5920: 5916: 5912: 5908: 5894: 5881: 5871: 5857: 5852: 5849: 5836: 5833: 5828: 5822: 5805: 5799: 5758: 5757: 5747: 5742: 5737: 5732: 5731: 5723: 5718: 5713: 5711: 5707: 5701: 5696: 5678: 5677: 5667: 5662: 5657: 5652: 5651: 5643: 5638: 5633: 5631: 5627: 5621: 5616: 5599: 5598: 5588: 5583: 5578: 5573: 5572: 5564: 5559: 5554: 5552: 5548: 5542: 5537: 5516: 5515: 5505: 5500: 5495: 5490: 5489: 5481: 5476: 5471: 5469: 5465: 5459: 5454: 5447: 5443: 5442: 5423: 5421: 5411: 5410: 5406: 5404: 5401: 5400: 5387: 5381: 5343:ion inside cell 5341: 5337: 5328: 5324: 5322: 5313: 5309: 5299: 5291: 5289: 5274:ion inside cell 5272: 5268: 5259: 5255: 5253: 5237: 5229: 5227: 5219: 5216: 5215: 5207: 5204: 5198: 5166: 5160: 5149: 5145: 5144: 5141: 5127: 5120: 5114: 5110: 5109: 5086: 5082: 5080: 5077: 5076: 5055: 5051: 5049: 5046: 5045: 5044:So, at pH = 7, 5043: 5042:(SHE: pH = 1). 5022: 5017: 5011: 5008: 5007: 5005: 4968: 4964: 4962: 4959: 4958: 4953: 4949: 4926: 4922: 4920: 4917: 4916: 4915:So, at pH = 7, 4914: 4913:(SHE: pH = 1). 4893: 4888: 4882: 4879: 4878: 4876: 4842: 4838: 4836: 4833: 4832: 4827: 4783: 4778: 4765: 4761: 4759: 4756: 4755: 4746: 4735: 4728: 4726: 4717: 4710: 4700: 4696: 4692: 4691: 4685: 4674: 4671:2 H + 2 e ⇌ H 4670: 4669: 4663: 4653: 4649: 4647: 4613: 4609: 4575: 4569: 4548: 4541: 4522: 4518: 4516: 4513: 4512: 4491: 4487: 4485: 4482: 4481: 4464: 4460: 4458: 4455: 4454: 4452: 4448: 4444: 4425: 4421: 4419: 4416: 4415: 4387: 4383: 4374: 4371: 4370: 4353: 4349: 4347: 4344: 4343: 4319: 4305: 4303: 4287: 4283: 4271: 4267: 4260: 4253: 4249: 4237: 4233: 4226: 4224: 4220: 4204: 4195: 4190: 4177: 4173: 4164: 4160: 4158: 4155: 4154: 4134: 4130: 4128: 4125: 4124: 4116: 4112: 4091: 4087: 4082: 4079: 4078: 4054: 4047: 4043: 4039: 4037: 4023: 4014: 4009: 4003: 4000: 3999: 3979: 3974: 3968: 3965: 3964: 3918: 3911: 3910: 3908: 3900: 3893: 3891: 3890: 3888: 3887: 3880: 3876: 3862: 3858: 3857: 3831: 3828: 3827: 3795: 3791: 3789: 3786: 3785: 3768: 3764: 3762: 3759: 3758: 3735: 3731: 3729: 3726: 3725: 3723: 3699: 3695: 3693: 3690: 3689: 3686: 3680: 3654: 3650: 3648: 3645: 3644: 3627: 3622: 3616: 3613: 3612: 3576: 3575: 3570: 3564: 3561: 3560: 3515: 3514: 3509: 3503: 3500: 3499: 3496: 3490: 3460: 3459: 3454: 3448: 3445: 3444: 3415: 3414: 3409: 3403: 3400: 3399: 3379: 3375: 3373: 3370: 3369: 3346: 3342: 3340: 3337: 3336: 3294: 3289: 3288: 3283: 3276: 3271: 3270: 3265: 3263: 3252: 3248: 3242: 3238: 3236: 3234: 3231: 3230: 3223: 3216: 3193:oxidation state 3182: 3175: 3171: 3130: 3125: 3093: 3092: 3087: 3081: 3078: 3077: 3076:is included in 3058: 3054: 3048: 3044: 3042: 3040: 3037: 3036: 3014: 3006: 3003: 3002: 2973: 2969: 2963: 2959: 2957: 2955: 2952: 2951: 2930: 2929: 2924: 2911: 2907: 2905: 2902: 2901: 2873: 2869: 2863: 2859: 2857: 2855: 2852: 2851: 2834: 2829: 2816: 2812: 2810: 2807: 2806: 2793: 2789: 2786: 2784: 2780: 2779: 2777: 2776: 2755: 2751: 2749: 2746: 2745: 2724: 2723: 2718: 2712: 2709: 2708: 2705: 2699: 2691: 2687: 2684: 2682: 2678: 2677: 2675: 2674: 2649: 2648: 2643: 2637: 2634: 2633: 2608: 2604: 2598: 2594: 2592: 2590: 2587: 2586: 2565: 2564: 2559: 2553: 2550: 2549: 2527: 2526: 2521: 2515: 2512: 2511: 2485: 2484: 2479: 2473: 2470: 2469: 2433: 2432: 2427: 2421: 2418: 2417: 2395: 2391: 2385: 2381: 2379: 2363: 2355: 2353: 2340: 2339: 2334: 2321: 2317: 2315: 2312: 2311: 2292: 2288: 2282: 2278: 2276: 2260: 2252: 2250: 2241: 2236: 2219: 2218: 2213: 2207: 2204: 2203: 2182: 2181: 2176: 2170: 2167: 2166: 2162: 2156: 2133: 2129: 2123: 2119: 2117: 2101: 2093: 2091: 2078: 2077: 2072: 2059: 2055: 2053: 2050: 2049: 2026: 2025: 2020: 2014: 2011: 2010: 1993: 1989: 1987: 1984: 1983: 1962: 1961: 1956: 1950: 1947: 1946: 1930: 1927: 1926: 1901: 1897: 1891: 1887: 1885: 1869: 1861: 1859: 1844: 1843: 1838: 1833: 1815: 1811: 1805: 1801: 1799: 1783: 1775: 1773: 1764: 1759: 1754: 1750: 1748: 1738: 1734: 1732: 1729: 1728: 1703: 1699: 1693: 1689: 1687: 1670: 1666: 1660: 1656: 1654: 1647: 1643: 1633: 1625: 1623: 1614: 1609: 1596: 1592: 1590: 1587: 1586: 1561: 1557: 1551: 1547: 1545: 1537: 1533: 1527: 1523: 1521: 1520: 1516: 1500: 1492: 1490: 1481: 1476: 1463: 1459: 1457: 1454: 1453: 1435: 1432: 1431: 1407: 1406: 1401: 1395: 1392: 1391: 1387: 1386:of the species 1380: 1374: 1371: 1365: 1358: 1352: 1349: 1343: 1340: 1334: 1330: 1319: 1311: 1279: 1275: 1269: 1265: 1263: 1254: 1250: 1238: 1234: 1230: 1228: 1219: 1215: 1204: 1200: 1194: 1190: 1188: 1171: 1167: 1165: 1156: 1152: 1144: 1141: 1140: 1098: 1096: 1087: 1083: 1081: 1078: 1077: 1075:thermal voltage 1071: 1069:Thermal voltage 1062: 1056: 1053: 1047: 1039: 1034: 1028: 1019: 1016: 1013: 1009: 1007: 1002: 990: 976: 966: 957: 954: 951: 948: 946: 941: 933: 922: 919: 918: 917: 913: 904: 898: 884: 881: 880: 879: 875: 866: 860: 838: 834: 818: 810: 808: 799: 794: 781: 777: 775: 772: 771: 749: 745: 739: 735: 733: 717: 709: 707: 698: 693: 680: 676: 660: 652: 650: 641: 636: 623: 619: 617: 614: 613: 605: 598: 592: 586: 576: 568: 531: 528: 527: 523: 512: 506: 489: 485: 464: 460: 446: 443: 442: 437: 435: 434: 433: 428: 418: 393: 389: 383: 379: 377: 369: 366: 365: 357: 351: 344: 335: 331: 299: 288: 286: 275: 271: 265: 261: 259: 250: 246: 244: 241: 240: 206: 202: 195: 191: 171: 167: 135: 131: 124: 122: 119: 118: 111: 104: 96: 93: 88: 42:of a reaction ( 32:Nernst equation 24: 17: 12: 11: 5: 10959: 10949: 10948: 10943: 10938: 10936:Walther Nernst 10924: 10923: 10904: 10899: 10894: 10889: 10882: 10881:External links 10879: 10876: 10875: 10856:(3): 630–635. 10840: 10833: 10812: 10796: 10790: 10770: 10764: 10744: 10711: 10699: 10674: 10662: 10642: 10627: 10620: 10598: 10573: 10540: 10512: 10488: 10433: 10408: 10390: 10371: 10356: 10337: 10336: 10334: 10331: 10330: 10329: 10324: 10319: 10314: 10309: 10304: 10299: 10294: 10289: 10284: 10279: 10274: 10269: 10262: 10259: 10227:nuclear fusion 10217:immersed in a 10203: 10200: 10195: 10192: 10158: 10155: 10124: 10121: 10118: 10101: 10094: 10090: 10086: 10080: 10072: 10068: 10064: 10057: 10053: 10049: 10043: 10040: 10037: 10032: 10028: 10014:standard state 9992: 9989: 9982: 9978: 9974: 9971: 9965: 9962: 9960: 9958: 9955: 9952: 9949: 9948: 9943: 9939: 9935: 9932: 9930: 9928: 9925: 9922: 9916: 9913: 9908: 9905: 9899: 9898: 9895: 9892: 9889: 9883: 9880: 9875: 9872: 9866: 9861: 9857: 9853: 9850: 9848: 9846: 9843: 9842: 9829: 9828: 9824: 9816: 9805: 9791: 9759: 9758: 9746: 9742: 9739: 9733: 9730: 9725: 9722: 9716: 9711: 9706: 9703: 9700: 9697: 9693: 9678: 9677: 9665: 9661: 9658: 9655: 9652: 9649: 9646: 9641: 9636: 9633: 9630: 9627: 9623: 9619: 9616: 9613: 9596: 9595: 9582: 9577: 9574: 9571: 9568: 9564: 9560: 9557: 9554: 9551: 9546: 9542: 9538: 9513: 9508: 9505: 9502: 9499: 9495: 9468: 9464: 9460: 9449: 9448: 9436: 9432: 9429: 9426: 9423: 9420: 9417: 9412: 9408: 9404: 9372: 9368: 9364: 9349: 9346: 9338:ionic strength 9318: 9315: 9310: 9287: 9283: 9252: 9247: 9243: 9239: 9236: 9230: 9227: 9222: 9219: 9213: 9208: 9204: 9200: 9197: 9195: 9193: 9187: 9183: 9180: 9176: 9171: 9167: 9164: 9161: 9157: 9151: 9148: 9142: 9139: 9134: 9131: 9125: 9120: 9116: 9112: 9109: 9107: 9105: 9099: 9095: 9092: 9088: 9083: 9079: 9076: 9073: 9069: 9063: 9060: 9054: 9051: 9046: 9043: 9037: 9032: 9028: 9024: 9021: 9019: 9017: 9014: 9013: 8993: 8987: 8983: 8980: 8976: 8971: 8967: 8964: 8961: 8957: 8951: 8946: 8942: 8908: 8903: 8899: 8895: 8892: 8886: 8883: 8878: 8875: 8869: 8864: 8860: 8856: 8853: 8833: 8828: 8824: 8820: 8817: 8814: 8811: 8808: 8803: 8799: 8795: 8792: 8789: 8786: 8783: 8780: 8777: 8774: 8771: 8768: 8765: 8650: 8616: 8594: 8581: 8562: 8554: 8550: 8545: 8541: 8536: 8532: 8527: 8523: 8516: 8512: 8507: 8503: 8498: 8494: 8489: 8485: 8479: 8469: 8465: 8459: 8455: 8449: 8445: 8435: 8431: 8425: 8421: 8415: 8411: 8404: 8399: 8395: 8368: 8360: 8356: 8351: 8347: 8342: 8338: 8333: 8329: 8322: 8318: 8313: 8309: 8304: 8300: 8295: 8291: 8285: 8282: 8279: 8276: 8271: 8265: 8262: 8259: 8254: 8250: 8247: 8242: 8237: 8233: 8229: 8226: 8223: 8220: 8217: 8213: 8209: 8206: 8203: 8198: 8193: 8188: 8183: 8179: 8175: 8172: 8169: 8166: 8163: 8159: 8155: 8152: 8149: 8144: 8139: 8133: 8130: 8127: 8122: 8118: 8090: 8071: 8067: 8046: 8043: 8039: 8035: 8032: 8029: 8026: 8023: 8020: 8016: 8012: 8007: 8003: 7999: 7996: 7992: 7988: 7985: 7972: 7963: 7945: 7938: 7934: 7928: 7924: 7918: 7915: 7912: 7909: 7904: 7900: 7896: 7891: 7887: 7866: 7859: 7855: 7849: 7845: 7839: 7836: 7833: 7830: 7827: 7822: 7818: 7814: 7809: 7805: 7801: 7798: 7795: 7773: 7770: 7767: 7764: 7760: 7757: 7754: 7751: 7748: 7745: 7742: 7739: 7735: 7729: 7726: 7723: 7720: 7717: 7714: 7711: 7708: 7704: 7701: 7698: 7695: 7692: 7689: 7686: 7683: 7679: 7673: 7670: 7667: 7664: 7661: 7633: 7622: 7600: 7589: 7539: 7536: 7533: 7530: 7527: 7516: 7513: 7510: 7504: 7494: 7475: 7462: 7406: 7403: 7387: 7381: 7377: 7374: 7370: 7365: 7361: 7358: 7355: 7351: 7345: 7342: 7337: 7333: 7330: 7324: 7319: 7315: 7311: 7308: 7306: 7304: 7298: 7294: 7291: 7287: 7282: 7278: 7275: 7272: 7268: 7262: 7259: 7254: 7250: 7247: 7241: 7236: 7232: 7228: 7225: 7223: 7221: 7218: 7217: 7141: 7135: 7131: 7128: 7124: 7119: 7115: 7112: 7109: 7105: 7099: 7096: 7093: 7090: 7087: 7082: 7076: 7071: 7067: 7061: 7056: 7031: 7013: 7007: 7003: 7000: 6996: 6991: 6987: 6984: 6981: 6977: 6971: 6968: 6965: 6962: 6959: 6953: 6948: 6921: 6917: 6911: 6908: 6901: 6896: 6890: 6886: 6883: 6880: 6877: 6875: 6873: 6866: 6862: 6859: 6855: 6851: 6843: 6840: 6836: 6832: 6829: 6823: 6819: 6816: 6812: 6808: 6800: 6797: 6793: 6789: 6786: 6780: 6777: 6775: 6770: 6766: 6763: 6759: 6754: 6750: 6747: 6744: 6740: 6734: 6733: 6698: 6688: 6687: 6677: 6674: 6672: 6669: 6657: 6652: 6643: 6640: 6637: 6631: 6626: 6621: 6618: 6613: 6604: 6599: 6596: 6590: 6586: 6580: 6577: 6571: 6566: 6561: 6558: 6553: 6544: 6539: 6536: 6530: 6526: 6520: 6517: 6511: 6506: 6501: 6496: 6487: 6482: 6476: 6472: 6464: 6461: 6455: 6450: 6445: 6442: 6437: 6428: 6423: 6420: 6414: 6410: 6404: 6401: 6398: 6392: 6387: 6382: 6379: 6374: 6365: 6360: 6357: 6351: 6347: 6341: 6338: 6335: 6329: 6324: 6319: 6314: 6305: 6300: 6294: 6290: 6284: 6279: 6276: 6271: 6267: 6264: 6258: 6253: 6249: 6224: 6219: 6210: 6207: 6201: 6196: 6191: 6188: 6183: 6174: 6169: 6166: 6160: 6156: 6150: 6147: 6141: 6136: 6131: 6126: 6117: 6112: 6106: 6102: 6094: 6091: 6088: 6082: 6077: 6072: 6069: 6064: 6055: 6050: 6047: 6041: 6037: 6031: 6028: 6025: 6019: 6014: 6009: 6004: 5995: 5990: 5984: 5980: 5974: 5969: 5966: 5961: 5957: 5954: 5948: 5943: 5939: 5926: 5922: 5918: 5914: 5910: 5906: 5890: 5889: 5879: 5869: 5855: 5850: 5847: 5834: 5831: 5826: 5820: 5803: 5782: 5777: 5767: 5764: 5761: 5755: 5750: 5745: 5740: 5735: 5726: 5721: 5716: 5710: 5704: 5699: 5695: 5690: 5684: 5681: 5675: 5670: 5665: 5660: 5655: 5646: 5641: 5636: 5630: 5624: 5619: 5615: 5605: 5602: 5596: 5591: 5586: 5581: 5576: 5567: 5562: 5557: 5551: 5545: 5540: 5536: 5531: 5525: 5522: 5519: 5513: 5508: 5503: 5498: 5493: 5484: 5479: 5474: 5468: 5462: 5457: 5453: 5446: 5441: 5438: 5433: 5429: 5426: 5420: 5414: 5409: 5383:Main article: 5380: 5377: 5354: 5348: 5340: 5335: 5327: 5321: 5316: 5312: 5305: 5302: 5297: 5294: 5288: 5285: 5279: 5271: 5266: 5258: 5252: 5249: 5243: 5240: 5235: 5232: 5226: 5223: 5200:Main article: 5197: 5194: 5159: 5156: 5139: 5085: 5073: 5072: 5054: 5025: 5016: 4994: 4991: 4985: 4982: 4979: 4976: 4967: 4951: 4947: 4944: 4943: 4925: 4909:= 0 V for the 4896: 4887: 4865: 4862: 4856: 4853: 4850: 4841: 4825: 4815: 4814: 4803: 4800: 4794: 4791: 4786: 4777: 4773: 4764: 4744: 4724: 4706: 4705: 4698: 4694: 4688: 4687: 4683: 4679: 4678: 4672: 4666: 4665: 4661: 4651: 4645: 4611: 4571:Main article: 4568: 4565: 4547: 4544: 4539: 4521: 4494: 4490: 4463: 4450: 4446: 4442: 4424: 4399: 4394: 4391: 4386: 4381: 4378: 4352: 4336: 4335: 4316: 4312: 4308: 4302: 4298: 4290: 4286: 4282: 4279: 4274: 4270: 4266: 4263: 4256: 4252: 4248: 4245: 4240: 4236: 4232: 4229: 4223: 4219: 4216: 4211: 4208: 4203: 4198: 4189: 4185: 4176: 4172: 4167: 4163: 4137: 4133: 4094: 4090: 4086: 4075: 4074: 4060: 4057: 4050: 4046: 4042: 4036: 4033: 4030: 4022: 4017: 4008: 3982: 3973: 3960:The half-cell 3958: 3957: 3946: 3942: 3939: 3936: 3932: 3921: 3914: 3903: 3896: 3883: 3879: 3874: 3871: 3865: 3855: 3852: 3849: 3845: 3842: 3839: 3835: 3794: 3771: 3767: 3738: 3734: 3702: 3698: 3679: 3676: 3653: 3630: 3621: 3582: 3579: 3569: 3553:standard state 3521: 3518: 3508: 3489: 3486: 3466: 3463: 3453: 3437:ionic strength 3421: 3418: 3408: 3385: 3382: 3378: 3355: 3352: 3349: 3345: 3320: 3319: 3308: 3305: 3292: 3286: 3274: 3268: 3262: 3251: 3241: 3173: 3128: 3120:(mol/L, M) or 3099: 3096: 3086: 3057: 3047: 3024: 3021: 3017: 3013: 3010: 2999: 2998: 2986: 2983: 2972: 2962: 2936: 2933: 2923: 2919: 2910: 2886: 2883: 2872: 2862: 2837: 2828: 2824: 2815: 2791: 2782: 2754: 2730: 2727: 2717: 2698: 2689: 2680: 2671: 2655: 2652: 2642: 2621: 2618: 2607: 2597: 2571: 2568: 2558: 2533: 2530: 2520: 2491: 2488: 2478: 2459:ionic strength 2439: 2436: 2426: 2394: 2384: 2378: 2375: 2369: 2366: 2361: 2358: 2352: 2346: 2343: 2333: 2329: 2320: 2291: 2281: 2275: 2272: 2266: 2263: 2258: 2255: 2249: 2244: 2235: 2231: 2225: 2222: 2212: 2188: 2185: 2175: 2155: 2152: 2132: 2122: 2116: 2113: 2107: 2104: 2099: 2096: 2090: 2084: 2081: 2071: 2067: 2058: 2032: 2029: 2019: 1992: 1968: 1965: 1955: 1934: 1900: 1890: 1884: 1881: 1875: 1872: 1867: 1864: 1858: 1850: 1847: 1837: 1830: 1826: 1814: 1804: 1798: 1795: 1789: 1786: 1781: 1778: 1772: 1767: 1758: 1753: 1746: 1737: 1714: 1702: 1692: 1686: 1683: 1680: 1669: 1659: 1653: 1650: 1646: 1639: 1636: 1631: 1628: 1622: 1617: 1608: 1604: 1595: 1572: 1560: 1550: 1536: 1526: 1519: 1515: 1512: 1506: 1503: 1498: 1495: 1489: 1484: 1475: 1471: 1462: 1439: 1413: 1410: 1400: 1378: 1369: 1363: 1356: 1347: 1338: 1323:standard state 1318: 1315: 1309: 1289: 1278: 1268: 1262: 1257: 1253: 1247: 1241: 1237: 1233: 1227: 1222: 1218: 1214: 1203: 1193: 1187: 1184: 1179: 1174: 1170: 1164: 1159: 1155: 1151: 1148: 1133:) rather than 1108: 1104: 1101: 1095: 1090: 1086: 1070: 1067: 1066: 1065: 1060: 1051: 1037: 1032: 1026: 1001:of electrons: 988: 974: 964: 931: 920: 911: 902: 896: 882: 873: 864: 841: 837: 833: 830: 824: 821: 816: 813: 807: 802: 793: 789: 780: 759: 748: 738: 732: 729: 723: 720: 715: 712: 706: 701: 692: 688: 683: 679: 675: 672: 666: 663: 658: 655: 649: 644: 635: 631: 622: 596: 584: 556: 553: 550: 547: 544: 541: 538: 535: 510: 492: 488: 484: 481: 478: 475: 472: 467: 463: 459: 456: 453: 450: 436: 426:standard state 412: 411: 392: 382: 376: 373: 349: 342: 333: 323: 322: 308: 305: 302: 297: 294: 291: 285: 274: 264: 258: 253: 249: 234:concentrations 204: 193: 169: 159: 158: 143: 138: 130: 103:of electrons ( 92: 89: 87: 84: 76:Walther Nernst 60:redox reaction 21:Ernst equation 15: 9: 6: 4: 3: 2: 10958: 10947: 10944: 10942: 10939: 10937: 10934: 10933: 10931: 10913: 10909: 10905: 10903: 10900: 10898: 10895: 10893: 10890: 10888: 10885: 10884: 10871: 10867: 10863: 10859: 10855: 10851: 10844: 10836: 10830: 10826: 10822: 10816: 10808: 10807: 10800: 10793: 10791:9788122417913 10787: 10783: 10782: 10774: 10767: 10765:9783642295515 10761: 10757: 10756: 10748: 10741: 10737: 10733: 10730:(in German), 10729: 10725: 10721: 10715: 10708: 10703: 10688: 10684: 10678: 10672: 10667: 10661: 10657: 10652: 10647: 10641: 10637: 10631: 10623: 10617: 10613: 10609: 10602: 10588: 10584: 10577: 10570: 10568: 10563: 10559: 10555: 10551: 10544: 10530: 10526: 10519: 10517: 10502: 10498: 10492: 10478: 10474: 10470: 10466: 10461: 10456: 10452: 10448: 10444: 10437: 10423: 10419: 10412: 10404: 10397: 10395: 10386: 10382: 10375: 10367: 10363: 10359: 10353: 10349: 10342: 10338: 10328: 10325: 10323: 10320: 10318: 10315: 10313: 10310: 10308: 10305: 10303: 10300: 10298: 10295: 10293: 10290: 10288: 10285: 10283: 10282:Galvanic cell 10280: 10278: 10275: 10273: 10270: 10268: 10265: 10264: 10258: 10255: 10251: 10247: 10243: 10239: 10234: 10232: 10228: 10224: 10220: 10216: 10213: 10209: 10199: 10191: 10189: 10185: 10180: 10171: 10169: 10168:overpotential 10165: 10154: 10152: 10148: 10143: 10122: 10119: 10116: 10099: 10092: 10088: 10084: 10078: 10070: 10066: 10062: 10055: 10051: 10047: 10041: 10038: 10035: 10030: 10026: 10017: 10015: 10010: 9990: 9987: 9980: 9976: 9972: 9969: 9963: 9961: 9956: 9953: 9950: 9941: 9937: 9933: 9931: 9926: 9923: 9920: 9914: 9911: 9906: 9903: 9893: 9890: 9887: 9881: 9878: 9873: 9870: 9864: 9859: 9855: 9851: 9849: 9844: 9832: 9823: 9819: 9812: 9811: 9810: 9804: 9799: 9794: 9786: 9780: 9775: 9771: 9767: 9762: 9744: 9740: 9737: 9731: 9728: 9723: 9720: 9714: 9709: 9704: 9701: 9698: 9695: 9691: 9683: 9682: 9681: 9663: 9659: 9656: 9653: 9650: 9647: 9644: 9639: 9634: 9631: 9628: 9625: 9621: 9617: 9614: 9611: 9604: 9603: 9602: 9599: 9580: 9575: 9572: 9569: 9566: 9562: 9558: 9555: 9552: 9549: 9544: 9540: 9529: 9528: 9527: 9511: 9506: 9503: 9500: 9497: 9493: 9466: 9462: 9434: 9430: 9427: 9424: 9421: 9418: 9415: 9410: 9406: 9395: 9394: 9393: 9392:as follows: 9388: 9370: 9366: 9355: 9352:The standard 9345: 9343: 9339: 9335: 9316: 9313: 9308: 9285: 9281: 9272: 9267: 9250: 9245: 9241: 9237: 9234: 9228: 9225: 9220: 9217: 9211: 9206: 9202: 9198: 9196: 9149: 9146: 9140: 9137: 9132: 9129: 9123: 9118: 9114: 9110: 9108: 9061: 9058: 9052: 9049: 9044: 9041: 9035: 9030: 9026: 9022: 9020: 9015: 9004:and we have: 8991: 8949: 8944: 8940: 8922: 8919: 8906: 8901: 8897: 8893: 8890: 8884: 8881: 8876: 8873: 8867: 8862: 8858: 8854: 8851: 8831: 8826: 8822: 8818: 8815: 8812: 8809: 8806: 8801: 8797: 8790: 8787: 8781: 8778: 8775: 8769: 8766: 8754: 8749: 8744: 8738: 8734: 8730: 8724: 8718: 8713: 8709: 8704: 8698: 8692: 8688: 8681: 8675: 8670: 8660: 8649: 8641: 8636: 8632: 8627: 8621: 8608: 8603: 8597: 8589: 8584: 8576: 8560: 8552: 8534: 8514: 8496: 8477: 8467: 8463: 8457: 8453: 8447: 8443: 8433: 8429: 8423: 8419: 8413: 8409: 8402: 8397: 8393: 8384: 8379: 8366: 8358: 8340: 8320: 8302: 8283: 8280: 8277: 8274: 8269: 8252: 8245: 8224: 8221: 8218: 8204: 8201: 8191: 8170: 8167: 8164: 8150: 8147: 8137: 8120: 8089: 8087: 8069: 8065: 8044: 8030: 8027: 8024: 8021: 8005: 8001: 7997: 7983: 7971: 7962: 7956: 7943: 7936: 7932: 7926: 7922: 7916: 7913: 7910: 7907: 7902: 7898: 7894: 7889: 7885: 7864: 7857: 7853: 7847: 7843: 7837: 7834: 7831: 7828: 7825: 7820: 7816: 7812: 7807: 7803: 7799: 7796: 7784: 7771: 7765: 7762: 7727: 7724: 7721: 7718: 7715: 7709: 7706: 7671: 7668: 7665: 7662: 7659: 7648: 7647:concentration 7644: 7632: 7621: 7599: 7588: 7580: 7576: 7570: 7566: 7560: 7550: 7537: 7531: 7528: 7525: 7502: 7492: 7484: 7482: 7474: 7470: 7461: 7457: 7452: 7447: 7443: 7438: 7434: 7429: 7425: 7420: 7416: 7412: 7402: 7385: 7343: 7340: 7335: 7331: 7328: 7322: 7317: 7313: 7309: 7307: 7260: 7257: 7252: 7248: 7245: 7239: 7234: 7230: 7226: 7224: 7219: 7207: 7194: 7186: 7174: 7166: 7152: 7139: 7097: 7094: 7091: 7088: 7085: 7080: 7069: 7065: 7054: 7030: 7024: 7011: 6969: 6966: 6963: 6960: 6957: 6946: 6936: 6919: 6915: 6909: 6906: 6894: 6888: 6884: 6881: 6878: 6876: 6864: 6860: 6857: 6853: 6838: 6834: 6830: 6827: 6821: 6817: 6814: 6810: 6795: 6791: 6787: 6784: 6778: 6776: 6723: 6709: 6705: 6697: 6693: 6683: 6682: 6681: 6668: 6655: 6650: 6629: 6624: 6611: 6602: 6588: 6584: 6569: 6564: 6551: 6542: 6528: 6524: 6509: 6504: 6494: 6485: 6474: 6470: 6453: 6448: 6435: 6426: 6412: 6408: 6390: 6385: 6372: 6363: 6349: 6345: 6327: 6322: 6312: 6303: 6292: 6288: 6282: 6277: 6274: 6269: 6265: 6262: 6256: 6251: 6247: 6238: 6235: 6222: 6217: 6199: 6194: 6181: 6172: 6158: 6154: 6139: 6134: 6124: 6115: 6104: 6100: 6080: 6075: 6062: 6053: 6039: 6035: 6017: 6012: 6002: 5993: 5982: 5978: 5972: 5967: 5964: 5959: 5955: 5952: 5946: 5941: 5937: 5904: 5900: 5887: 5880: 5877: 5870: 5867: 5863: 5856: 5848: 5845: 5841: 5832: 5825: 5821: 5818: 5814: 5810: 5802: 5798: 5797: 5796: 5793: 5780: 5775: 5753: 5748: 5743: 5733: 5724: 5719: 5708: 5702: 5697: 5693: 5688: 5673: 5668: 5663: 5653: 5644: 5639: 5628: 5622: 5617: 5613: 5594: 5589: 5584: 5574: 5565: 5560: 5549: 5543: 5538: 5534: 5529: 5511: 5506: 5501: 5491: 5482: 5477: 5466: 5460: 5455: 5451: 5444: 5439: 5436: 5431: 5427: 5424: 5418: 5407: 5398: 5396: 5392: 5386: 5376: 5374: 5370: 5365: 5352: 5319: 5314: 5310: 5303: 5300: 5295: 5292: 5286: 5283: 5250: 5247: 5241: 5238: 5233: 5230: 5224: 5221: 5213: 5210: 5203: 5193: 5191: 5187: 5183: 5182:cell membrane 5179: 5175: 5171: 5165: 5155: 5153: 5136: 5135:stoichiometry 5132: 5125: 5118: 5107:on the ratio 5106: 5083: 5052: 5041: 5023: 5014: 4992: 4989: 4983: 4980: 4977: 4974: 4965: 4957: 4956: 4955: 4923: 4912: 4894: 4885: 4863: 4860: 4854: 4851: 4848: 4839: 4831: 4830: 4829: 4822: 4820: 4801: 4798: 4792: 4789: 4784: 4775: 4771: 4762: 4754: 4753: 4752: 4749: 4747: 4740: 4733: 4722: 4715: 4690: 4689: 4681: 4680: 4668: 4667: 4659: 4658: 4657: 4643: 4639: 4635: 4631: 4627: 4623: 4619: 4608: 4604: 4595: 4591: 4587: 4583: 4579: 4574: 4564: 4561: 4557: 4552: 4543: 4519: 4510: 4492: 4488: 4461: 4422: 4412: 4397: 4392: 4389: 4384: 4379: 4376: 4350: 4341: 4314: 4310: 4306: 4300: 4296: 4288: 4280: 4272: 4264: 4254: 4246: 4238: 4230: 4221: 4217: 4214: 4209: 4206: 4201: 4196: 4187: 4183: 4174: 4170: 4165: 4161: 4153: 4152: 4151: 4135: 4131: 4122: 4110: 4092: 4088: 4058: 4055: 4048: 4044: 4034: 4031: 4015: 4006: 3998: 3997: 3996: 3980: 3971: 3963: 3944: 3940: 3937: 3934: 3930: 3912: 3901: 3881: 3877: 3872: 3869: 3863: 3853: 3850: 3847: 3843: 3840: 3837: 3833: 3826: 3825: 3824: 3822: 3818: 3815:(SHE). For a 3814: 3792: 3769: 3765: 3754: 3736: 3732: 3722: 3718: 3700: 3696: 3685: 3675: 3673: 3651: 3628: 3619: 3610: 3605: 3603: 3599: 3580: 3577: 3567: 3558: 3554: 3550: 3546: 3542: 3538: 3519: 3516: 3506: 3495: 3485: 3481: 3464: 3461: 3451: 3442: 3438: 3419: 3416: 3406: 3383: 3380: 3376: 3353: 3350: 3347: 3343: 3335: 3330: 3328: 3323: 3306: 3303: 3284: 3266: 3260: 3249: 3239: 3229: 3228: 3227: 3222: 3214: 3210: 3206: 3200: 3198: 3194: 3190: 3184: 3180: 3169: 3165: 3161: 3157: 3151: 3149: 3145: 3141: 3137: 3132: 3123: 3119: 3114: 3097: 3094: 3084: 3055: 3045: 3022: 3019: 3015: 3011: 3008: 2984: 2981: 2970: 2960: 2934: 2931: 2921: 2917: 2908: 2900: 2899: 2898: 2884: 2881: 2870: 2860: 2835: 2826: 2822: 2813: 2803: 2800: 2774: 2752: 2728: 2725: 2715: 2704: 2670: 2653: 2650: 2640: 2619: 2616: 2605: 2595: 2569: 2566: 2556: 2531: 2528: 2518: 2509: 2489: 2486: 2476: 2466: 2464: 2460: 2456: 2437: 2434: 2424: 2414: 2392: 2382: 2376: 2373: 2367: 2364: 2359: 2356: 2350: 2344: 2341: 2331: 2327: 2318: 2289: 2279: 2273: 2270: 2264: 2261: 2256: 2253: 2247: 2242: 2233: 2229: 2223: 2220: 2210: 2186: 2183: 2173: 2161: 2151: 2130: 2120: 2114: 2111: 2105: 2102: 2097: 2094: 2088: 2082: 2079: 2069: 2065: 2056: 2047: 2030: 2027: 2017: 1990: 1966: 1963: 1953: 1945:) is denoted 1932: 1924: 1919: 1898: 1888: 1882: 1879: 1873: 1870: 1865: 1862: 1856: 1848: 1845: 1835: 1828: 1824: 1812: 1802: 1796: 1793: 1787: 1784: 1779: 1776: 1770: 1765: 1756: 1751: 1744: 1735: 1726: 1712: 1700: 1690: 1684: 1681: 1678: 1667: 1657: 1651: 1648: 1644: 1637: 1634: 1629: 1626: 1620: 1615: 1606: 1602: 1593: 1584: 1570: 1558: 1548: 1534: 1524: 1517: 1513: 1510: 1504: 1501: 1496: 1493: 1487: 1482: 1473: 1469: 1460: 1451: 1437: 1428: 1411: 1408: 1398: 1385: 1377: 1368: 1362: 1355: 1346: 1337: 1328: 1324: 1314: 1312: 1305: 1300: 1287: 1276: 1266: 1260: 1255: 1251: 1245: 1239: 1235: 1231: 1225: 1220: 1216: 1212: 1201: 1191: 1185: 1182: 1177: 1172: 1168: 1162: 1157: 1153: 1149: 1146: 1138: 1136: 1132: 1128: 1124: 1106: 1102: 1099: 1093: 1088: 1084: 1076: 1059: 1050: 1045: 1038: 1031: 1027: 1005: 1000: 996: 989: 986: 985:half-reaction 982: 975: 972: 965: 960: J K mol 944: 939: 932: 929: 916: 912: 909: 901: 897: 894: 892: 878: 874: 871: 863: 859: 858: 857: 854: 839: 835: 831: 828: 822: 819: 814: 811: 805: 800: 791: 787: 778: 757: 746: 736: 730: 727: 721: 718: 713: 710: 704: 699: 690: 686: 681: 677: 673: 670: 664: 661: 656: 653: 647: 642: 633: 629: 620: 611: 603: 595: 589: 583: 579: 574: 567:The constant 554: 551: 548: 545: 542: 539: 536: 521: 518:and R is the 517: 509: 490: 486: 482: 479: 476: 473: 470: 465: 461: 454: 451: 432: 427: 422: 417: 390: 380: 374: 371: 364: 363: 362: 360: 355: 348: 341: 337: 328: 303: 292: 283: 272: 262: 256: 251: 247: 239: 238: 237: 235: 231: 227: 223: 222:concentration 219: 215: 211: 200: 189: 185: 181: 177: 173: 164: 136: 128: 117: 116: 115: 109: 102: 83: 81: 77: 73: 69: 65: 61: 57: 53: 49: 45: 41: 37: 33: 29: 22: 10916:. Retrieved 10914:. 2014-11-18 10911: 10853: 10849: 10843: 10824: 10815: 10805: 10799: 10780: 10773: 10754: 10747: 10731: 10727: 10714: 10702: 10691:. Retrieved 10689:. 2014-11-18 10686: 10677: 10665: 10659: 10655: 10651:gas constant 10645: 10639: 10635: 10630: 10611: 10601: 10590:. Retrieved 10586: 10576: 10566: 10565: 10553: 10549: 10543: 10532:. Retrieved 10528: 10504:. Retrieved 10500: 10491: 10480:. Retrieved 10453:(1): 29–46. 10450: 10446: 10436: 10425:. Retrieved 10421: 10411: 10402: 10384: 10380: 10374: 10347: 10341: 10253: 10235: 10205: 10197: 10172: 10160: 10144: 10018: 10011: 9833: 9830: 9821: 9814: 9802: 9789: 9778: 9763: 9760: 9679: 9600: 9597: 9450: 9351: 9268: 8923: 8920: 8752: 8742: 8736: 8732: 8728: 8722: 8716: 8702: 8696: 8690: 8686: 8679: 8668: 8658: 8647: 8639: 8625: 8611: 8601: 8592: 8579: 8380: 8108: 7969: 7960: 7957: 7785: 7630: 7619: 7597: 7586: 7578: 7574: 7558: 7551: 7485: 7472: 7468: 7459: 7455: 7445: 7436: 7433:gas constant 7427: 7418: 7408: 7208: 7203:Ox + e ⇌ Red 7192: 7184: 7172: 7164: 7153: 7028: 7025: 6937: 6695: 6689: 6685:Ox + e ⇌ Red 6679: 6239: 6236: 5902: 5891: 5864:(joules per 5823: 5800: 5794: 5399: 5388: 5366: 5214: 5208: 5205: 5167: 5143: 5130: 5108: 5104: 5074: 4945: 4823: 4816: 4750: 4738: 4720: 4707: 4624:between two 4618:electrolysis 4600: 4555: 4553: 4549: 4511:(SHE) whose 4413: 4337: 4150:as follows: 4076: 3995:is given by 3959: 3820: 3687: 3606: 3541:cell biology 3537:biochemistry 3497: 3482: 3331: 3327:voltammogram 3324: 3321: 3226:(1 mol/L): 3202: 3186: 3178: 3167: 3159: 3155: 3152: 3150:potential. 3147: 3143: 3115: 3000: 2804: 2801: 2772: 2706: 2507: 2467: 2415: 2163: 2048: 1920: 1727: 1585: 1452: 1429: 1375: 1366: 1360: 1353: 1344: 1335: 1326: 1320: 1307: 1303: 1301: 1139: 1126: 1072: 1057: 1048: 1029: 1003: 942: 914: 899: 890: 876: 861: 855: 593: 587: 581: 577: 507: 430: 420: 413: 356: 346: 339: 330: 329:, the ratio 324: 225: 183: 175: 166: 160: 107: 100: 94: 31: 25: 10734:(1): 5–16, 10219:heavy water 10208:cold fusion 10157:Limitations 9831:Therefore, 8637:reactions ( 5917:(Na) + 1.5J 4701:+ 4 H + 4 e 3557:redox scale 3207:(M) or one 1022: C mol 212:(γ) by its 78:, a German 10930:Categories 10918:2021-12-06 10693:2021-12-06 10592:2021-12-15 10534:2021-12-06 10506:2021-12-06 10482:2021-12-02 10427:2021-11-24 10333:References 8575:activities 6671:Derivation 5868:per mole), 5174:physiology 5162:See also: 4626:electrodes 4340:activities 3682:See also: 3492:See also: 3160:vice versa 3136:activities 2701:See also: 2158:See also: 1123:logarithms 86:Expression 64:activities 10870:0013-4651 10562:0002-7863 10477:0034-6691 10469:1884-7692 10212:palladium 10093:⊖ 10063:λ 10056:⊖ 10036:⁡ 9981:⊖ 9954:⁡ 9942:⊖ 9924:⁡ 9891:⁡ 9865:− 9860:⊖ 9741:⁡ 9710:⊖ 9660:⁡ 9648:− 9640:⊖ 9612:− 9581:⊖ 9553:− 9545:⊖ 9537:Δ 9512:⊖ 9467:⊖ 9459:Δ 9431:⁡ 9419:− 9411:⊖ 9403:Δ 9371:⊖ 9363:Δ 9314:⊖ 9286:⊖ 9238:⁡ 9212:− 9207:⊖ 9150:⁡ 9124:− 9119:⊖ 9062:⁡ 9036:− 9031:⊖ 8894:⁡ 8868:− 8863:⊖ 8819:⁡ 8802:⊖ 8794:Δ 8785:Δ 8779:− 8773:Δ 8764:Δ 8478:≈ 8464:ν 8444:∏ 8430:ν 8410:∏ 8284:⁡ 8275:− 8270:⊖ 8249:Δ 8192:− 8117:Δ 8070:⊖ 8031:⁡ 8022:− 8006:⊖ 7917:⁡ 7908:− 7838:⁡ 7829:− 7813:− 7794:Δ 7763:× 7728:⁡ 7719:− 7707:× 7672:⁡ 7569:ideal gas 7535:Ω 7532:⁡ 7413:, and so 7344:⁡ 7323:− 7318:⊖ 7261:⁡ 7240:− 7235:⊖ 7098:⁡ 7081:⊖ 7070:μ 7055:μ 6970:⁡ 6947:μ 6895:μ 6885:⁡ 6839:− 6831:⁡ 6796:− 6788:⁡ 6625:− 6603:− 6449:− 6427:− 6278:⁡ 5968:⁡ 5749:− 5725:− 5694:∑ 5614:∑ 5590:− 5566:− 5535:∑ 5452:∑ 5440:⁡ 5320:⁡ 5251:⁡ 5024:⊖ 4981:− 4895:⊖ 4852:− 4790:− 4785:⊖ 4614:–pH plot) 4597:consumed. 4377:− 4301:− 4218:⁡ 4202:− 4197:⊖ 4093:⊖ 4085:Δ 4049:⊖ 4041:Δ 4035:− 4016:⊖ 3981:⊖ 3920:⇀ 3913:− 3902:− 3895:↽ 3882:− 3817:half cell 3629:⊖ 3578:⊖ 3517:⊖ 3462:⊖ 3417:⊖ 3377:γ 3344:γ 3095:⊖ 3056:γ 3046:γ 3012:⁡ 2932:⊖ 2836:⊖ 2802:Indeed: 2726:⊖ 2651:⊖ 2567:⊖ 2529:⊖ 2487:⊖ 2435:⊖ 2377:⁡ 2351:− 2342:⊖ 2290:γ 2280:γ 2274:⁡ 2248:− 2243:⊖ 2221:⊖ 2184:⊖ 2115:⁡ 2089:− 2080:⊖ 2028:⊖ 1964:⊖ 1933:γ 1883:⁡ 1857:− 1846:⊖ 1829:⏟ 1813:γ 1803:γ 1797:⁡ 1771:− 1766:⊖ 1685:⁡ 1668:γ 1658:γ 1652:⁡ 1621:− 1616:⊖ 1535:γ 1525:γ 1514:⁡ 1488:− 1483:⊖ 1438:γ 1409:⊖ 1261:⁡ 1232:λ 1226:− 1221:⊖ 1186:⁡ 1163:− 1158:⊖ 981:electrons 832:⁡ 806:− 801:⊖ 731:⁡ 705:− 700:⊖ 674:⁡ 648:− 643:⊖ 543:− 534:Δ 483:⁡ 466:⊖ 458:Δ 449:Δ 188:reductant 142:⟶ 137:− 72:oxidation 48:full cell 44:half-cell 10823:(1993). 10529:PalmSens 10366:19124885 10261:See also 10149:and the 10113:at 9317:′ 8748:enthalpy 8740:, where 8694:, where 7422:and the 5909:(Na) + J 5006:because 4950:into 2 H 4654:–pH plot 4630:hydrogen 4111:change, 3581:′ 3520:′ 3465:′ 3420:′ 3221:molarity 3179:de facto 3124:(mol/kg 3098:′ 3001:because 2935:′ 2729:′ 2654:′ 2570:′ 2532:′ 2490:′ 2438:′ 2345:′ 2224:′ 2187:′ 2083:′ 2031:′ 1967:′ 1849:′ 1427:used. 1412:′ 1373:, where 1044:activity 995:coulombs 891:standard 610:electron 591:, where 10215:cathode 10104: V 10100:0.05916 8930:e → Red 8746:is the 8706:is the 8676:change 8663:⁠ 8644:⁠ 8629:is the 7638:⁠ 7616:⁠ 7605:⁠ 7583:⁠ 7567:for an 7481:entropy 7197:⁠ 7181:⁠ 7177:⁠ 7161:⁠ 7044:⁠ 7038:⁠ 6718:⁠ 6712:⁠ 5884:is the 5876:kelvins 5860:is the 5817:coulomb 5168:Beside 5148:⁄ 5128: 5121: 5113:⁄ 4984:0.05916 4855:0.05916 4793:0.05916 4736: 4729: 4718: 4711: 4697:O ⇌ O 4634:cathode 4380:0.05916 4307:0.05916 4207:0.05916 4119:is the 3674:(SHE). 3195:is one 2950:, when 2850:, when 2796:⁠ 2778:⁠ 2775:, when 2694:⁠ 2676:⁠ 1382:is the 971:kelvins 936:is the 926:is the 888:is the 856:where: 600:is the 514:is the 199:oxidant 105: 10868: 10831: 10788: 10762: 10669:; see 10649:; see 10618: 10560: 10475: 10467: 10364: 10354: 10244:, the 10126: 10123:298.15 10012:Or at 9781:) = 0 9772:, the 9273:(STP) 8057:where 7731: 7675: 7552:where 7523: 7496: 7479:. The 5866:kelvin 5813:joules 5795:where 5287:2.3026 4987: 4858: 4796: 4638:oxygen 4445:into H 4334: 4077:where 3624:red H+ 3439:, and 3213:formal 3197:formal 3148:formal 3144:formal 1302:where 997:) per 505:where 62:, and 30:, the 10567:Quote 10465:eISSN 10238:redox 9768:, or 9601:So, 8926:Ox + 8635:redox 5840:moles 5809:volts 5180:of a 4978:1.229 4741:with 4727:and 4 4723:for H 4642:anode 3755:plot) 3598:redox 3209:molal 3205:molar 3122:molal 3118:molar 947:8.314 571:(the 218:molal 214:molar 34:is a 10866:ISSN 10829:ISBN 10786:ISBN 10760:ISBN 10616:ISBN 10558:ISSN 10473:ISSN 10362:OCLC 10352:ISBN 9809:): 8750:and 8102:Y + 8098:B → 8094:A + 7466:and 7440:and 7411:mole 5927:pump 5925:= −J 5923:e.c. 5919:e.c. 5915:e.c. 5911:e.c. 5907:e.c. 5815:per 5105:i.e. 4556:i.e. 4025:volt 3821:i.e. 3715:and 3688:The 3539:and 3368:and 3332:The 3168:i.e. 3156:i.e. 2805:as, 2773:i.e. 2508:i.e. 1327:i.e. 1127:i.e. 1020:0184 1012:.332 999:mole 921:cell 903:cell 796:cell 783:cell 604:and 161:The 10858:doi 10854:136 10736:doi 10455:doi 10027:log 9764:At 9526:): 8932:, 8691:zFE 8689:= − 8666:). 7581:ln( 7036:at 7034:≠ 0 7026:If 6882:exp 6828:exp 6785:exp 5835:out 5827:ion 5311:log 5186:ion 5088:red 5057:red 5019:red 4970:red 4928:red 4890:red 4844:red 4780:red 4767:red 4693:2 H 4590:SHE 4540:gas 4524:red 4466:red 4427:red 4355:red 4215:log 4192:red 4179:red 4011:red 3976:red 3797:red 3656:red 3572:red 3511:red 3456:red 3411:red 3278:red 3244:red 3219:in 3174:gas 3113:. 3089:red 3050:red 2965:red 2926:red 2913:red 2897:, 2865:red 2831:red 2818:red 2783:red 2757:red 2720:red 2697:= 1 2681:red 2645:red 2600:red 2561:red 2523:red 2481:red 2429:red 2387:Red 2336:red 2323:red 2284:Red 2238:red 2215:red 2178:red 2125:Red 2074:red 2061:red 2022:red 1995:red 1958:red 1893:Red 1840:red 1807:Red 1761:red 1740:red 1695:Red 1662:Red 1611:red 1598:red 1553:Red 1529:Red 1478:red 1465:red 1403:red 1271:Red 1252:log 1196:Red 1052:Red 1017:310 1014:123 1010:485 955:153 952:618 949:462 883:red 865:red 741:Red 695:red 638:red 625:red 385:Red 343:Red 325:At 293:Red 267:Red 194:Red 176:IAP 145:Red 112:Red 46:or 26:In 10932:: 10910:. 10864:. 10852:. 10732:12 10685:. 10658:= 10638:= 10610:. 10585:. 10564:. 10554:71 10552:. 10527:. 10515:^ 10499:. 10471:. 10463:. 10451:48 10449:. 10445:. 10420:. 10393:^ 10385:96 10383:. 10360:. 10175:±∞ 10031:10 10016:, 9951:ln 9921:ln 9888:ln 9825:eq 9820:= 9806:eq 9738:ln 9657:ln 9483:zF 9428:ln 9342:pH 9340:, 9235:ln 9147:ln 9059:ln 8891:ln 8816:ln 8737:TS 8735:− 8731:= 8642:= 8590:, 8577:, 8385:: 8281:ln 8028:ln 7914:ln 7835:ln 7725:ln 7669:ln 7579:nR 7577:= 7529:ln 7473:eN 7471:= 7460:kN 7458:= 7453:: 7341:ln 7258:ln 7206:: 7179:= 7095:ln 6967:ln 6275:ln 5965:ln 5851:in 5844:SI 5819:), 5437:ln 5315:10 5248:ln 5192:. 4734:/4 4716:/2 4709:(2 4610:(E 4594:pH 4453:. 4321:pH 3757:. 3753:pH 3751:– 3717:pH 3549:pH 3443:, 3441:pH 3296:ox 3254:ox 3199:". 3060:ox 3009:ln 2975:ox 2875:ox 2792:ox 2690:ox 2610:ox 2465:. 2457:, 2455:pH 2397:Ox 2374:ln 2294:Ox 2271:ln 2135:Ox 2112:ln 1903:Ox 1880:ln 1817:Ox 1794:ln 1705:Ox 1682:ln 1672:Ox 1649:ln 1563:Ox 1539:Ox 1511:ln 1359:= 1333:, 1308:λV 1281:Ox 1256:10 1206:Ox 1183:ln 1129:, 1061:Ox 1008:96 1006:= 958:24 945:= 940:: 829:ln 751:Ox 728:ln 671:ln 580:= 480:ln 395:Ox 350:Ox 304:Ox 277:Ox 205:Ox 201:, 190:, 133:ze 126:Ox 97:Ox 54:, 10921:. 10872:. 10860:: 10837:. 10738:: 10696:. 10666:e 10663:A 10660:N 10656:F 10646:k 10643:A 10640:N 10636:R 10624:. 10595:. 10537:. 10509:. 10485:. 10457:: 10430:. 10368:. 10254:K 10130:K 10120:= 10117:T 10089:E 10085:z 10079:= 10071:T 10067:V 10052:E 10048:z 10042:= 10039:K 9991:T 9988:R 9977:E 9973:F 9970:z 9964:= 9957:K 9938:E 9934:= 9927:K 9915:F 9912:z 9907:T 9904:R 9894:K 9882:F 9879:z 9874:T 9871:R 9856:E 9852:= 9845:0 9822:K 9817:r 9815:Q 9803:K 9800:( 9792:r 9790:Q 9787:( 9779:E 9777:( 9745:K 9732:F 9729:z 9724:T 9721:R 9715:= 9705:l 9702:l 9699:e 9696:c 9692:E 9664:K 9654:T 9651:R 9645:= 9635:l 9632:l 9629:e 9626:c 9622:E 9618:F 9615:z 9576:l 9573:l 9570:e 9567:c 9563:E 9559:F 9556:z 9550:= 9541:G 9507:l 9504:l 9501:e 9498:c 9494:E 9463:G 9435:K 9425:T 9422:R 9416:= 9407:G 9390:K 9367:G 9309:E 9282:E 9251:. 9246:r 9242:Q 9229:F 9226:z 9221:T 9218:R 9203:E 9199:= 9186:] 9182:x 9179:O 9175:[ 9170:] 9166:d 9163:e 9160:R 9156:[ 9141:F 9138:z 9133:T 9130:R 9115:E 9111:= 9098:] 9094:x 9091:O 9087:[ 9082:] 9078:d 9075:e 9072:R 9068:[ 9053:e 9050:z 9045:T 9042:k 9027:E 9023:= 9016:E 8992:, 8986:] 8982:x 8979:O 8975:[ 8970:] 8966:d 8963:e 8960:R 8956:[ 8950:= 8945:r 8941:Q 8928:z 8907:. 8902:r 8898:Q 8885:e 8882:z 8877:T 8874:k 8859:E 8855:= 8852:E 8832:, 8827:r 8823:Q 8813:T 8810:k 8807:+ 8798:G 8791:= 8788:S 8782:T 8776:H 8770:= 8767:G 8753:T 8743:H 8733:H 8729:G 8723:E 8717:G 8715:Δ 8703:F 8697:n 8687:G 8685:Δ 8680:G 8678:Δ 8669:E 8659:e 8655:/ 8651:c 8648:μ 8640:E 8626:E 8617:j 8612:a 8602:t 8595:j 8593:ν 8582:j 8580:a 8561:, 8553:b 8549:] 8544:B 8540:[ 8535:a 8531:] 8526:A 8522:[ 8515:y 8511:] 8506:Y 8502:[ 8497:z 8493:] 8488:Z 8484:[ 8468:i 8458:i 8454:a 8448:i 8434:j 8424:j 8420:a 8414:j 8403:= 8398:r 8394:Q 8367:. 8359:b 8355:] 8350:B 8346:[ 8341:a 8337:] 8332:A 8328:[ 8321:z 8317:] 8312:Z 8308:[ 8303:y 8299:] 8294:Y 8290:[ 8278:k 8264:n 8261:x 8258:r 8253:S 8246:= 8241:) 8236:) 8232:B 8228:( 8225:S 8222:b 8219:+ 8216:) 8212:A 8208:( 8205:S 8202:a 8197:( 8187:) 8182:) 8178:Z 8174:( 8171:S 8168:z 8165:+ 8162:) 8158:Y 8154:( 8151:S 8148:y 8143:( 8138:= 8132:n 8129:x 8126:r 8121:S 8106:Z 8104:z 8100:y 8096:b 8092:a 8066:S 8045:, 8042:] 8038:A 8034:[ 8025:k 8019:) 8015:A 8011:( 8002:S 7998:= 7995:) 7991:A 7987:( 7984:S 7973:2 7970:c 7964:1 7961:c 7944:. 7937:1 7933:c 7927:2 7923:c 7911:k 7903:1 7899:S 7895:= 7890:2 7886:S 7865:, 7858:1 7854:c 7848:2 7844:c 7832:k 7826:= 7821:1 7817:S 7808:2 7804:S 7800:= 7797:S 7772:. 7769:) 7766:c 7759:t 7756:n 7753:a 7750:t 7747:s 7744:n 7741:o 7738:c 7734:( 7722:k 7716:= 7713:) 7710:V 7703:t 7700:n 7697:a 7694:t 7691:s 7688:n 7685:o 7682:c 7678:( 7666:k 7663:= 7660:S 7650:c 7634:1 7631:V 7627:/ 7623:2 7620:V 7611:n 7607:) 7601:1 7598:V 7594:/ 7590:2 7587:V 7575:S 7573:Δ 7559:V 7554:Ω 7538:, 7526:k 7515:f 7512:e 7509:d 7503:= 7493:S 7476:A 7469:F 7463:A 7456:R 7446:F 7437:R 7428:e 7419:k 7386:. 7380:] 7376:x 7373:O 7369:[ 7364:] 7360:d 7357:e 7354:R 7350:[ 7336:F 7332:T 7329:R 7314:E 7310:= 7297:] 7293:x 7290:O 7286:[ 7281:] 7277:d 7274:e 7271:R 7267:[ 7253:e 7249:T 7246:k 7231:E 7227:= 7220:E 7193:F 7189:/ 7185:R 7173:e 7169:/ 7165:k 7156:e 7140:. 7134:] 7130:x 7127:O 7123:[ 7118:] 7114:d 7111:e 7108:R 7104:[ 7092:T 7089:k 7086:+ 7075:c 7066:= 7060:c 7041:/ 7032:c 7029:μ 7012:. 7006:] 7002:x 6999:O 6995:[ 6990:] 6986:d 6983:e 6980:R 6976:[ 6964:T 6961:k 6958:= 6952:c 6920:. 6916:) 6910:T 6907:k 6900:c 6889:( 6879:= 6865:) 6861:T 6858:k 6854:/ 6850:] 6842:[ 6835:( 6822:) 6818:T 6815:k 6811:/ 6807:] 6799:[ 6792:( 6779:= 6769:] 6765:x 6762:O 6758:[ 6753:] 6749:d 6746:e 6743:R 6739:[ 6715:/ 6699:c 6696:μ 6656:. 6651:) 6642:t 6639:u 6636:o 6630:] 6620:l 6617:C 6612:[ 6598:l 6595:C 6589:P 6585:+ 6579:n 6576:i 6570:] 6565:+ 6560:a 6557:N 6552:[ 6543:+ 6538:a 6535:N 6529:P 6525:+ 6519:n 6516:i 6510:] 6505:+ 6500:K 6495:[ 6486:+ 6481:K 6475:P 6471:r 6463:n 6460:i 6454:] 6444:l 6441:C 6436:[ 6422:l 6419:C 6413:P 6409:+ 6403:t 6400:u 6397:o 6391:] 6386:+ 6381:a 6378:N 6373:[ 6364:+ 6359:a 6356:N 6350:P 6346:+ 6340:t 6337:u 6334:o 6328:] 6323:+ 6318:K 6313:[ 6304:+ 6299:K 6293:P 6289:r 6283:( 6270:F 6266:T 6263:R 6257:= 6252:m 6248:E 6223:. 6218:) 6209:n 6206:i 6200:] 6195:+ 6190:a 6187:N 6182:[ 6173:+ 6168:a 6165:N 6159:P 6155:+ 6149:n 6146:i 6140:] 6135:+ 6130:K 6125:[ 6116:+ 6111:K 6105:P 6101:r 6093:t 6090:u 6087:o 6081:] 6076:+ 6071:a 6068:N 6063:[ 6054:+ 6049:a 6046:N 6040:P 6036:+ 6030:t 6027:u 6024:o 6018:] 6013:+ 6008:K 6003:[ 5994:+ 5989:K 5983:P 5979:r 5973:( 5960:F 5956:T 5953:R 5947:= 5942:m 5938:E 5905:J 5895:r 5882:F 5878:, 5872:T 5858:R 5824:P 5804:m 5801:E 5781:, 5776:) 5766:t 5763:u 5760:o 5754:] 5744:j 5739:A 5734:[ 5720:j 5715:A 5709:P 5703:M 5698:j 5689:+ 5683:n 5680:i 5674:] 5669:+ 5664:i 5659:M 5654:[ 5645:+ 5640:i 5635:M 5629:P 5623:N 5618:i 5604:n 5601:i 5595:] 5585:j 5580:A 5575:[ 5561:j 5556:A 5550:P 5544:M 5539:j 5530:+ 5524:t 5521:u 5518:o 5512:] 5507:+ 5502:i 5497:M 5492:[ 5483:+ 5478:i 5473:M 5467:P 5461:N 5456:i 5445:( 5432:F 5428:T 5425:R 5419:= 5413:m 5408:E 5353:. 5347:] 5339:[ 5334:] 5326:[ 5304:F 5301:z 5296:T 5293:R 5284:= 5278:] 5270:[ 5265:] 5257:[ 5242:F 5239:z 5234:T 5231:R 5225:= 5222:E 5209:z 5150:z 5146:h 5140:h 5138:E 5131:e 5124:H 5115:z 5111:h 5084:E 5053:E 5015:E 4993:H 4990:p 4975:= 4966:E 4952:2 4948:2 4924:E 4886:E 4864:H 4861:p 4849:= 4840:E 4826:2 4802:H 4799:p 4776:E 4772:= 4763:E 4745:2 4743:O 4739:e 4732:H 4725:2 4721:e 4714:H 4699:2 4695:2 4686:: 4684:h 4673:2 4664:: 4662:h 4652:h 4650:E 4646:2 4612:h 4520:E 4493:h 4489:E 4462:E 4451:2 4447:2 4443:2 4423:E 4398:) 4393:z 4390:h 4385:( 4351:E 4315:z 4311:h 4297:) 4289:b 4285:} 4281:B 4278:{ 4273:a 4269:} 4265:A 4262:{ 4255:d 4251:} 4247:D 4244:{ 4239:c 4235:} 4231:C 4228:{ 4222:( 4210:z 4188:E 4184:= 4175:E 4171:= 4166:h 4162:E 4136:h 4132:E 4117:F 4113:z 4089:G 4059:F 4056:z 4045:G 4032:= 4029:) 4021:( 4007:E 3972:E 3945:D 3941:d 3938:+ 3935:C 3931:c 3878:e 3873:z 3870:+ 3864:+ 3860:H 3854:h 3851:+ 3848:B 3844:b 3841:+ 3838:A 3834:a 3793:E 3770:h 3766:E 3737:h 3733:E 3724:( 3701:h 3697:E 3652:E 3620:E 3568:E 3507:E 3452:E 3407:E 3384:x 3381:o 3354:d 3351:e 3348:r 3307:1 3304:= 3291:M 3285:1 3273:M 3267:1 3261:= 3250:C 3240:C 3224:M 3217:C 3172:P 3166:( 3131:O 3129:2 3127:H 3085:E 3023:0 3020:= 3016:1 2997:, 2985:1 2982:= 2971:C 2961:C 2922:E 2918:= 2909:E 2885:1 2882:= 2871:a 2861:a 2827:E 2823:= 2814:E 2790:C 2787:/ 2781:C 2753:E 2716:E 2688:C 2685:/ 2679:C 2641:E 2620:1 2617:= 2606:C 2596:C 2557:E 2519:E 2477:E 2425:E 2393:C 2383:C 2368:F 2365:z 2360:T 2357:R 2332:E 2328:= 2319:E 2265:F 2262:z 2257:T 2254:R 2234:E 2230:= 2211:E 2174:E 2165:( 2131:C 2121:C 2106:F 2103:z 2098:T 2095:R 2070:E 2066:= 2057:E 2018:E 1991:E 1954:E 1925:( 1899:C 1889:C 1874:F 1871:z 1866:T 1863:R 1836:E 1825:) 1788:F 1785:z 1780:T 1777:R 1757:E 1752:( 1745:= 1736:E 1713:) 1701:C 1691:C 1679:+ 1645:( 1638:F 1635:z 1630:T 1627:R 1607:E 1603:= 1594:E 1571:) 1559:C 1549:C 1518:( 1505:F 1502:z 1497:T 1494:R 1474:E 1470:= 1461:E 1399:E 1388:i 1379:i 1376:γ 1370:i 1367:C 1364:i 1361:γ 1357:i 1354:a 1348:i 1345:C 1339:i 1336:a 1331:i 1310:T 1304:λ 1288:. 1277:a 1267:a 1246:z 1240:T 1236:V 1217:E 1213:= 1202:a 1192:a 1178:z 1173:T 1169:V 1154:E 1150:= 1147:E 1125:( 1107:F 1103:T 1100:R 1094:= 1089:T 1085:V 1058:a 1049:a 1040:a 1033:r 1030:Q 1025:, 1004:F 991:F 987:, 977:z 973:, 967:T 963:, 943:R 934:R 930:, 915:E 900:E 895:, 877:E 862:E 840:r 836:Q 823:F 820:z 815:T 812:R 792:E 788:= 779:E 758:. 747:a 737:a 722:F 719:z 714:T 711:R 691:E 687:= 682:r 678:Q 665:F 662:z 657:T 654:R 634:E 630:= 621:E 606:q 597:A 594:N 588:q 585:A 582:N 578:F 569:F 555:. 552:E 549:F 546:z 540:= 537:G 524:E 511:r 508:Q 491:r 487:Q 477:T 474:R 471:+ 462:G 455:= 452:G 431:G 429:Δ 421:G 419:Δ 391:a 381:a 375:= 372:K 358:K 347:a 340:a 334:r 332:Q 307:] 301:[ 296:] 290:[ 284:= 273:a 263:a 257:= 252:r 248:Q 226:C 203:a 192:a 184:a 182:( 170:r 168:Q 165:( 129:+ 108:e 101:z 23:.

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Index