8097:
8054:
2021:
1081:
20:
92:
8014:
7994:
7974:
1431:
8074:
8034:
2016:{\displaystyle K={\frac {\{C\}^{c}\{D\}^{d}}{\{A\}^{a}\{B\}^{b}\{{\ce {H+}}\}^{h}}}={\frac {(\gamma _{c})^{c}\left^{c}\ (\gamma _{d})^{d}\left^{d}}{(\gamma _{a})^{a}\left^{a}\ (\gamma _{b})^{b}\left^{b}\ (\gamma _{h+})^{h}\left^{h}}}={\frac {(\gamma _{c})^{c}(\gamma _{d})^{d}}{(\gamma _{a})^{a}(\gamma _{b})^{b}(\gamma _{h})^{h}}}{\text{×}}{\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}\left^{h}}}}
6932:, above the top line the out of equilibrium condition involves oxygen gas production, and oxygen will bubble off of the electrode until equilibrium is reached, or water totally consumed. Likewise, below the bottom line, the out of equilibrium condition involves hydrogen gas production, and hydrogen will bubble off of the electrode until equilibrium is reached, or water totally consumed.
6913:
3387:
2860:
2605:
6936:
In many cases, the possible conditions in a system are limited by the stability region of water. In the
Pourbaix diagram for uranium presented here above, the limits of stability of water are marked by the two dashed green lines, and the stability region for water falls between these two lines. It is
67:
or kinetic effects. Beside potential and pH, the equilibrium concentrations are also dependent upon, e.g., temperature, pressure, and concentration. Pourbaix diagrams are commonly given at room temperature, atmospheric pressure, and molar concentrations of 10 and changing any of these parameters will
1027:
In order to draw the position of the lines with the Nernst equation, the activity of the chemical species at equilibrium must be defined. Usually, the activity of a species is approximated as equal to the concentration (for soluble species) or partial pressure (for gases). The same values should be
6176:
7961:
values in environmental chemistry ranges from −12 to +25, since at low or high potentials water will be respectively reduced or oxidized. In environmental applications, the concentration of dissolved species is usually set to a value between 10 M and 10 M for the determination of the
4549:
4075:
6658:
4701:
5406:
1055:
A simplified
Pourbaix diagram indicates regions of "immunity", "corrosion" and "passivity", instead of the stable species. They thus give a guide to the stability of a particular metal in a specific environment. Immunity means that the metal is not attacked, while
4865:
5239:
3907:
3203:
2684:
1018:
6823:
2411:
5061:
59:) of an aqueous electrochemical system. Boundaries (50 %/50 %) between the predominant chemical species (aqueous ions in solution, or solid phases) are represented by lines. As such a Pourbaix diagram can be read much like a standard
7804:
1023:
The lines in the
Pourbaix diagram show the equilibrium conditions, that is, where the activities are equal, for the species on each side of that line. On either side of the line, one form of the species will instead be said to be predominant.
1108:) has a great effect upon the diagram for uranium. (See diagrams at right). The presence of trace amounts of certain species such as chloride ions can also greatly affect the stability of certain species by destroying passivating layers.
644:
5748:
2327:
784:
4287:
6402:
5987:
1416:
492:
7620:
at standard temperature and pressure. Above this line, water is oxidized to form oxygen gas, and it will usually not be possible to pass beyond this line as long as there is still water present in the system to be oxidized.
5998:
3543:
3738:
4357:
6895:
3918:
6456:
7562:
5554:
4349:
345:
7479:
7132:
7615:
7209:
4573:
7372:
2077:
Activities correspond to thermodynamic concentrations and take into account the electrostatic interactions between ions present in solution. When the concentrations are not too high, the activity (
5250:
2932:
5838:
7256:
7025:
4722:
262:
6444:
5088:
888:
4922:
3597:
3382:{\displaystyle E_{h}=E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {0.05916}{z}}\log \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)-{\frac {0.05916\,h}{z}}{\text{pH}}}
2855:{\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}}}
2248:
840:
2210:
7852:
3749:
5786:
2360:
7261:
Below this line, water is reduced to hydrogen, and it will usually not be possible to pass beyond this line as long as there is still water present in the system to be reduced.
7624:
The two upper and lower stability lines having the same negative slope (−59 mV/pH unit), they are parallel in a
Pourbaix diagram and the reduction potential decreases with pH.
2600:{\displaystyle E_{h}=E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\log \left({\frac {\{C\}^{c}\{D\}^{d}}{\{A\}^{a}\{B\}^{b}}}\right)-{\frac {RT\,h}{zF}}{\text{pH}}}
904:
7711:
6697:
3059:
3001:
2962:
2890:
1270:
4930:
3164:
2156:
2658:
7952:
2064:
503:
5599:
3195:
3133:
3098:
3028:
2403:
2129:
2102:
1243:
1210:
1177:
5629:
1129:
Does not indicate whether passivation (in the form of oxides or hydroxides) is protective or not. Diffusion of oxygen ions through thin oxide layers are possible.
2256:
655:
4105:
1049:
In addition, changes in temperature and concentration of solvated ions in solution will shift the equilibrium lines in accordance with the Nernst equation.
6203:
5861:
1290:
1031:
For soluble species, the lines are often drawn for concentrations of 1 M or 10 M. Sometimes additional lines are drawn for other concentrations.
6171:{\displaystyle E_{h}={E^{\circ }}-{\frac {V_{T}\lambda }{z}}\left(\log \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)+h\,{\ce {pH}}\right)}
1052:
The diagrams also do not take kinetic effects into account, meaning that species shown as unstable might not react to any significant degree in practice.
353:
8530:(Report). Tsukuba, Ibaraki, Japan: National Institute of Advanced Industrial Science and Technology: Research Center for Deep Geological Environments
1143:
Usually applicable only to temperature of 25 °C (77 °F), which is assumed by default. The
Pourbaix diagrams for higher temperatures exist.
3434:
3428:/deprotonation of dissolved species. The boundary line will be a vertical line at a particular value of pH. The reaction equation may be written:
4544:{\displaystyle {\ce {pH}}=-{\frac {1}{6}}\left({\frac {\Delta G^{\circ }}{RT\lambda }}+\log \left({\frac {{\ce {}}}{{\ce {^2^3}}}}\right)\right)}
6663:
As, the activities, or the concentrations, of the solid phases and water are always taken equal to unity by convention in the definition of the
3613:
5855:
In this case, both electrons and H ions are involved and the electrode potential is a function of pH. The reaction equation may be written:
4070:{\displaystyle \Delta G^{\circ }=-RT\lambda \,\left(\log \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)+h\,{\ce {pH}}\right)}
6834:
6653:{\displaystyle E_{h}={E^{\circ }}-{\frac {V_{T}\lambda }{2}}\left(\log \left({\frac {{\ce {^2^3}}}{{\ce {}}}}\right)+6\ {\ce {pH}}\right)}
8633:
6937:
also depicted here beside by the two dashed red lines in the simplified
Pourbaix diagram restricted to the water stability region only.
1064:
occurs when the metal forms a stable coating of an oxide or other salt on its surface, the best example being the relative stability of
8331:
7154:
for a gas) at 1, the equation for the lower stability line of water in the
Pourbaix diagram at standard temperature and pressure is:
1116:
Even though
Pourbaix diagrams are useful for a metal corrosion potential estimation they have, however, some important limitations:
7503:
5439:
4696:{\displaystyle {\ce {pH}}=-{\frac {1}{6}}\left({\frac {\Delta G^{\circ }}{RT\lambda }}+\log \left({\frac {1}{^{2}}}\right)\right)}
8609:
4295:
273:
1084:
The
Pourbaix diagram for uranium in carbonate solution. The dashed green lines show the stability limits of water in the system.
7384:
5401:{\displaystyle E_{h}={E^{\circ }}-{\frac {V_{T}\lambda }{z}}\log \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)}
7037:
1088:
While such diagrams can be drawn for any chemical system, it is important to note that the addition of a metal binding agent (
8299:
8267:
7570:
7160:
8524:
7277:
6920:(STP). The vertical scale (ordinate) is the electrode potential (of a hydrogen or non-interacting electrode) relative to a
2895:
5791:
4860:{\displaystyle a\,A+b\,B+z\,e^{-}\quad {\ce {<=>}}\quad c\,C+d\,D\qquad (z>0{\text{, but without}}\ {\ce {H+}})}
7217:
5234:{\displaystyle E_{h}={E^{\circ }}-{\frac {V_{T}}{z}}\ln \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)}
8513:
8494:
8475:
6917:
2663:
169:
8642:
Public website that can generate
Pourbaix diagrams from a large database of computed material properties, hosted at
6953:
5992:
Using the expressions for the free energy in terms of potentials, the energy balance is given by a Nernst equation:
6411:
857:
8623:
8427:
Noyhouzer, Tomer; Bellemare-Alford, Daphnée; Payne, Nicholas A.; Martineau, Eric; Mauzeroll, Janine (July 2018).
7648:. Using the Pourbaix diagram correctly will help shedding light not only on the nature of the species present in
4876:
3551:
8346:
3902:{\displaystyle \Delta G^{\circ }=-RT\ln \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}\left^{h}}}\right)}
2221:
795:
2164:
1034:
If the diagram involves the equilibrium between a dissolved species and a gas, the pressure is usually set to
8603:
137:. The "H" stands for hydrogen, although other standards may be used, and they are for room temperature only.
8222:
4714:
When H and OH ions are not involved in the reaction, the boundary line is horizontal and independent of pH.
7812:
3420:
only depends on and is not affected by the electrode potential. In this case, the reaction is a classical
2216:
1013:{\displaystyle {\text{pH}}=-\log _{10}(a_{{\ce {H+}}})=\log _{10}\left({\frac {1}{a_{{\ce {H+}}}}}\right).}
8126:
7143:
6921:
6818:{\displaystyle E_{h}={E^{\circ }}-{\frac {V_{T}\lambda }{2}}\left(\log \ {\ce {^2}}+6\ {\ce {pH}}\right)}
5756:
5433:, taken as example here, considering the boundary line between Fe and Fe, the half-reaction equation is:
3031:
2335:
1273:
130:
8664:
7497:= 1.229 V for water oxidation, gives an upper stability limit of water as a function of the pH value:
5056:{\displaystyle \Delta G^{\circ }=-RT\ln \left({\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}}}\right)}
8659:
7875:
8096:
7799:{\displaystyle pe={\frac {E_{H}}{V_{T}\lambda }}={\frac {E_{H}}{0.05916}}=16.903\,{\text{×}}\,E_{H}}
3037:
2979:
2940:
2868:
1248:
1046:, the minimum pressure required for gas evolution from an aqueous solution at standard conditions.
3392:
There are three types of line boundaries in a Pourbaix diagram: Vertical, horizontal, and sloped.
8378:
8146:
3142:
2134:
1061:
8053:
4554:
Because the activities (or the concentrations) of the solid phases and water are equal to unity:
2619:
8549:
7151:
1183:
of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram
639:{\displaystyle E_{\text{H}}=E^{0}-{\frac {V_{T}\lambda }{z}}\log {\frac {^{c}^{d}}{^{a}^{b}}},}
8428:
7906:
5743:{\displaystyle E_{h}={E^{\circ }}-V_{T}\lambda \log \left({\frac {{\ce {}}}{{\ce {}}}}\right)}
1080:
7645:
2375:
2049:
8352:
8627:
8567:
6664:
5577:
3604:
3173:
3136:
3111:
3076:
3006:
2381:
2322:{\displaystyle E_{\text{red}}^{\ominus }({\text{volt}})=-{\frac {\Delta G^{\ominus }}{zF}}}
2107:
2080:
2067:
2027:
1221:
1188:
1155:
157:
141:
56:
6916:
Pourbaix diagram for water, including stability regions for water, oxygen and hydrogen at
3166:) tend to one, the term regrouping all the activity coefficients is equal to one, and the
8:
7677:
3101:
2035:
779:{\displaystyle E_{\text{H}}=E^{0}-{\frac {0.05916}{z}}\log {\frac {^{c}^{d}}{^{a}^{b}}},}
126:
8448:
7672:
Pourbaix diagrams are widely used to describe the behaviour of chemical species in the
7657:
6688:
4282:{\displaystyle {\ce {2 Fe^{3+}(aq) + 3 H_2 O (l) <=> Fe_2 O_3 (s) + 6 H^+ (aq)}}}
3421:
8555:
6397:{\displaystyle {\ce {Fe2O3(s) + 6 H+(aq) + 2 e^- <=> 2 Fe^{2+}(aq) + 3 H2O(l)}}}
5982:{\displaystyle a\,A+b\,B+h\,{\ce {H+}}+z\,e^{-}\quad {\ce {<=>}}\quad c\,C+d\,D}
1411:{\displaystyle a\,A+b\,B+h\,{\ce {H+}}+z\,e^{-}\quad {\ce {<=>}}\quad c\,C+d\,D}
8509:
8490:
8471:
8452:
8342:
8305:
8295:
8263:
8131:
8073:
8013:
7993:
7973:
4871:
4083:
For example consider the iron and water system, and the equilibrium line between the
2363:
7146:(SHE, serving as reference in the reduction potentials series) and the hydrogen gas
487:{\displaystyle E_{\text{H}}=E^{0}-{\frac {RT}{zF}}\ln {\frac {^{c}^{d}}{^{a}^{b}}},}
91:
8556:
DoITPoMS Teaching and Learning Package- "The Nernst Equation and Pourbaix Diagrams"
8440:
8200:
7887:
7649:
5079:
28:
8136:
8121:
7855:
5572:
3167:
2611:
843:
134:
96:
72:
63:
with a different set of axes. Similarly to phase diagrams, they do not allow for
5567:= 0.771 V with only one electron involved in the redox reaction. The potential E
8033:
7653:
8581:
8444:
4351:. The pH of the vertical line on the Pourbaix diagram can then be calculated:
8653:
8636:
Commercial software for thermodynamic calculations from Thermo-Calc Software.
8399:
8309:
8141:
6929:
3538:{\displaystyle a\,A+b\,B+h\,{\ce {H+}}\quad {\ce {<=>}}\quad c\,C+d\,D}
2071:
64:
60:
16:
Plot of thermodynamically stable phases of an aqueous electrochemical system
8151:
7863:
7641:
3733:{\displaystyle K={\frac {\left^{c}\left^{d}}{\left^{a}\left^{b}\left^{h}}}}
3061:= 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P
19:
8289:
8220:(2004) KTH Royal Institute of Technology, freely downloadable software at
7632:
Pourbaix diagrams have many applications in different fields dealing with
6181:
For the iron and water example, considering the boundary line between the
95:
The Pourbaix diagram for uranium in a non-complexing aqueous medium (e.g.
7673:
6182:
3425:
8593:
1147:
8426:
6450:
The equation of the boundary line, expressed in base-10 logarithms is:
23:
Pourbaix diagram of iron. The Y axis corresponds to voltage potential.
6890:{\displaystyle E_{h}={1.0826}-{0.1775}\ {pH}\quad ({\text{in volts}})}
8580:
Commercial thermodynamic databank software, also available in a free
7691:
7637:
1277:
1093:
1065:
1057:
8590:
Commercial geochemical modeling software from Aqueous Solutions LLC.
8525:
Atlas of Eh-pH diagrams (Intercomparison of thermodynamic databases)
8596:
Free download of the popular geochemical modeling software package.
8253:
8251:
8249:
8247:
8245:
8243:
7147:
6186:
4088:
3105:
2039:
1123:
The diagram does not provide information on actual corrosion rates.
8602:
Free software for creating chemical equilibrium diagrams from the
8587:
8613:
8226:
1069:
80:
8639:
8599:
8240:
8218:
Hydra/Medusa Chemical Equilibrium Database and Plotting Software
6912:
1120:
Equilibrium is always assumed, though in practice it may differ.
7879:
5601:
and directly depends on the ratio of the concentrations of the
4084:
1089:
76:
4556:= = 1, the pH only depends on the concentration in dissolved
8643:
8571:
8508:(2nd ed.). National Association of Corrosion Engineers.
7557:{\displaystyle E_{{\ce {H}}}=E^{0}-V_{T}\lambda \,{\ce {pH}}}
5560:
5549:{\displaystyle {\ce {Fe^3+ (aq) + e^- <=> Fe^2+ (aq)}}}
8619:
6928:
of the electrolyte (otherwise non-interacting). Assuming no
3065:= 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0).
2964:
at higher pH values. This is observed for the reduction of O
8577:
8262:(3rd ed.). Oxford University Press. pp. 235–248.
7663:
4344:{\displaystyle \Delta G^{\circ }=-8242.5\,\mathrm {J/mol} }
340:{\displaystyle E_{\text{H}}=E^{0}-{\frac {RT}{zF}}\ln {K},}
140:
For a reversible redox reaction described by the following
8570:
Free software for calculation of chemical equilibria from
7474:{\displaystyle {\ce {4 OH^- -> O2(g) + 2 H_2O + 4e^-}}}
6673:
The Nernst equation thus limited to the dissolved species
2131:) by a linear relationship with the activity coefficient (
1280:
equation, conventionally written as a reduction reaction (
8332:"Simplified Procedure for Constructing Pourbaix Diagrams"
7485:
Using the Nernst equation as above, but with E = −ΔG
7447:
7416:
7332:
7296:
7264:
Correspondingly, under highly oxidizing conditions (high
7127:{\displaystyle {\ce {2 H2O + 2e^- -> H2(g) + 2 OH^-}}}
7092:
7056:
7002:
6617:
6604:
6572:
6376:
6231:
6218:
5847:= 0.771 volts. The potential will vary with temperature.
4513:
4460:
4447:
4236:
4223:
4156:
51:, is a plot of possible thermodynamically stable phases (
8506:
Atlas of electrochemical equilibria in aqueous solutions
7610:{\displaystyle E_{{\ce {H}}}=1.229V-0.05916\,{\ce {pH}}}
7204:{\displaystyle E_{{\ce {H}}}=-V_{T}\lambda \,{\ce {pH}}}
5753:
For both ionic species at the same concentration (e.g.,
7698:
is a dimensionless number and can easily be related to
7367:{\displaystyle {\ce {2 H2O -> 4 H+ + O2(g) + 4e^-}}}
6925:
1213:
1180:
895:
8257:
6311:
5941:
5502:
4783:
4194:
3497:
1370:
1284:, electrons accepted by an oxidant on the left side):
7909:
7815:
7714:
7573:
7506:
7387:
7280:
7220:
7163:
7040:
6956:
6900:
Note the negative slope (-0.1775) of this line in a E
6837:
6700:
6459:
6414:
6206:
6001:
5864:
5794:
5759:
5632:
5580:
5442:
5253:
5091:
4933:
4879:
4725:
4576:
4360:
4298:
4108:
3921:
3752:
3616:
3554:
3437:
3206:
3176:
3145:
3114:
3079:
3040:
3009:
2982:
2943:
2927:{\displaystyle -0.05916\,\left({\frac {h}{z}}\right)}
2898:
2871:
2865:
This equation is the equation of a straight line for
2687:
2622:
2414:
2384:
2338:
2259:
2224:
2167:
2137:
2110:
2083:
2052:
1434:
1293:
1251:
1224:
1191:
1158:
1148:
Expression of the Nernst equation as a function of pH
907:
860:
798:
658:
506:
356:
276:
172:
8622:
Free program for making geochemical plots using the
8612:
Commercial thermochemical calculation software from
5833:{\displaystyle E_{h}=E^{\circ }=0.771\,\mathrm {V} }
4080:
which may be solved for the particular value of pH.
3068:
649:or, more simply directly expressed numerically as:
8429:"Unfolding the Hidden Reactions in Galvanic Cells"
7954:, an expression with a similar form to that of pH.
7946:
7846:
7798:
7609:
7556:
7473:
7366:
7271:) water is oxidized into oxygen gas according to:
7251:{\displaystyle E_{{\ce {H}}}=-0.05916\,{\ce {pH}}}
7250:
7203:
7126:
7019:
6924:electrode, the horizontal scale (abscissa) is the
6889:
6817:
6652:
6438:
6396:
6170:
5981:
5832:
5780:
5742:
5593:
5548:
5400:
5233:
5055:
4916:
4859:
4695:
4543:
4343:
4281:
4069:
3901:
3732:
3591:
3537:
3381:
3189:
3158:
3135:) at sufficiently diluted concentrations when the
3127:
3092:
3053:
3022:
2995:
2956:
2926:
2884:
2854:
2652:
2599:
2397:
2354:
2321:
2242:
2204:
2150:
2123:
2104:) can be related to the measurable concentration (
2096:
2058:
2015:
1410:
1264:
1237:
1204:
1171:
1012:
882:
834:
778:
638:
486:
339:
256:
110:-pH diagrams due to the labeling of the two axes.
8223:"KTH - Chemistry / Chemical Equilibrium Software"
6319:
6318:
6301:
6300:
5949:
5948:
5931:
5930:
5510:
5509:
5492:
5491:
4791:
4790:
4773:
4772:
4202:
4201:
4184:
4183:
3505:
3504:
3487:
3486:
1378:
1377:
1360:
1359:
1072:layer formed on its surface when exposed to air.
8651:
7690:. The main advantage is to directly work with a
6907:
5840:, and the boundary will be a horizontal line at
5066:Using the definition of the electrode potential
8489:(2nd ed.). Prentice Hall. pp. 50–52.
7020:{\displaystyle {\ce {2 H+ + 2e^- -> H2(g)}}}
3170:can be written simply with the concentrations (
1092:) will often modify the diagram. For instance,
257:{\displaystyle K={\frac {^{c}^{d}}{^{a}^{b}}},}
8260:Environmental Chemistry – a global perspective
6947:), water is reduced to hydrogen according to:
5082:, this may be rewritten as a Nernst equation:
2662:is used, which has a value of 0.02569... V at
1075:
31:, and more generally in solution chemistry, a
898:for the −log function of the H ion activity.
846:or the "Nernst slope" at standard temperature
6439:{\displaystyle E^{\circ }=0.728\mathrm {V} }
2812:
2805:
2796:
2789:
2778:
2771:
2762:
2755:
2549:
2542:
2533:
2526:
2515:
2508:
2499:
2492:
1526:
1510:
1501:
1494:
1485:
1478:
1467:
1460:
1451:
1444:
1028:used for all species present in the system.
883:{\displaystyle V_{T}\lambda \approx 0.05916}
8170:Though it can be expanded and calculated.
4709:
8370:
8287:
4917:{\displaystyle \Delta G^{\circ }=-RT\ln K}
4706:At STP, for = 10, this yields pH = 1.76.
3592:{\displaystyle \Delta G^{\circ }=-RT\ln K}
8407:Geological Survey Water-Supply Paper 1459
7785:
7779:
7601:
7548:
7459:
7436:
7392:
7352:
7308:
7285:
7242:
7195:
7112:
7068:
7045:
6978:
6961:
6779:
6541:
6365:
6342:
6333:
6279:
6251:
6157:
5975:
5965:
5907:
5888:
5878:
5868:
5824:
5723:
5699:
4817:
4807:
4749:
4739:
4729:
4664:
4482:
4321:
4256:
4145:
4122:
4113:
4056:
3950:
3531:
3521:
3461:
3451:
3441:
3395:
3364:
2905:
2837:
2577:
2370:is the number of electrons involved, and
2243:{\displaystyle E_{\text{red}}^{\ominus }}
2191:
1404:
1394:
1336:
1317:
1307:
1297:
835:{\displaystyle V_{T}=RT/F\approx 0.02569}
8503:
8465:
8325:
8323:
8321:
8319:
8212:
8210:
6911:
2205:{\displaystyle a_{i}=\gamma _{i}\,C_{i}}
1079:
90:
18:
8376:
8258:van Loon, Gary; Duffy, Stephen (2011).
8127:Dependency of reduction potential on pH
7142:= 0 V as defined by convention for the
6294:
5924:
5850:
5559:Since H ions are not involved in this
5485:
4766:
4716:The reaction equation is thus written:
4177:
3480:
2972:O, or OH, and for reduction of H into H
2610:In the following, the Nernst slope (or
1353:
8652:
8522:
8487:Principles and Prevention of Corrosion
8392:
8329:
8179:This is possible to estimate though.
7656:, but may also help to understand the
6940:Under highly reducing conditions (low
2074:coefficients are shown as exponents.
1060:shows that general attack will occur.
8484:
8316:
8207:
7847:{\displaystyle V_{T}={\frac {RT}{F}}}
5571:is a function of temperature via the
3548:and the energy balance is written as
2666:. When base-10 logarithms are used,
2378:. The Nernst equation relates pH and
2026:where curly braces { } indicate
1132:Excludes corrosion by chloride ions (
8400:"Chemistry of Iron in Natural Water"
8283:
8281:
8279:
5563:reaction, it is independent of pH.
3197:) denoted here with square braces :
3100:) can be considered as equal to the
2892:as a function of pH with a slope of
854: = ln(10) ≈ 2.30, so that
103:Pourbaix diagrams are also known as
7138:Using the Nernst equation, setting
5781:{\displaystyle 10^{-6}\mathrm {M} }
2355:{\displaystyle \Delta G^{\ominus }}
13:
6432:
5826:
5774:
4934:
4880:
4606:
4390:
4337:
4334:
4331:
4323:
4299:
3922:
3753:
3555:
3030:to indicate that it refers to the
2339:
2295:
14:
8676:
8543:
8291:Introduction to corrosion science
8276:
7897:). Lambda, λ = ln(10) ≈ 2.3026.
6918:standard temperature and pressure
3400:When no electrons are exchanged (
3069:Calculation of a Pourbaix diagram
8095:
8072:
8052:
8032:
8012:
7992:
7972:
7882:(298.15 K = 25 °C = 77 °F), and
1425:of this reduction reaction is:
8468:Eh-pH Diagrams for Geochemistry
8420:
7627:
6875:
5961:
5918:
4821:
4803:
4760:
3517:
3474:
1390:
1347:
894:The horizontal axis is labeled
8341:. John Wiley & Sons, Inc.
8337:. In Revie, R. Winston (ed.).
8193:
8173:
8164:
7941:
7928:
7426:
7420:
7403:
7342:
7336:
7302:
7102:
7096:
7079:
7012:
7006:
6989:
6884:
6876:
6785:
6768:
6620:
6591:
6578:
6559:
6547:
6530:
6389:
6383:
6355:
6349:
6321:
6296:
6269:
6263:
6241:
6235:
5951:
5926:
5729:
5712:
5705:
5688:
5541:
5535:
5512:
5487:
5464:
5458:
5244:or, using base-10 logarithms:
4854:
4822:
4793:
4768:
4672:
4652:
4519:
4500:
4488:
4471:
4463:
4434:
4274:
4268:
4246:
4240:
4204:
4179:
4169:
4163:
4135:
4129:
3507:
3482:
3404:= 0), the equilibrium between
3054:{\displaystyle E_{\text{red}}}
2996:{\displaystyle E_{\text{red}}}
2957:{\displaystyle E_{\text{red}}}
2885:{\displaystyle E_{\text{red}}}
2283:
2275:
1889:
1875:
1866:
1852:
1843:
1829:
1818:
1804:
1795:
1781:
1736:
1719:
1689:
1675:
1645:
1631:
1602:
1588:
1558:
1544:
1380:
1355:
1265:{\displaystyle E_{\text{red}}}
1111:
954:
932:
761:
754:
745:
738:
727:
720:
711:
704:
621:
614:
605:
598:
587:
580:
571:
564:
469:
462:
453:
446:
435:
428:
419:
412:
239:
232:
223:
216:
205:
198:
189:
182:
1:
8186:
6908:The stability region of water
2937:This equation predicts lower
118:The vertical axis is labeled
71:The diagrams are named after
7890:(96 485 coulomb/mol of
6828:For, = 10 M, this yields:
6197:, the reaction equation is:
4099:. The reaction equation is:
2674:= 0.05916... V at STP where
2217:standard reduction potential
2034:), rectangle braces denote
7:
8561:
8339:Uhlig 's Corrosion Handbook
8201:"Western Oregon University"
8115:
7144:standard hydrogen electrode
3912:or, in base-10 logarithms,
3159:{\displaystyle \gamma _{i}}
3032:standard hydrogen electrode
2151:{\displaystyle \gamma _{i}}
1274:standard hydrogen electrode
1076:Applicable chemical systems
133:(SHE) as calculated by the
131:standard hydrogen electrode
68:yield a different diagram.
10:
8681:
8588:The Geochemist's Workbench
8523:Takeno, Naoto (May 2005).
7965:
7668:in environmental chemistry
2653:{\displaystyle V_{T}=RT/F}
497:sometimes formulated as:
113:
8445:10.1007/s12678-018-0459-1
8330:Verink, E.D. Jr. (2000).
7683:is often used instead of
5788:) at STP, log 1 = 0, so,
2934:volt (pH has no units).
1421:The equilibrium constant
1126:Does not apply to alloys.
267:The Nernst equation is:
86:
8606:Department of Chemistry.
8485:Jones, Denny A. (1996).
8157:
7947:{\displaystyle pe=-\log}
7374: (at low pH)
4710:Horizontal boundary line
8466:Brookins, D.G. (1988).
8288:McCafferty, E. (2010).
8216:. Ignasi Puigdomenech,
8147:Ionic partition diagram
3003:is then often noted as
2059:{\displaystyle \gamma }
156:With the corresponding
150:a A + b B ⇌ c C + d D
8377:Kopeliovich, Dimitri.
8294:. New York: Springer.
7948:
7848:
7800:
7646:environmental sciences
7611:
7558:
7475:
7368:
7252:
7205:
7128:
7021:
6933:
6891:
6819:
6654:
6440:
6398:
6172:
5983:
5834:
5782:
5744:
5595:
5550:
5402:
5235:
5057:
4918:
4861:
4697:
4545:
4345:
4283:
4071:
3903:
3734:
3593:
3539:
3396:Vertical boundary line
3383:
3191:
3160:
3129:
3094:
3055:
3024:
2997:
2958:
2928:
2886:
2856:
2654:
2601:
2399:
2356:
2323:
2244:
2206:
2152:
2125:
2098:
2060:
2017:
1412:
1266:
1239:
1206:
1173:
1085:
1014:
884:
836:
780:
640:
488:
341:
258:
100:
24:
8594:GWB Community Edition
8504:Pourbaix, M. (1974).
7949:
7849:
7801:
7612:
7559:
7476:
7369:
7253:
7206:
7129:
7022:
6915:
6892:
6820:
6655:
6441:
6399:
6173:
5984:
5835:
5783:
5745:
5596:
5594:{\displaystyle V_{T}}
5551:
5403:
5236:
5058:
4919:
4862:
4698:
4546:
4346:
4284:
4072:
3904:
3735:
3594:
3540:
3384:
3192:
3190:{\displaystyle C_{i}}
3161:
3137:activity coefficients
3130:
3128:{\displaystyle C_{i}}
3095:
3093:{\displaystyle a_{i}}
3073:When the activities (
3056:
3025:
3023:{\displaystyle E_{h}}
2998:
2959:
2929:
2887:
2857:
2655:
2602:
2400:
2398:{\displaystyle E_{h}}
2357:
2324:
2245:
2207:
2153:
2126:
2124:{\displaystyle C_{i}}
2099:
2097:{\displaystyle a_{i}}
2068:activity coefficients
2061:
2018:
1413:
1272:expressed versus the
1267:
1240:
1238:{\displaystyle E_{h}}
1207:
1205:{\displaystyle E_{h}}
1174:
1172:{\displaystyle E_{h}}
1083:
1015:
885:
837:
781:
641:
489:
342:
259:
94:
22:
7907:
7876:absolute temperature
7813:
7712:
7571:
7504:
7385:
7278:
7218:
7161:
7038:
6954:
6835:
6698:
6665:equilibrium constant
6457:
6412:
6204:
5999:
5862:
5851:Sloped boundary line
5792:
5757:
5630:
5578:
5440:
5411:For the equilibrium
5251:
5089:
4931:
4877:
4723:
4574:
4358:
4296:
4106:
3919:
3750:
3614:
3605:equilibrium constant
3552:
3435:
3204:
3174:
3143:
3112:
3077:
3038:
3007:
2980:
2941:
2896:
2869:
2685:
2620:
2412:
2382:
2336:
2257:
2222:
2165:
2135:
2108:
2081:
2050:
1432:
1291:
1249:
1222:
1189:
1156:
905:
858:
796:
656:
504:
354:
274:
170:
158:equilibrium constant
142:chemical equilibrium
129:with respect to the
57:chemical equilibrium
37:potential/pH diagram
8634:Thermo-Calc Windows
8552:— Corrosion Doctors
8470:. Springer-Verlag.
8379:"Pourbaix Diagrams"
7962:equilibrium lines.
7678:reduction potential
7676:. In this context,
7449:
7418:
7334:
7298:
7094:
7058:
7004:
6619:
6606:
6574:
6378:
6307:
6233:
6220:
5937:
5498:
4779:
4515:
4462:
4449:
4238:
4225:
4190:
4158:
3493:
3247:
2728:
2455:
2274:
2239:
1366:
1245:explicitly denotes
99:/ sodium hydroxide)
83:who invented them.
7944:
7868:8.314 J⋅K⋅mol
7844:
7796:
7658:reaction mechanism
7607:
7554:
7471:
7437:
7406:
7364:
7322:
7286:
7248:
7201:
7150:(corresponding to
7124:
7082:
7046:
7017:
6992:
6934:
6887:
6815:
6650:
6607:
6594:
6562:
6436:
6394:
6366:
6326:
6221:
6208:
6168:
5979:
5956:
5830:
5778:
5740:
5591:
5546:
5517:
5398:
5231:
5053:
4914:
4857:
4798:
4693:
4541:
4503:
4450:
4437:
4341:
4279:
4226:
4213:
4209:
4146:
4067:
3899:
3730:
3589:
3535:
3512:
3422:acid-base reaction
3379:
3233:
3187:
3156:
3125:
3108:, concentrations (
3090:
3051:
3020:
2993:
2954:
2924:
2882:
2852:
2714:
2650:
2597:
2441:
2395:
2376:Faraday's constant
2352:
2319:
2260:
2240:
2225:
2202:
2148:
2121:
2094:
2056:
2013:
1408:
1385:
1262:
1235:
1202:
1169:
1086:
1010:
880:
842: volt is the
832:
776:
636:
484:
337:
254:
101:
35:, also known as a
25:
8665:Phase transitions
8640:Materials Project
8301:978-1-4419-0454-6
8269:978-0-19-922886-7
8132:Ellingham diagram
8109:
8089:
8066:
8046:
8026:
8006:
7986:
7842:
7783:
7771:
7751:
7705:by the equation:
7605:
7582:
7552:
7515:
7463:
7452:
7440:
7425:
7409:
7396:
7356:
7341:
7325:
7312:
7301:
7289:
7246:
7229:
7199:
7172:
7152:chemical activity
7116:
7101:
7085:
7072:
7061:
7049:
7011:
6995:
6982:
6965:
6882:
6866:
6808:
6804:
6774:
6764:
6749:
6643:
6639:
6625:
6610:
6597:
6577:
6565:
6536:
6508:
6388:
6381:
6369:
6354:
6337:
6328:
6283:
6268:
6255:
6240:
6224:
6211:
6161:
6145:
6050:
5958:
5893:
5734:
5718:
5694:
5540:
5524:
5519:
5474:
5463:
5447:
5392:
5302:
5225:
5135:
5047:
4872:Gibbs free energy
4870:As, the standard
4846:
4841:
4837:
4800:
4682:
4659:
4631:
4596:
4580:
4530:
4518:
4506:
4477:
4453:
4440:
4415:
4380:
4364:
4273:
4260:
4245:
4229:
4216:
4211:
4168:
4161:
4149:
4134:
4117:
4060:
4044:
3893:
3874:
3728:
3709:
3514:
3466:
3377:
3372:
3349:
3259:
3240:
3227:
3048:
2990:
2951:
2918:
2879:
2850:
2845:
2822:
2740:
2721:
2708:
2595:
2590:
2559:
2477:
2448:
2435:
2364:Gibbs free energy
2317:
2281:
2267:
2232:
2011:
1992:
1904:
1899:
1773:
1754:
1718:
1674:
1587:
1536:
1517:
1387:
1322:
1259:
1001:
991:
944:
911:
771:
693:
666:
631:
553:
514:
479:
401:
364:
321:
284:
249:
127:voltage potential
75:(1904–1998), the
8672:
8660:Electrochemistry
8538:
8536:
8535:
8529:
8519:
8500:
8481:
8457:
8456:
8433:Electrocatalysis
8424:
8418:
8417:
8415:
8414:
8404:
8396:
8390:
8389:
8387:
8386:
8374:
8368:
8367:
8365:
8363:
8358:on 6 August 2020
8357:
8351:. Archived from
8336:
8327:
8314:
8313:
8285:
8274:
8273:
8255:
8238:
8237:
8235:
8234:
8225:. Archived from
8214:
8205:
8204:
8197:
8180:
8177:
8171:
8168:
8103:
8099:
8080:
8076:
8060:
8056:
8040:
8036:
8020:
8016:
8000:
7996:
7980:
7976:
7960:
7953:
7951:
7950:
7945:
7940:
7939:
7893:
7888:Faraday constant
7885:
7873:
7869:
7861:
7853:
7851:
7850:
7845:
7843:
7838:
7830:
7825:
7824:
7805:
7803:
7802:
7797:
7795:
7794:
7784:
7781:
7772:
7767:
7766:
7757:
7752:
7750:
7746:
7745:
7735:
7734:
7725:
7704:
7697:
7689:
7682:
7667:
7650:aqueous solution
7616:
7614:
7613:
7608:
7606:
7603:
7585:
7584:
7583:
7580:
7563:
7561:
7560:
7555:
7553:
7550:
7544:
7543:
7531:
7530:
7518:
7517:
7516:
7513:
7480:
7478:
7477:
7472:
7470:
7469:
7468:
7461:
7450:
7448:
7445:
7438:
7429:
7423:
7417:
7414:
7407:
7402:
7401:
7394:
7373:
7371:
7370:
7365:
7363:
7362:
7361:
7354:
7345:
7339:
7333:
7330:
7323:
7318:
7317:
7310:
7299:
7297:
7294:
7287:
7257:
7255:
7254:
7249:
7247:
7244:
7232:
7231:
7230:
7227:
7210:
7208:
7207:
7202:
7200:
7197:
7191:
7190:
7175:
7174:
7173:
7170:
7133:
7131:
7130:
7125:
7123:
7122:
7121:
7114:
7105:
7099:
7093:
7090:
7083:
7078:
7077:
7070:
7059:
7057:
7054:
7047:
7026:
7024:
7023:
7018:
7016:
7015:
7009:
7003:
7000:
6993:
6988:
6987:
6980:
6971:
6970:
6963:
6896:
6894:
6893:
6888:
6883:
6880:
6874:
6864:
6863:
6855:
6847:
6846:
6824:
6822:
6821:
6816:
6814:
6810:
6809:
6806:
6802:
6795:
6794:
6793:
6788:
6784:
6783:
6772:
6762:
6750:
6745:
6741:
6740:
6730:
6725:
6724:
6723:
6710:
6709:
6691:is written as:
6687:
6683:
6682:
6681:
6669:
6659:
6657:
6656:
6651:
6649:
6645:
6644:
6641:
6637:
6630:
6626:
6624:
6623:
6618:
6615:
6608:
6605:
6602:
6595:
6588:
6587:
6586:
6581:
6575:
6573:
6570:
6563:
6556:
6555:
6550:
6546:
6545:
6534:
6526:
6509:
6504:
6500:
6499:
6489:
6484:
6483:
6482:
6469:
6468:
6445:
6443:
6442:
6437:
6435:
6424:
6423:
6403:
6401:
6400:
6395:
6393:
6392:
6386:
6379:
6377:
6374:
6367:
6358:
6352:
6347:
6346:
6335:
6329:
6327:
6325:
6324:
6317:
6309:
6308:
6306:
6299:
6291:
6289:
6288:
6281:
6272:
6266:
6261:
6260:
6253:
6244:
6238:
6232:
6229:
6222:
6219:
6216:
6209:
6177:
6175:
6174:
6169:
6167:
6163:
6162:
6159:
6150:
6146:
6144:
6143:
6142:
6137:
6125:
6124:
6119:
6106:
6105:
6104:
6099:
6087:
6086:
6081:
6068:
6051:
6046:
6042:
6041:
6031:
6026:
6025:
6024:
6011:
6010:
5988:
5986:
5985:
5980:
5960:
5959:
5957:
5955:
5954:
5947:
5939:
5938:
5936:
5929:
5921:
5917:
5916:
5900:
5899:
5898:
5891:
5839:
5837:
5836:
5831:
5829:
5817:
5816:
5804:
5803:
5787:
5785:
5784:
5779:
5777:
5772:
5771:
5749:
5747:
5746:
5741:
5739:
5735:
5733:
5732:
5728:
5727:
5716:
5709:
5708:
5704:
5703:
5692:
5685:
5670:
5669:
5657:
5656:
5655:
5642:
5641:
5622:
5621:
5620:
5611:
5610:
5609:
5600:
5598:
5597:
5592:
5590:
5589:
5555:
5553:
5552:
5547:
5545:
5544:
5538:
5533:
5532:
5522:
5520:
5518:
5516:
5515:
5508:
5500:
5499:
5497:
5490:
5482:
5480:
5479:
5472:
5467:
5461:
5456:
5455:
5445:
5432:
5431:
5430:
5421:
5420:
5419:
5407:
5405:
5404:
5399:
5397:
5393:
5391:
5390:
5389:
5384:
5372:
5371:
5366:
5353:
5352:
5351:
5346:
5334:
5333:
5328:
5315:
5303:
5298:
5294:
5293:
5283:
5278:
5277:
5276:
5263:
5262:
5240:
5238:
5237:
5232:
5230:
5226:
5224:
5223:
5222:
5217:
5205:
5204:
5199:
5186:
5185:
5184:
5179:
5167:
5166:
5161:
5148:
5136:
5131:
5130:
5121:
5116:
5115:
5114:
5101:
5100:
5080:Faraday constant
5062:
5060:
5059:
5054:
5052:
5048:
5046:
5045:
5044:
5039:
5027:
5026:
5021:
5008:
5007:
5006:
5001:
4989:
4988:
4983:
4970:
4946:
4945:
4923:
4921:
4920:
4915:
4892:
4891:
4866:
4864:
4863:
4858:
4853:
4852:
4851:
4844:
4839:
4838:
4835:
4802:
4801:
4799:
4797:
4796:
4789:
4781:
4780:
4778:
4771:
4763:
4759:
4758:
4702:
4700:
4699:
4694:
4692:
4688:
4687:
4683:
4681:
4680:
4679:
4670:
4669:
4668:
4657:
4647:
4632:
4630:
4619:
4618:
4617:
4604:
4597:
4589:
4581:
4578:
4566:
4565:
4564:
4550:
4548:
4547:
4542:
4540:
4536:
4535:
4531:
4529:
4528:
4527:
4522:
4516:
4514:
4511:
4504:
4497:
4496:
4491:
4487:
4486:
4475:
4467:
4466:
4461:
4458:
4451:
4448:
4445:
4438:
4431:
4416:
4414:
4403:
4402:
4401:
4388:
4381:
4373:
4365:
4362:
4350:
4348:
4347:
4342:
4340:
4330:
4311:
4310:
4288:
4286:
4285:
4280:
4278:
4277:
4271:
4266:
4265:
4258:
4249:
4243:
4237:
4234:
4227:
4224:
4221:
4214:
4212:
4210:
4208:
4207:
4200:
4192:
4191:
4189:
4182:
4174:
4172:
4166:
4159:
4157:
4154:
4147:
4138:
4132:
4127:
4126:
4115:
4076:
4074:
4073:
4068:
4066:
4062:
4061:
4058:
4049:
4045:
4043:
4042:
4041:
4036:
4024:
4023:
4018:
4005:
4004:
4003:
3998:
3986:
3985:
3980:
3967:
3934:
3933:
3908:
3906:
3905:
3900:
3898:
3894:
3892:
3891:
3890:
3885:
3881:
3880:
3879:
3872:
3864:
3863:
3858:
3846:
3845:
3840:
3827:
3826:
3825:
3820:
3808:
3807:
3802:
3789:
3765:
3764:
3739:
3737:
3736:
3731:
3729:
3727:
3726:
3725:
3720:
3716:
3715:
3714:
3707:
3699:
3698:
3693:
3681:
3680:
3675:
3662:
3661:
3660:
3655:
3643:
3642:
3637:
3624:
3602:
3598:
3596:
3595:
3590:
3567:
3566:
3544:
3542:
3541:
3536:
3516:
3515:
3513:
3511:
3510:
3503:
3495:
3494:
3492:
3485:
3477:
3473:
3472:
3471:
3464:
3424:involving only
3419:
3415:
3411:
3407:
3388:
3386:
3385:
3380:
3378:
3375:
3373:
3368:
3359:
3354:
3350:
3348:
3347:
3346:
3341:
3329:
3328:
3323:
3310:
3309:
3308:
3303:
3291:
3290:
3285:
3272:
3260:
3252:
3246:
3241:
3238:
3229:
3228:
3225:
3216:
3215:
3196:
3194:
3193:
3188:
3186:
3185:
3165:
3163:
3162:
3157:
3155:
3154:
3134:
3132:
3131:
3126:
3124:
3123:
3099:
3097:
3096:
3091:
3089:
3088:
3060:
3058:
3057:
3052:
3050:
3049:
3046:
3029:
3027:
3026:
3021:
3019:
3018:
3002:
3000:
2999:
2994:
2992:
2991:
2988:
2963:
2961:
2960:
2955:
2953:
2952:
2949:
2933:
2931:
2930:
2925:
2923:
2919:
2911:
2891:
2889:
2888:
2883:
2881:
2880:
2877:
2861:
2859:
2858:
2853:
2851:
2848:
2846:
2841:
2832:
2827:
2823:
2821:
2820:
2819:
2804:
2803:
2787:
2786:
2785:
2770:
2769:
2753:
2741:
2733:
2727:
2722:
2719:
2710:
2709:
2706:
2697:
2696:
2678:= ln = 2.3026.
2661:
2659:
2657:
2656:
2651:
2646:
2632:
2631:
2606:
2604:
2603:
2598:
2596:
2593:
2591:
2589:
2581:
2569:
2564:
2560:
2558:
2557:
2556:
2541:
2540:
2524:
2523:
2522:
2507:
2506:
2490:
2478:
2476:
2468:
2460:
2454:
2449:
2446:
2437:
2436:
2433:
2424:
2423:
2404:
2402:
2401:
2396:
2394:
2393:
2373:
2369:
2362:is the standard
2361:
2359:
2358:
2353:
2351:
2350:
2328:
2326:
2325:
2320:
2318:
2316:
2308:
2307:
2306:
2293:
2282:
2279:
2273:
2268:
2265:
2249:
2247:
2246:
2241:
2238:
2233:
2230:
2211:
2209:
2208:
2203:
2201:
2200:
2190:
2189:
2177:
2176:
2157:
2155:
2154:
2149:
2147:
2146:
2130:
2128:
2127:
2122:
2120:
2119:
2103:
2101:
2100:
2095:
2093:
2092:
2065:
2063:
2062:
2057:
2045:
2042:concentrations (
2033:
2022:
2020:
2019:
2014:
2012:
2010:
2009:
2008:
2003:
1999:
1998:
1997:
1990:
1982:
1981:
1976:
1964:
1963:
1958:
1945:
1944:
1943:
1938:
1926:
1925:
1920:
1907:
1905:
1902:
1900:
1898:
1897:
1896:
1887:
1886:
1874:
1873:
1864:
1863:
1851:
1850:
1841:
1840:
1827:
1826:
1825:
1816:
1815:
1803:
1802:
1793:
1792:
1779:
1774:
1772:
1771:
1770:
1765:
1761:
1760:
1759:
1752:
1744:
1743:
1734:
1733:
1716:
1715:
1714:
1709:
1697:
1696:
1687:
1686:
1672:
1671:
1670:
1665:
1653:
1652:
1643:
1642:
1629:
1628:
1627:
1622:
1610:
1609:
1600:
1599:
1585:
1584:
1583:
1578:
1566:
1565:
1556:
1555:
1542:
1537:
1535:
1534:
1533:
1524:
1523:
1522:
1515:
1509:
1508:
1493:
1492:
1476:
1475:
1474:
1459:
1458:
1442:
1424:
1417:
1415:
1414:
1409:
1389:
1388:
1386:
1384:
1383:
1376:
1368:
1367:
1365:
1358:
1350:
1346:
1345:
1329:
1328:
1327:
1320:
1271:
1269:
1268:
1263:
1261:
1260:
1257:
1244:
1242:
1241:
1236:
1234:
1233:
1217:
1211:
1209:
1208:
1203:
1201:
1200:
1178:
1176:
1175:
1170:
1168:
1167:
1139:
1135:
1107:
1106:
1105:
1102:
1045:
1043:
1019:
1017:
1016:
1011:
1006:
1002:
1000:
999:
998:
997:
996:
989:
978:
969:
968:
953:
952:
951:
950:
949:
942:
928:
927:
912:
909:
889:
887:
886:
881:
870:
869:
841:
839:
838:
833:
822:
808:
807:
785:
783:
782:
777:
772:
770:
769:
768:
753:
752:
736:
735:
734:
719:
718:
702:
694:
686:
681:
680:
668:
667:
664:
645:
643:
642:
637:
632:
630:
629:
628:
613:
612:
596:
595:
594:
579:
578:
562:
554:
549:
545:
544:
534:
529:
528:
516:
515:
512:
493:
491:
490:
485:
480:
478:
477:
476:
461:
460:
444:
443:
442:
427:
426:
410:
402:
400:
392:
384:
379:
378:
366:
365:
362:
346:
344:
343:
338:
333:
322:
320:
312:
304:
299:
298:
286:
285:
282:
263:
261:
260:
255:
250:
248:
247:
246:
231:
230:
214:
213:
212:
197:
196:
180:
162:
152:
151:
33:Pourbaix diagram
29:electrochemistry
8680:
8679:
8675:
8674:
8673:
8671:
8670:
8669:
8650:
8649:
8582:web application
8564:
8550:Marcel Pourbaix
8546:
8541:
8533:
8531:
8527:
8516:
8497:
8478:
8461:
8460:
8425:
8421:
8412:
8410:
8402:
8398:
8397:
8393:
8384:
8382:
8375:
8371:
8361:
8359:
8355:
8349:
8334:
8328:
8317:
8302:
8286:
8277:
8270:
8256:
8241:
8232:
8230:
8221:
8215:
8208:
8199:
8198:
8194:
8189:
8184:
8183:
8178:
8174:
8169:
8165:
8160:
8137:Latimer diagram
8122:Nernst equation
8118:
8111:
8110:
8107:
8100:
8091:
8090:
8088:
8084:
8077:
8068:
8067:
8064:
8057:
8048:
8047:
8044:
8037:
8028:
8027:
8024:
8017:
8008:
8007:
8004:
7997:
7988:
7987:
7984:
7977:
7968:
7958:
7935:
7931:
7908:
7905:
7904:
7891:
7883:
7871:
7867:
7859:
7856:thermal voltage
7831:
7829:
7820:
7816:
7814:
7811:
7810:
7790:
7786:
7780:
7762:
7758:
7756:
7741:
7737:
7736:
7730:
7726:
7724:
7713:
7710:
7709:
7703:
7699:
7695:
7688:
7684:
7680:
7670:
7665:
7630:
7602:
7579:
7578:
7574:
7572:
7569:
7568:
7549:
7539:
7535:
7526:
7522:
7512:
7511:
7507:
7505:
7502:
7501:
7492:
7490:
7464:
7460:
7446:
7441:
7419:
7415:
7410:
7397:
7393:
7388:
7386:
7383:
7382:
7357:
7353:
7335:
7331:
7326:
7313:
7309:
7295:
7290:
7281:
7279:
7276:
7275:
7270:
7243:
7226:
7225:
7221:
7219:
7216:
7215:
7196:
7186:
7182:
7169:
7168:
7164:
7162:
7159:
7158:
7117:
7113:
7095:
7091:
7086:
7073:
7069:
7055:
7050:
7041:
7039:
7036:
7035:
7005:
7001:
6996:
6983:
6979:
6966:
6962:
6957:
6955:
6952:
6951:
6946:
6910:
6903:
6879:
6867:
6859:
6851:
6842:
6838:
6836:
6833:
6832:
6805:
6789:
6775:
6771:
6767:
6766:
6765:
6755:
6751:
6736:
6732:
6731:
6729:
6719:
6715:
6714:
6705:
6701:
6699:
6696:
6695:
6685:
6680:
6678:
6677:
6676:
6674:
6667:
6640:
6616:
6611:
6603:
6598:
6590:
6589:
6582:
6571:
6566:
6558:
6557:
6551:
6537:
6533:
6529:
6528:
6527:
6525:
6521:
6514:
6510:
6495:
6491:
6490:
6488:
6478:
6474:
6473:
6464:
6460:
6458:
6455:
6454:
6431:
6419:
6415:
6413:
6410:
6409:
6382:
6375:
6370:
6348:
6338:
6334:
6320:
6313:
6312:
6310:
6302:
6295:
6293:
6292:
6290:
6284:
6280:
6262:
6256:
6252:
6234:
6230:
6225:
6217:
6212:
6207:
6205:
6202:
6201:
6196:
6192:
6158:
6138:
6127:
6126:
6120:
6109:
6108:
6107:
6100:
6089:
6088:
6082:
6071:
6070:
6069:
6067:
6063:
6056:
6052:
6037:
6033:
6032:
6030:
6020:
6016:
6015:
6006:
6002:
6000:
5997:
5996:
5950:
5943:
5942:
5940:
5932:
5925:
5923:
5922:
5920:
5919:
5912:
5908:
5894:
5890:
5889:
5863:
5860:
5859:
5853:
5845:
5825:
5812:
5808:
5799:
5795:
5793:
5790:
5789:
5773:
5764:
5760:
5758:
5755:
5754:
5719:
5715:
5711:
5710:
5695:
5691:
5687:
5686:
5684:
5680:
5665:
5661:
5651:
5647:
5646:
5637:
5633:
5631:
5628:
5627:
5619:
5617:
5616:
5615:
5613:
5608:
5606:
5605:
5604:
5602:
5585:
5581:
5579:
5576:
5575:
5573:thermal voltage
5570:
5534:
5525:
5521:
5511:
5504:
5503:
5501:
5493:
5486:
5484:
5483:
5481:
5475:
5471:
5457:
5448:
5444:
5443:
5441:
5438:
5437:
5429:
5427:
5426:
5425:
5423:
5418:
5416:
5415:
5414:
5412:
5385:
5374:
5373:
5367:
5356:
5355:
5354:
5347:
5336:
5335:
5329:
5318:
5317:
5316:
5314:
5310:
5289:
5285:
5284:
5282:
5272:
5268:
5267:
5258:
5254:
5252:
5249:
5248:
5218:
5207:
5206:
5200:
5189:
5188:
5187:
5180:
5169:
5168:
5162:
5151:
5150:
5149:
5147:
5143:
5126:
5122:
5120:
5110:
5106:
5105:
5096:
5092:
5090:
5087:
5086:
5040:
5029:
5028:
5022:
5011:
5010:
5009:
5002:
4991:
4990:
4984:
4973:
4972:
4971:
4969:
4965:
4941:
4937:
4932:
4929:
4928:
4887:
4883:
4878:
4875:
4874:
4847:
4843:
4842:
4834:
4792:
4785:
4784:
4782:
4774:
4767:
4765:
4764:
4762:
4761:
4754:
4750:
4724:
4721:
4720:
4715:
4712:
4675:
4671:
4660:
4656:
4655:
4651:
4646:
4642:
4620:
4613:
4609:
4605:
4603:
4602:
4598:
4588:
4577:
4575:
4572:
4571:
4563:
4561:
4560:
4559:
4557:
4555:
4523:
4512:
4507:
4499:
4498:
4492:
4478:
4474:
4470:
4469:
4468:
4459:
4454:
4446:
4441:
4433:
4432:
4430:
4426:
4404:
4397:
4393:
4389:
4387:
4386:
4382:
4372:
4361:
4359:
4356:
4355:
4326:
4322:
4306:
4302:
4297:
4294:
4293:
4267:
4261:
4257:
4239:
4235:
4230:
4222:
4217:
4203:
4196:
4195:
4193:
4185:
4178:
4176:
4175:
4173:
4162:
4155:
4150:
4128:
4118:
4114:
4109:
4107:
4104:
4103:
4098:
4094:
4087:ion Fe ion and
4057:
4037:
4026:
4025:
4019:
4008:
4007:
4006:
3999:
3988:
3987:
3981:
3970:
3969:
3968:
3966:
3962:
3955:
3951:
3929:
3925:
3920:
3917:
3916:
3886:
3875:
3871:
3870:
3866:
3865:
3859:
3848:
3847:
3841:
3830:
3829:
3828:
3821:
3810:
3809:
3803:
3792:
3791:
3790:
3788:
3784:
3760:
3756:
3751:
3748:
3747:
3721:
3710:
3706:
3705:
3701:
3700:
3694:
3683:
3682:
3676:
3665:
3664:
3663:
3656:
3645:
3644:
3638:
3627:
3626:
3625:
3623:
3615:
3612:
3611:
3600:
3562:
3558:
3553:
3550:
3549:
3506:
3499:
3498:
3496:
3488:
3481:
3479:
3478:
3476:
3475:
3467:
3463:
3462:
3436:
3433:
3432:
3417:
3413:
3409:
3405:
3398:
3374:
3360:
3358:
3342:
3331:
3330:
3324:
3313:
3312:
3311:
3304:
3293:
3292:
3286:
3275:
3274:
3273:
3271:
3267:
3251:
3242:
3237:
3224:
3220:
3211:
3207:
3205:
3202:
3201:
3181:
3177:
3175:
3172:
3171:
3168:Nernst equation
3150:
3146:
3144:
3141:
3140:
3119:
3115:
3113:
3110:
3109:
3084:
3080:
3078:
3075:
3074:
3071:
3064:
3045:
3041:
3039:
3036:
3035:
3014:
3010:
3008:
3005:
3004:
2987:
2983:
2981:
2978:
2977:
2975:
2971:
2967:
2948:
2944:
2942:
2939:
2938:
2910:
2906:
2897:
2894:
2893:
2876:
2872:
2870:
2867:
2866:
2847:
2833:
2831:
2815:
2811:
2799:
2795:
2788:
2781:
2777:
2765:
2761:
2754:
2752:
2748:
2732:
2723:
2718:
2705:
2701:
2692:
2688:
2686:
2683:
2682:
2671:
2642:
2627:
2623:
2621:
2618:
2617:
2615:
2612:thermal voltage
2592:
2582:
2570:
2568:
2552:
2548:
2536:
2532:
2525:
2518:
2514:
2502:
2498:
2491:
2489:
2485:
2469:
2461:
2459:
2450:
2445:
2432:
2428:
2419:
2415:
2413:
2410:
2409:
2389:
2385:
2383:
2380:
2379:
2371:
2367:
2346:
2342:
2337:
2334:
2333:
2309:
2302:
2298:
2294:
2292:
2278:
2269:
2264:
2258:
2255:
2254:
2234:
2229:
2223:
2220:
2219:
2196:
2192:
2185:
2181:
2172:
2168:
2166:
2163:
2162:
2142:
2138:
2136:
2133:
2132:
2115:
2111:
2109:
2106:
2105:
2088:
2084:
2082:
2079:
2078:
2051:
2048:
2047:
2043:
2031:
2004:
1993:
1989:
1988:
1984:
1983:
1977:
1966:
1965:
1959:
1948:
1947:
1946:
1939:
1928:
1927:
1921:
1910:
1909:
1908:
1906:
1901:
1892:
1888:
1882:
1878:
1869:
1865:
1859:
1855:
1846:
1842:
1836:
1832:
1828:
1821:
1817:
1811:
1807:
1798:
1794:
1788:
1784:
1780:
1778:
1766:
1755:
1751:
1750:
1746:
1745:
1739:
1735:
1726:
1722:
1710:
1699:
1698:
1692:
1688:
1682:
1678:
1666:
1655:
1654:
1648:
1644:
1638:
1634:
1630:
1623:
1612:
1611:
1605:
1601:
1595:
1591:
1579:
1568:
1567:
1561:
1557:
1551:
1547:
1543:
1541:
1529:
1525:
1518:
1514:
1513:
1504:
1500:
1488:
1484:
1477:
1470:
1466:
1454:
1450:
1443:
1441:
1433:
1430:
1429:
1422:
1379:
1372:
1371:
1369:
1361:
1354:
1352:
1351:
1349:
1348:
1341:
1337:
1323:
1319:
1318:
1292:
1289:
1288:
1256:
1252:
1250:
1247:
1246:
1229:
1225:
1223:
1220:
1219:
1196:
1192:
1190:
1187:
1186:
1184:
1163:
1159:
1157:
1154:
1153:
1150:
1137:
1133:
1114:
1103:
1100:
1099:
1097:
1078:
1068:because of the
1041:
1039:
1038:= 1 atm =
992:
988:
987:
986:
982:
977:
973:
964:
960:
945:
941:
940:
939:
935:
923:
919:
908:
906:
903:
902:
865:
861:
859:
856:
855:
844:thermal voltage
818:
803:
799:
797:
794:
793:
764:
760:
748:
744:
737:
730:
726:
714:
710:
703:
701:
685:
676:
672:
663:
659:
657:
654:
653:
624:
620:
608:
604:
597:
590:
586:
574:
570:
563:
561:
540:
536:
535:
533:
524:
520:
511:
507:
505:
502:
501:
472:
468:
456:
452:
445:
438:
434:
422:
418:
411:
409:
393:
385:
383:
374:
370:
361:
357:
355:
352:
351:
329:
313:
305:
303:
294:
290:
281:
277:
275:
272:
271:
242:
238:
226:
222:
215:
208:
204:
192:
188:
181:
179:
171:
168:
167:
160:
149:
148:
135:Nernst equation
124:
116:
109:
97:perchloric acid
89:
73:Marcel Pourbaix
44:
17:
12:
11:
5:
8678:
8668:
8667:
8662:
8648:
8647:
8637:
8631:
8617:
8607:
8597:
8591:
8585:
8575:
8563:
8560:
8559:
8558:
8553:
8545:
8544:External links
8542:
8540:
8539:
8520:
8514:
8501:
8495:
8482:
8476:
8462:
8459:
8458:
8439:(4): 531–538.
8419:
8391:
8369:
8347:
8315:
8300:
8275:
8268:
8239:
8206:
8191:
8190:
8188:
8185:
8182:
8181:
8172:
8162:
8161:
8159:
8156:
8155:
8154:
8149:
8144:
8139:
8134:
8129:
8124:
8117:
8114:
8113:
8112:
8105:
8102:
8101:
8094:
8092:
8086:
8082:
8079:
8078:
8071:
8069:
8062:
8059:
8058:
8051:
8049:
8042:
8039:
8038:
8031:
8029:
8022:
8019:
8018:
8011:
8009:
8002:
7999:
7998:
7991:
7989:
7982:
7979:
7978:
7971:
7967:
7964:
7956:
7955:
7943:
7938:
7934:
7930:
7927:
7924:
7921:
7918:
7915:
7912:
7841:
7837:
7834:
7828:
7823:
7819:
7807:
7806:
7793:
7789:
7778:
7775:
7770:
7765:
7761:
7755:
7749:
7744:
7740:
7733:
7729:
7723:
7720:
7717:
7701:
7686:
7669:
7662:
7629:
7626:
7618:
7617:
7600:
7597:
7594:
7591:
7588:
7577:
7565:
7564:
7547:
7542:
7538:
7534:
7529:
7525:
7521:
7510:
7488:
7486:
7483:
7482:
7467:
7458:
7455:
7444:
7435:
7432:
7428:
7422:
7413:
7405:
7400:
7391:
7376:
7375:
7360:
7351:
7348:
7344:
7338:
7329:
7321:
7316:
7307:
7304:
7293:
7284:
7268:
7259:
7258:
7241:
7238:
7235:
7224:
7212:
7211:
7194:
7189:
7185:
7181:
7178:
7167:
7136:
7135:
7120:
7111:
7108:
7104:
7098:
7089:
7081:
7076:
7067:
7064:
7053:
7044:
7029:
7028:
7014:
7008:
6999:
6991:
6986:
6977:
6974:
6969:
6960:
6944:
6909:
6906:
6901:
6898:
6897:
6886:
6878:
6873:
6870:
6862:
6858:
6854:
6850:
6845:
6841:
6826:
6825:
6813:
6801:
6798:
6792:
6787:
6782:
6778:
6770:
6761:
6758:
6754:
6748:
6744:
6739:
6735:
6728:
6722:
6718:
6713:
6708:
6704:
6679:
6661:
6660:
6648:
6636:
6633:
6629:
6622:
6614:
6601:
6593:
6585:
6580:
6569:
6561:
6554:
6549:
6544:
6540:
6532:
6524:
6520:
6517:
6513:
6507:
6503:
6498:
6494:
6487:
6481:
6477:
6472:
6467:
6463:
6448:
6447:
6434:
6430:
6427:
6422:
6418:
6405:
6404:
6391:
6385:
6373:
6364:
6361:
6357:
6351:
6345:
6341:
6332:
6323:
6316:
6305:
6298:
6287:
6278:
6275:
6271:
6265:
6259:
6250:
6247:
6243:
6237:
6228:
6215:
6194:
6190:
6179:
6178:
6166:
6156:
6153:
6149:
6141:
6136:
6133:
6130:
6123:
6118:
6115:
6112:
6103:
6098:
6095:
6092:
6085:
6080:
6077:
6074:
6066:
6062:
6059:
6055:
6049:
6045:
6040:
6036:
6029:
6023:
6019:
6014:
6009:
6005:
5990:
5989:
5978:
5974:
5971:
5968:
5964:
5953:
5946:
5935:
5928:
5915:
5911:
5906:
5903:
5897:
5887:
5884:
5881:
5877:
5874:
5871:
5867:
5852:
5849:
5843:
5828:
5823:
5820:
5815:
5811:
5807:
5802:
5798:
5776:
5770:
5767:
5763:
5751:
5750:
5738:
5731:
5726:
5722:
5714:
5707:
5702:
5698:
5690:
5683:
5679:
5676:
5673:
5668:
5664:
5660:
5654:
5650:
5645:
5640:
5636:
5618:
5607:
5588:
5584:
5568:
5557:
5556:
5543:
5537:
5531:
5528:
5514:
5507:
5496:
5489:
5478:
5470:
5466:
5460:
5454:
5451:
5428:
5417:
5409:
5408:
5396:
5388:
5383:
5380:
5377:
5370:
5365:
5362:
5359:
5350:
5345:
5342:
5339:
5332:
5327:
5324:
5321:
5313:
5309:
5306:
5301:
5297:
5292:
5288:
5281:
5275:
5271:
5266:
5261:
5257:
5242:
5241:
5229:
5221:
5216:
5213:
5210:
5203:
5198:
5195:
5192:
5183:
5178:
5175:
5172:
5165:
5160:
5157:
5154:
5146:
5142:
5139:
5134:
5129:
5125:
5119:
5113:
5109:
5104:
5099:
5095:
5064:
5063:
5051:
5043:
5038:
5035:
5032:
5025:
5020:
5017:
5014:
5005:
5000:
4997:
4994:
4987:
4982:
4979:
4976:
4968:
4964:
4961:
4958:
4955:
4952:
4949:
4944:
4940:
4936:
4913:
4910:
4907:
4904:
4901:
4898:
4895:
4890:
4886:
4882:
4868:
4867:
4856:
4850:
4833:
4830:
4827:
4824:
4820:
4816:
4813:
4810:
4806:
4795:
4788:
4777:
4770:
4757:
4753:
4748:
4745:
4742:
4738:
4735:
4732:
4728:
4711:
4708:
4704:
4703:
4691:
4686:
4678:
4674:
4667:
4663:
4654:
4650:
4645:
4641:
4638:
4635:
4629:
4626:
4623:
4616:
4612:
4608:
4601:
4595:
4592:
4587:
4584:
4562:
4552:
4551:
4539:
4534:
4526:
4521:
4510:
4502:
4495:
4490:
4485:
4481:
4473:
4465:
4457:
4444:
4436:
4429:
4425:
4422:
4419:
4413:
4410:
4407:
4400:
4396:
4392:
4385:
4379:
4376:
4371:
4368:
4339:
4336:
4333:
4329:
4325:
4320:
4317:
4314:
4309:
4305:
4301:
4290:
4289:
4276:
4270:
4264:
4255:
4252:
4248:
4242:
4233:
4220:
4206:
4199:
4188:
4181:
4171:
4165:
4153:
4144:
4141:
4137:
4131:
4125:
4121:
4112:
4096:
4092:
4078:
4077:
4065:
4055:
4052:
4048:
4040:
4035:
4032:
4029:
4022:
4017:
4014:
4011:
4002:
3997:
3994:
3991:
3984:
3979:
3976:
3973:
3965:
3961:
3958:
3954:
3949:
3946:
3943:
3940:
3937:
3932:
3928:
3924:
3910:
3909:
3897:
3889:
3884:
3878:
3869:
3862:
3857:
3854:
3851:
3844:
3839:
3836:
3833:
3824:
3819:
3816:
3813:
3806:
3801:
3798:
3795:
3787:
3783:
3780:
3777:
3774:
3771:
3768:
3763:
3759:
3755:
3741:
3740:
3724:
3719:
3713:
3704:
3697:
3692:
3689:
3686:
3679:
3674:
3671:
3668:
3659:
3654:
3651:
3648:
3641:
3636:
3633:
3630:
3622:
3619:
3588:
3585:
3582:
3579:
3576:
3573:
3570:
3565:
3561:
3557:
3546:
3545:
3534:
3530:
3527:
3524:
3520:
3509:
3502:
3491:
3484:
3470:
3460:
3457:
3454:
3450:
3447:
3444:
3440:
3397:
3394:
3390:
3389:
3371:
3367:
3363:
3357:
3353:
3345:
3340:
3337:
3334:
3327:
3322:
3319:
3316:
3307:
3302:
3299:
3296:
3289:
3284:
3281:
3278:
3270:
3266:
3263:
3258:
3255:
3250:
3245:
3236:
3232:
3223:
3219:
3214:
3210:
3184:
3180:
3153:
3149:
3122:
3118:
3087:
3083:
3070:
3067:
3062:
3044:
3017:
3013:
2986:
2973:
2969:
2965:
2947:
2922:
2917:
2914:
2909:
2904:
2901:
2875:
2863:
2862:
2844:
2840:
2836:
2830:
2826:
2818:
2814:
2810:
2807:
2802:
2798:
2794:
2791:
2784:
2780:
2776:
2773:
2768:
2764:
2760:
2757:
2751:
2747:
2744:
2739:
2736:
2731:
2726:
2717:
2713:
2704:
2700:
2695:
2691:
2669:
2649:
2645:
2641:
2638:
2635:
2630:
2626:
2608:
2607:
2588:
2585:
2580:
2576:
2573:
2567:
2563:
2555:
2551:
2547:
2544:
2539:
2535:
2531:
2528:
2521:
2517:
2513:
2510:
2505:
2501:
2497:
2494:
2488:
2484:
2481:
2475:
2472:
2467:
2464:
2458:
2453:
2444:
2440:
2431:
2427:
2422:
2418:
2392:
2388:
2349:
2345:
2341:
2330:
2329:
2315:
2312:
2305:
2301:
2297:
2291:
2288:
2285:
2277:
2272:
2263:
2237:
2228:
2215:The half-cell
2213:
2212:
2199:
2195:
2188:
2184:
2180:
2175:
2171:
2145:
2141:
2118:
2114:
2091:
2087:
2072:stoichiometric
2066:represent the
2055:
2024:
2023:
2007:
2002:
1996:
1987:
1980:
1975:
1972:
1969:
1962:
1957:
1954:
1951:
1942:
1937:
1934:
1931:
1924:
1919:
1916:
1913:
1895:
1891:
1885:
1881:
1877:
1872:
1868:
1862:
1858:
1854:
1849:
1845:
1839:
1835:
1831:
1824:
1820:
1814:
1810:
1806:
1801:
1797:
1791:
1787:
1783:
1777:
1769:
1764:
1758:
1749:
1742:
1738:
1732:
1729:
1725:
1721:
1713:
1708:
1705:
1702:
1695:
1691:
1685:
1681:
1677:
1669:
1664:
1661:
1658:
1651:
1647:
1641:
1637:
1633:
1626:
1621:
1618:
1615:
1608:
1604:
1598:
1594:
1590:
1582:
1577:
1574:
1571:
1564:
1560:
1554:
1550:
1546:
1540:
1532:
1528:
1521:
1512:
1507:
1503:
1499:
1496:
1491:
1487:
1483:
1480:
1473:
1469:
1465:
1462:
1457:
1453:
1449:
1446:
1440:
1437:
1419:
1418:
1407:
1403:
1400:
1397:
1393:
1382:
1375:
1364:
1357:
1344:
1340:
1335:
1332:
1326:
1316:
1313:
1310:
1306:
1303:
1300:
1296:
1255:
1232:
1228:
1199:
1195:
1166:
1162:
1149:
1146:
1145:
1144:
1141:
1130:
1127:
1124:
1121:
1113:
1110:
1077:
1074:
1021:
1020:
1009:
1005:
995:
985:
981:
976:
972:
967:
963:
959:
956:
948:
938:
934:
931:
926:
922:
918:
915:
892:
891:
879:
876:
873:
868:
864:
848:
847:
831:
828:
825:
821:
817:
814:
811:
806:
802:
787:
786:
775:
767:
763:
759:
756:
751:
747:
743:
740:
733:
729:
725:
722:
717:
713:
709:
706:
700:
697:
692:
689:
684:
679:
675:
671:
662:
647:
646:
635:
627:
623:
619:
616:
611:
607:
603:
600:
593:
589:
585:
582:
577:
573:
569:
566:
560:
557:
552:
548:
543:
539:
532:
527:
523:
519:
510:
495:
494:
483:
475:
471:
467:
464:
459:
455:
451:
448:
441:
437:
433:
430:
425:
421:
417:
414:
408:
405:
399:
396:
391:
388:
382:
377:
373:
369:
360:
348:
347:
336:
332:
328:
325:
319:
316:
311:
308:
302:
297:
293:
289:
280:
265:
264:
253:
245:
241:
237:
234:
229:
225:
221:
218:
211:
207:
203:
200:
195:
191:
187:
184:
178:
175:
154:
153:
122:
115:
112:
107:
88:
85:
79:-born Belgian
42:
15:
9:
6:
4:
3:
2:
8677:
8666:
8663:
8661:
8658:
8657:
8655:
8645:
8641:
8638:
8635:
8632:
8629:
8625:
8621:
8618:
8615:
8611:
8610:HSC Chemistry
8608:
8605:
8601:
8598:
8595:
8592:
8589:
8586:
8583:
8579:
8576:
8573:
8569:
8566:
8565:
8557:
8554:
8551:
8548:
8547:
8526:
8521:
8517:
8515:9780915567980
8511:
8507:
8502:
8498:
8496:0-13-359993-0
8492:
8488:
8483:
8479:
8477:0-387-18485-6
8473:
8469:
8464:
8463:
8454:
8450:
8446:
8442:
8438:
8434:
8430:
8423:
8408:
8401:
8395:
8380:
8373:
8354:
8350:
8344:
8340:
8333:
8326:
8324:
8322:
8320:
8311:
8307:
8303:
8297:
8293:
8292:
8284:
8282:
8280:
8271:
8265:
8261:
8254:
8252:
8250:
8248:
8246:
8244:
8229:on 2007-09-29
8228:
8224:
8219:
8213:
8211:
8202:
8196:
8192:
8176:
8167:
8163:
8153:
8150:
8148:
8145:
8143:
8142:Frost diagram
8140:
8138:
8135:
8133:
8130:
8128:
8125:
8123:
8120:
8119:
8098:
8093:
8075:
8070:
8055:
8050:
8035:
8030:
8015:
8010:
7995:
7990:
7975:
7970:
7969:
7963:
7936:
7932:
7925:
7922:
7919:
7916:
7913:
7910:
7903:
7902:
7901:
7898:
7896:
7889:
7881:
7877:
7865:
7857:
7839:
7835:
7832:
7826:
7821:
7817:
7791:
7787:
7776:
7773:
7768:
7763:
7759:
7753:
7747:
7742:
7738:
7731:
7727:
7721:
7718:
7715:
7708:
7707:
7706:
7693:
7679:
7675:
7661:
7659:
7655:
7651:
7647:
7643:
7639:
7635:
7625:
7622:
7598:
7595:
7592:
7589:
7586:
7575:
7567:
7566:
7545:
7540:
7536:
7532:
7527:
7523:
7519:
7508:
7500:
7499:
7498:
7496:
7465:
7456:
7453:
7442:
7433:
7430:
7411:
7398:
7389:
7381:
7380:
7379:
7358:
7349:
7346:
7327:
7319:
7314:
7305:
7291:
7282:
7274:
7273:
7272:
7267:
7262:
7239:
7236:
7233:
7222:
7214:
7213:
7192:
7187:
7183:
7179:
7176:
7165:
7157:
7156:
7155:
7153:
7149:
7145:
7141:
7118:
7109:
7106:
7087:
7074:
7065:
7062:
7051:
7042:
7034:
7033:
7032:
6997:
6984:
6975:
6972:
6967:
6958:
6950:
6949:
6948:
6943:
6938:
6931:
6930:overpotential
6927:
6923:
6919:
6914:
6905:
6904:–pH diagram.
6871:
6868:
6860:
6856:
6852:
6848:
6843:
6839:
6831:
6830:
6829:
6811:
6799:
6796:
6790:
6780:
6776:
6759:
6756:
6752:
6746:
6742:
6737:
6733:
6726:
6720:
6716:
6711:
6706:
6702:
6694:
6693:
6692:
6690:
6671:
6666:
6646:
6634:
6631:
6627:
6612:
6599:
6583:
6567:
6552:
6542:
6538:
6522:
6518:
6515:
6511:
6505:
6501:
6496:
6492:
6485:
6479:
6475:
6470:
6465:
6461:
6453:
6452:
6451:
6428:
6425:
6420:
6416:
6407:
6406:
6371:
6362:
6359:
6343:
6339:
6330:
6314:
6303:
6285:
6276:
6273:
6257:
6248:
6245:
6226:
6213:
6200:
6199:
6198:
6188:
6184:
6164:
6154:
6151:
6147:
6139:
6134:
6131:
6128:
6121:
6116:
6113:
6110:
6101:
6096:
6093:
6090:
6083:
6078:
6075:
6072:
6064:
6060:
6057:
6053:
6047:
6043:
6038:
6034:
6027:
6021:
6017:
6012:
6007:
6003:
5995:
5994:
5993:
5976:
5972:
5969:
5966:
5962:
5944:
5933:
5913:
5909:
5904:
5901:
5895:
5885:
5882:
5879:
5875:
5872:
5869:
5865:
5858:
5857:
5856:
5848:
5846:
5821:
5818:
5813:
5809:
5805:
5800:
5796:
5768:
5765:
5761:
5736:
5724:
5720:
5700:
5696:
5681:
5677:
5674:
5671:
5666:
5662:
5658:
5652:
5648:
5643:
5638:
5634:
5626:
5625:
5624:
5586:
5582:
5574:
5566:
5562:
5529:
5526:
5505:
5494:
5476:
5468:
5452:
5449:
5436:
5435:
5434:
5394:
5386:
5381:
5378:
5375:
5368:
5363:
5360:
5357:
5348:
5343:
5340:
5337:
5330:
5325:
5322:
5319:
5311:
5307:
5304:
5299:
5295:
5290:
5286:
5279:
5273:
5269:
5264:
5259:
5255:
5247:
5246:
5245:
5227:
5219:
5214:
5211:
5208:
5201:
5196:
5193:
5190:
5181:
5176:
5173:
5170:
5163:
5158:
5155:
5152:
5144:
5140:
5137:
5132:
5127:
5123:
5117:
5111:
5107:
5102:
5097:
5093:
5085:
5084:
5083:
5081:
5077:
5073:
5069:
5049:
5041:
5036:
5033:
5030:
5023:
5018:
5015:
5012:
5003:
4998:
4995:
4992:
4985:
4980:
4977:
4974:
4966:
4962:
4959:
4956:
4953:
4950:
4947:
4942:
4938:
4927:
4926:
4925:
4911:
4908:
4905:
4902:
4899:
4896:
4893:
4888:
4884:
4873:
4848:
4836:, but without
4831:
4828:
4825:
4818:
4814:
4811:
4808:
4804:
4786:
4775:
4755:
4751:
4746:
4743:
4740:
4736:
4733:
4730:
4726:
4719:
4718:
4717:
4707:
4689:
4684:
4676:
4665:
4661:
4648:
4643:
4639:
4636:
4633:
4627:
4624:
4621:
4614:
4610:
4599:
4593:
4590:
4585:
4582:
4570:
4569:
4568:
4537:
4532:
4524:
4508:
4493:
4483:
4479:
4455:
4442:
4427:
4423:
4420:
4417:
4411:
4408:
4405:
4398:
4394:
4383:
4377:
4374:
4369:
4366:
4354:
4353:
4352:
4327:
4318:
4315:
4312:
4307:
4303:
4262:
4253:
4250:
4231:
4218:
4197:
4186:
4151:
4142:
4139:
4123:
4119:
4110:
4102:
4101:
4100:
4090:
4086:
4081:
4063:
4053:
4050:
4046:
4038:
4033:
4030:
4027:
4020:
4015:
4012:
4009:
4000:
3995:
3992:
3989:
3982:
3977:
3974:
3971:
3963:
3959:
3956:
3952:
3947:
3944:
3941:
3938:
3935:
3930:
3926:
3915:
3914:
3913:
3895:
3887:
3882:
3876:
3867:
3860:
3855:
3852:
3849:
3842:
3837:
3834:
3831:
3822:
3817:
3814:
3811:
3804:
3799:
3796:
3793:
3785:
3781:
3778:
3775:
3772:
3769:
3766:
3761:
3757:
3746:
3745:
3744:
3722:
3717:
3711:
3702:
3695:
3690:
3687:
3684:
3677:
3672:
3669:
3666:
3657:
3652:
3649:
3646:
3639:
3634:
3631:
3628:
3620:
3617:
3610:
3609:
3608:
3606:
3586:
3583:
3580:
3577:
3574:
3571:
3568:
3563:
3559:
3532:
3528:
3525:
3522:
3518:
3500:
3489:
3468:
3458:
3455:
3452:
3448:
3445:
3442:
3438:
3431:
3430:
3429:
3427:
3423:
3403:
3393:
3369:
3365:
3361:
3355:
3351:
3343:
3338:
3335:
3332:
3325:
3320:
3317:
3314:
3305:
3300:
3297:
3294:
3287:
3282:
3279:
3276:
3268:
3264:
3261:
3256:
3253:
3248:
3243:
3234:
3230:
3221:
3217:
3212:
3208:
3200:
3199:
3198:
3182:
3178:
3169:
3151:
3147:
3138:
3120:
3116:
3107:
3103:
3085:
3081:
3066:
3042:
3033:
3015:
3011:
2984:
2945:
2935:
2920:
2915:
2912:
2907:
2902:
2899:
2873:
2842:
2838:
2834:
2828:
2824:
2816:
2808:
2800:
2792:
2782:
2774:
2766:
2758:
2749:
2745:
2742:
2737:
2734:
2729:
2724:
2715:
2711:
2702:
2698:
2693:
2689:
2681:
2680:
2679:
2677:
2673:
2665:
2647:
2643:
2639:
2636:
2633:
2628:
2624:
2613:
2586:
2583:
2578:
2574:
2571:
2565:
2561:
2553:
2545:
2537:
2529:
2519:
2511:
2503:
2495:
2486:
2482:
2479:
2473:
2470:
2465:
2462:
2456:
2451:
2442:
2438:
2429:
2425:
2420:
2416:
2408:
2407:
2406:
2390:
2386:
2377:
2365:
2347:
2343:
2313:
2310:
2303:
2299:
2289:
2286:
2270:
2261:
2253:
2252:
2251:
2235:
2226:
2218:
2197:
2193:
2186:
2182:
2178:
2173:
2169:
2161:
2160:
2159:
2143:
2139:
2116:
2112:
2089:
2085:
2075:
2073:
2069:
2053:
2041:
2037:
2029:
2005:
2000:
1994:
1985:
1978:
1973:
1970:
1967:
1960:
1955:
1952:
1949:
1940:
1935:
1932:
1929:
1922:
1917:
1914:
1911:
1893:
1883:
1879:
1870:
1860:
1856:
1847:
1837:
1833:
1822:
1812:
1808:
1799:
1789:
1785:
1775:
1767:
1762:
1756:
1747:
1740:
1730:
1727:
1723:
1711:
1706:
1703:
1700:
1693:
1683:
1679:
1667:
1662:
1659:
1656:
1649:
1639:
1635:
1624:
1619:
1616:
1613:
1606:
1596:
1592:
1580:
1575:
1572:
1569:
1562:
1552:
1548:
1538:
1530:
1519:
1505:
1497:
1489:
1481:
1471:
1463:
1455:
1447:
1438:
1435:
1428:
1427:
1426:
1405:
1401:
1398:
1395:
1391:
1373:
1362:
1342:
1338:
1333:
1330:
1324:
1314:
1311:
1308:
1304:
1301:
1298:
1294:
1287:
1286:
1285:
1283:
1279:
1276:(SHE). For a
1275:
1253:
1230:
1226:
1215:
1197:
1193:
1182:
1164:
1160:
1142:
1131:
1128:
1125:
1122:
1119:
1118:
1117:
1109:
1095:
1091:
1082:
1073:
1071:
1067:
1063:
1059:
1053:
1050:
1047:
1037:
1032:
1029:
1025:
1007:
1003:
993:
983:
979:
974:
970:
965:
961:
957:
946:
936:
929:
924:
920:
916:
913:
901:
900:
899:
897:
877:
874:
871:
866:
862:
853:
850:
849:
845:
829:
826:
823:
819:
815:
812:
809:
804:
800:
792:
791:
790:
773:
765:
757:
749:
741:
731:
723:
715:
707:
698:
695:
690:
687:
682:
677:
673:
669:
660:
652:
651:
650:
633:
625:
617:
609:
601:
591:
583:
575:
567:
558:
555:
550:
546:
541:
537:
530:
525:
521:
517:
508:
500:
499:
498:
481:
473:
465:
457:
449:
439:
431:
423:
415:
406:
403:
397:
394:
389:
386:
380:
375:
371:
367:
358:
350:
349:
334:
330:
326:
323:
317:
314:
309:
306:
300:
295:
291:
287:
278:
270:
269:
268:
251:
243:
235:
227:
219:
209:
201:
193:
185:
176:
173:
166:
165:
164:
159:
147:
146:
145:
143:
138:
136:
132:
128:
121:
111:
106:
98:
93:
84:
82:
78:
74:
69:
66:
65:reaction rate
62:
61:phase diagram
58:
54:
50:
49:pE/pH diagram
46:
38:
34:
30:
21:
8600:HYDRA/MEDUSA
8532:. Retrieved
8505:
8486:
8467:
8436:
8432:
8422:
8411:. Retrieved
8406:
8394:
8383:. Retrieved
8372:
8360:. Retrieved
8353:the original
8338:
8290:
8259:
8231:. Retrieved
8227:the original
8217:
8195:
8175:
8166:
8152:Bjerrum plot
7957:
7899:
7894:
7864:gas constant
7808:
7671:
7654:solid phases
7652:, or in the
7642:geochemistry
7633:
7631:
7628:Applications
7623:
7619:
7494:
7484:
7481:(at high pH)
7377:
7265:
7263:
7260:
7139:
7137:
7134:(at high pH)
7030:
6941:
6939:
6935:
6899:
6827:
6672:
6670:: = = 1.
6662:
6449:
6180:
5991:
5854:
5841:
5752:
5564:
5558:
5410:
5243:
5075:
5071:
5067:
5065:
4869:
4713:
4705:
4553:
4291:
4082:
4079:
3911:
3742:
3547:
3401:
3399:
3391:
3072:
3034:(SHE) whose
2936:
2864:
2675:
2667:
2609:
2405:as follows:
2331:
2250:is given by
2214:
2076:
2025:
1420:
1281:
1151:
1115:
1087:
1054:
1051:
1048:
1035:
1033:
1030:
1026:
1022:
893:
851:
788:
648:
496:
266:
155:
139:
119:
117:
104:
102:
70:
52:
48:
40:
36:
32:
26:
8362:12 February
7900:Moreover,
7674:hydrosphere
7664:Concept of
7027:(at low pH)
6183:ferrous ion
3426:protonation
1112:Limitations
1062:Passivation
890: volt.
45:–pH diagram
8654:Categories
8614:Outotec Oy
8534:2017-05-16
8413:2017-03-29
8385:2017-03-29
8381:. SubsTech
8348:0471157775
8233:2007-09-29
8187:References
7640:problems,
4292:which has
2070:, and the
2028:activities
8620:PhreePlot
8453:104177121
8310:663096583
7937:−
7926:
7920:−
7748:λ
7694:scale.
7692:logarithm
7638:corrosion
7596:−
7546:λ
7533:−
7466:−
7404:⟶
7399:−
7359:−
7303:⟶
7237:−
7193:λ
7180:−
7119:−
7080:⟶
7075:−
6990:⟶
6985:−
6857:−
6760:
6743:λ
6727:−
6721:∘
6519:
6502:λ
6486:−
6480:∘
6421:∘
6322:⇀
6315:−
6304:−
6297:↽
6286:−
6061:
6044:λ
6028:−
6022:∘
5952:⇀
5945:−
5934:−
5927:↽
5914:−
5814:∘
5766:−
5678:
5672:λ
5659:−
5653:∘
5513:⇀
5506:−
5495:−
5488:↽
5477:−
5308:
5296:λ
5280:−
5274:∘
5141:
5118:−
5112:∘
4963:
4951:−
4943:∘
4935:Δ
4909:
4897:−
4889:∘
4881:Δ
4794:⇀
4787:−
4776:−
4769:↽
4756:−
4640:
4628:λ
4615:∘
4607:Δ
4586:−
4424:
4412:λ
4399:∘
4391:Δ
4370:−
4316:−
4308:∘
4300:Δ
4205:⇀
4198:−
4187:−
4180:↽
3960:
3948:λ
3939:−
3931:∘
3923:Δ
3782:
3770:−
3762:∘
3754:Δ
3584:
3572:−
3564:∘
3556:Δ
3508:⇀
3501:−
3490:−
3483:↽
3356:−
3265:
3249:−
3244:⊖
3148:γ
3104:, or the
2900:−
2829:−
2746:
2730:−
2725:⊖
2566:−
2483:
2457:−
2452:⊖
2348:⊖
2340:Δ
2304:⊖
2296:Δ
2290:−
2271:⊖
2236:⊖
2183:γ
2140:γ
2054:γ
1880:γ
1857:γ
1834:γ
1809:γ
1786:γ
1724:γ
1680:γ
1636:γ
1593:γ
1549:γ
1381:⇀
1374:−
1363:−
1356:↽
1343:−
1278:half cell
1094:carbonate
1066:aluminium
1058:corrosion
971:
930:
917:−
875:≈
872:λ
827:≈
699:
683:−
559:
547:λ
531:−
407:
381:−
327:
301:−
8578:FactSage
8562:Software
8116:See also
7148:fugacity
6881:in volts
6187:hematite
5074:, where
4089:hematite
3599:, where
2366:change,
1044: Pa
789:where:
125:for the
8628:PHREEQC
8568:ChemEQL
7966:Gallery
7892:
7858:, with
7854:is the
7809:Where,
7769:0.05916
7599:0.05916
7240:0.05916
6686:
6185:Fe and
5078:is the
3603:is the
3362:0.05916
3254:0.05916
2903:0.05916
2835:0.05916
2735:0.05916
2660:
2616:
2374:is the
1070:alumina
878:0.05916
830:0.02569
688:0.05916
114:Diagram
81:chemist
77:Russian
8512:
8493:
8474:
8451:
8409:. 1962
8345:
8308:
8298:
8266:
7886:, the
7880:Kelvin
7874:, the
7862:, the
7782:×
7777:16.903
7644:, and
6865:
6861:0.1775
6853:1.0826
6803:
6763:
6638:
5623:ions:
4840:
4319:8242.5
4085:ferric
3743:Thus:
3416:, and
2968:into H
2676:λ
2672:λ
2332:where
1903:×
1717:
1673:
1586:
1140:etc.).
1090:ligand
87:Naming
8644:NERSC
8626:code
8572:Eawag
8528:(PDF)
8449:S2CID
8403:(PDF)
8356:(PDF)
8335:(PDF)
8158:Notes
7590:1.229
7378:and,
7031:and,
6429:0.728
6408:with
5822:0.771
5561:redox
3106:molal
3102:molar
2040:molal
2036:molar
1216:plot)
55:, at
47:or a
8624:USGS
8510:ISBN
8491:ISBN
8472:ISBN
8364:2021
8343:ISBN
8306:OCLC
8296:ISBN
8264:ISBN
8104:Ti–H
8085:O–CO
8081:Zn–H
8061:Mn–H
8041:Al–H
8021:Au–H
8001:Cu–H
7981:Fe–H
7634:e.g.
6684:and
5612:and
5072:-zFE
4829:>
2280:volt
2158:):
1282:i.e.
1179:and
1152:The
53:i.e.
8604:KTH
8441:doi
7923:log
7878:in
7870:),
6922:SHE
6757:log
6516:log
6058:log
5675:log
5305:log
4637:log
4421:log
3957:log
3607::
3262:log
3239:red
3226:red
3063:gas
3047:red
2989:red
2950:red
2878:red
2743:log
2720:red
2707:red
2664:STP
2480:log
2447:red
2434:red
2266:red
2231:red
2046:),
2038:or
1258:red
1042:325
1040:101
962:log
921:log
696:log
556:log
163::
144::
27:In
8656::
8447:.
8435:.
8431:.
8405:.
8318:^
8304:.
8278:^
8242:^
8209:^
7959:pe
7696:pe
7681:pe
7666:pe
7660:.
7636:,
7604:pH
7551:pH
7493:/2
7395:OH
7245:pH
7198:pH
7115:OH
6926:pH
6807:pH
6773:Fe
6675:Fe
6642:pH
6596:Fe
6535:Fe
6353:aq
6336:Fe
6267:aq
6210:Fe
6189:Fe
6160:pH
5762:10
5717:Fe
5693:Fe
5614:Fe
5603:Fe
5539:aq
5523:Fe
5462:aq
5446:Fe
5424:Fe
5413:Fe
5138:ln
5070:=
5068:∆G
4960:ln
4924::
4906:ln
4658:Fe
4579:pH
4567::
4558:Fe
4476:Fe
4439:Fe
4363:pH
4272:aq
4215:Fe
4133:aq
4116:Fe
4091:Fe
4059:pH
3779:ln
3581:ln
3412:,
3408:,
3376:pH
2976:.
2849:pH
2614:)
2594:pH
1218:.
1214:pH
1212:–
1181:pH
1138:Cl
1136:,
1134:Cl
1101:2−
1098:CO
966:10
925:10
910:pH
896:pH
404:ln
324:ln
39:,
8646:.
8630:.
8616:.
8584:.
8574:.
8537:.
8518:.
8499:.
8480:.
8455:.
8443::
8437:9
8416:.
8388:.
8366:.
8312:.
8272:.
8236:.
8203:.
8108:O
8106:2
8087:3
8083:2
8065:O
8063:2
8045:O
8043:2
8025:O
8023:2
8005:O
8003:2
7985:O
7983:2
7942:]
7933:e
7929:[
7917:=
7914:e
7911:p
7895:e
7884:F
7872:T
7866:(
7860:R
7840:F
7836:T
7833:R
7827:=
7822:T
7818:V
7792:H
7788:E
7774:=
7764:H
7760:E
7754:=
7743:T
7739:V
7732:H
7728:E
7722:=
7719:e
7716:p
7702:H
7700:E
7687:H
7685:E
7593:V
7587:=
7581:H
7576:E
7541:T
7537:V
7528:0
7524:E
7520:=
7514:H
7509:E
7495:F
7491:O
7489:2
7487:H
7462:e
7457:4
7454:+
7451:O
7443:2
7439:H
7434:2
7431:+
7427:)
7424:g
7421:(
7412:2
7408:O
7390:4
7355:e
7350:4
7347:+
7343:)
7340:g
7337:(
7328:2
7324:O
7320:+
7315:+
7311:H
7306:4
7300:O
7292:2
7288:H
7283:2
7269:H
7266:E
7234:=
7228:H
7223:E
7188:T
7184:V
7177:=
7171:H
7166:E
7140:E
7110:2
7107:+
7103:)
7100:g
7097:(
7088:2
7084:H
7071:e
7066:2
7063:+
7060:O
7052:2
7048:H
7043:2
7013:)
7010:g
7007:(
6998:2
6994:H
6981:e
6976:2
6973:+
6968:+
6964:H
6959:2
6945:H
6942:E
6902:h
6885:)
6877:(
6872:H
6869:p
6849:=
6844:h
6840:E
6812:)
6800:6
6797:+
6791:2
6786:]
6781:+
6777:2
6769:[
6753:(
6747:2
6738:T
6734:V
6717:E
6712:=
6707:h
6703:E
6689:H
6668:K
6647:)
6635:6
6632:+
6628:)
6621:]
6613:3
6609:O
6600:2
6592:[
6584:3
6579:]
6576:O
6568:2
6564:H
6560:[
6553:2
6548:]
6543:+
6539:2
6531:[
6523:(
6512:(
6506:2
6497:T
6493:V
6476:E
6471:=
6466:h
6462:E
6446:.
6433:V
6426:=
6417:E
6390:)
6387:l
6384:(
6380:O
6372:2
6368:H
6363:3
6360:+
6356:)
6350:(
6344:+
6340:2
6331:2
6282:e
6277:2
6274:+
6270:)
6264:(
6258:+
6254:H
6249:6
6246:+
6242:)
6239:s
6236:(
6227:3
6223:O
6214:2
6195:3
6193:O
6191:2
6165:)
6155:h
6152:+
6148:)
6140:b
6135:]
6132:B
6129:[
6122:a
6117:]
6114:A
6111:[
6102:d
6097:]
6094:D
6091:[
6084:c
6079:]
6076:C
6073:[
6065:(
6054:(
6048:z
6039:T
6035:V
6018:E
6013:=
6008:h
6004:E
5977:D
5973:d
5970:+
5967:C
5963:c
5910:e
5905:z
5902:+
5896:+
5892:H
5886:h
5883:+
5880:B
5876:b
5873:+
5870:A
5866:a
5844:h
5842:E
5827:V
5819:=
5810:E
5806:=
5801:h
5797:E
5775:M
5769:6
5737:)
5730:]
5725:+
5721:3
5713:[
5706:]
5701:+
5697:2
5689:[
5682:(
5667:T
5663:V
5649:E
5644:=
5639:h
5635:E
5587:T
5583:V
5569:h
5565:E
5542:)
5536:(
5530:+
5527:2
5473:e
5469:+
5465:)
5459:(
5453:+
5450:3
5422:/
5395:)
5387:b
5382:]
5379:B
5376:[
5369:a
5364:]
5361:A
5358:[
5349:d
5344:]
5341:D
5338:[
5331:c
5326:]
5323:C
5320:[
5312:(
5300:z
5291:T
5287:V
5270:E
5265:=
5260:h
5256:E
5228:)
5220:b
5215:]
5212:B
5209:[
5202:a
5197:]
5194:A
5191:[
5182:d
5177:]
5174:D
5171:[
5164:c
5159:]
5156:C
5153:[
5145:(
5133:z
5128:T
5124:V
5108:E
5103:=
5098:h
5094:E
5076:F
5050:)
5042:b
5037:]
5034:B
5031:[
5024:a
5019:]
5016:A
5013:[
5004:d
4999:]
4996:D
4993:[
4986:c
4981:]
4978:C
4975:[
4967:(
4957:T
4954:R
4948:=
4939:G
4912:K
4903:T
4900:R
4894:=
4885:G
4855:)
4849:+
4845:H
4832:0
4826:z
4823:(
4819:D
4815:d
4812:+
4809:C
4805:c
4752:e
4747:z
4744:+
4741:B
4737:b
4734:+
4731:A
4727:a
4690:)
4685:)
4677:2
4673:]
4666:+
4662:3
4653:[
4649:1
4644:(
4634:+
4625:T
4622:R
4611:G
4600:(
4594:6
4591:1
4583:=
4538:)
4533:)
4525:3
4520:]
4517:O
4509:2
4505:H
4501:[
4494:2
4489:]
4484:+
4480:3
4472:[
4464:]
4456:3
4452:O
4443:2
4435:[
4428:(
4418:+
4409:T
4406:R
4395:G
4384:(
4378:6
4375:1
4367:=
4338:l
4335:o
4332:m
4328:/
4324:J
4313:=
4304:G
4275:)
4269:(
4263:+
4259:H
4254:6
4251:+
4247:)
4244:s
4241:(
4232:3
4228:O
4219:2
4170:)
4167:l
4164:(
4160:O
4152:2
4148:H
4143:3
4140:+
4136:)
4130:(
4124:+
4120:3
4111:2
4097:3
4095:O
4093:2
4064:)
4054:h
4051:+
4047:)
4039:b
4034:]
4031:B
4028:[
4021:a
4016:]
4013:A
4010:[
4001:d
3996:]
3993:D
3990:[
3983:c
3978:]
3975:C
3972:[
3964:(
3953:(
3945:T
3942:R
3936:=
3927:G
3896:)
3888:h
3883:]
3877:+
3873:H
3868:[
3861:b
3856:]
3853:B
3850:[
3843:a
3838:]
3835:A
3832:[
3823:d
3818:]
3815:D
3812:[
3805:c
3800:]
3797:C
3794:[
3786:(
3776:T
3773:R
3767:=
3758:G
3723:h
3718:]
3712:+
3708:H
3703:[
3696:b
3691:]
3688:B
3685:[
3678:a
3673:]
3670:A
3667:[
3658:d
3653:]
3650:D
3647:[
3640:c
3635:]
3632:C
3629:[
3621:=
3618:K
3601:K
3587:K
3578:T
3575:R
3569:=
3560:G
3533:D
3529:d
3526:+
3523:C
3519:c
3469:+
3465:H
3459:h
3456:+
3453:B
3449:b
3446:+
3443:A
3439:a
3418:D
3414:C
3410:B
3406:A
3402:z
3370:z
3366:h
3352:)
3344:b
3339:]
3336:B
3333:[
3326:a
3321:]
3318:A
3315:[
3306:d
3301:]
3298:D
3295:[
3288:c
3283:]
3280:C
3277:[
3269:(
3257:z
3235:E
3231:=
3222:E
3218:=
3213:h
3209:E
3183:i
3179:C
3152:i
3139:(
3121:i
3117:C
3086:i
3082:a
3043:E
3016:h
3012:E
2985:E
2974:2
2970:2
2966:2
2946:E
2921:)
2916:z
2913:h
2908:(
2874:E
2843:z
2839:h
2825:)
2817:b
2813:}
2809:B
2806:{
2801:a
2797:}
2793:A
2790:{
2783:d
2779:}
2775:D
2772:{
2767:c
2763:}
2759:C
2756:{
2750:(
2738:z
2716:E
2712:=
2703:E
2699:=
2694:h
2690:E
2670:T
2668:V
2648:F
2644:/
2640:T
2637:R
2634:=
2629:T
2625:V
2587:F
2584:z
2579:h
2575:T
2572:R
2562:)
2554:b
2550:}
2546:B
2543:{
2538:a
2534:}
2530:A
2527:{
2520:d
2516:}
2512:D
2509:{
2504:c
2500:}
2496:C
2493:{
2487:(
2474:F
2471:z
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2443:E
2439:=
2430:E
2426:=
2421:h
2417:E
2391:h
2387:E
2372:F
2368:z
2344:G
2314:F
2311:z
2300:G
2287:=
2284:)
2276:(
2262:E
2227:E
2198:i
2194:C
2187:i
2179:=
2174:i
2170:a
2144:i
2117:i
2113:C
2090:i
2086:a
2044:C
2032:a
2030:(
2006:h
2001:]
1995:+
1991:H
1986:[
1979:b
1974:]
1971:B
1968:[
1961:a
1956:]
1953:A
1950:[
1941:d
1936:]
1933:D
1930:[
1923:c
1918:]
1915:C
1912:[
1894:h
1890:)
1884:h
1876:(
1871:b
1867:)
1861:b
1853:(
1848:a
1844:)
1838:a
1830:(
1823:d
1819:)
1813:d
1805:(
1800:c
1796:)
1790:c
1782:(
1776:=
1768:h
1763:]
1757:+
1753:H
1748:[
1741:h
1737:)
1731:+
1728:h
1720:(
1712:b
1707:]
1704:B
1701:[
1694:b
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1668:a
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1660:A
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1650:a
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1625:d
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1617:D
1614:[
1607:d
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1597:d
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1581:c
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1573:C
1570:[
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1553:c
1545:(
1539:=
1531:h
1527:}
1520:+
1516:H
1511:{
1506:b
1502:}
1498:B
1495:{
1490:a
1486:}
1482:A
1479:{
1472:d
1468:}
1464:D
1461:{
1456:c
1452:}
1448:C
1445:{
1439:=
1436:K
1423:K
1406:D
1402:d
1399:+
1396:C
1392:c
1339:e
1334:z
1331:+
1325:+
1321:H
1315:h
1312:+
1309:B
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1302:+
1299:A
1295:a
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1165:h
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1104:3
1096:(
1036:P
1008:.
1004:)
994:+
990:H
984:a
980:1
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958:=
955:)
947:+
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937:a
933:(
914:=
867:T
863:V
852:λ
824:F
820:/
816:T
813:R
810:=
805:T
801:V
774:,
766:b
762:]
758:B
755:[
750:a
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742:A
739:[
732:d
728:]
724:D
721:[
716:c
712:]
708:C
705:[
691:z
678:0
674:E
670:=
665:H
661:E
634:,
626:b
622:]
618:B
615:[
610:a
606:]
602:A
599:[
592:d
588:]
584:D
581:[
576:c
572:]
568:C
565:[
551:z
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538:V
526:0
522:E
518:=
513:H
509:E
482:,
474:b
470:]
466:B
463:[
458:a
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450:A
447:[
440:d
436:]
432:D
429:[
424:c
420:]
416:C
413:[
398:F
395:z
390:T
387:R
376:0
372:E
368:=
363:H
359:E
335:,
331:K
318:F
315:z
310:T
307:R
296:0
292:E
288:=
283:H
279:E
252:,
244:b
240:]
236:B
233:[
228:a
224:]
220:A
217:[
210:d
206:]
202:D
199:[
194:c
190:]
186:C
183:[
177:=
174:K
161:K
123:H
120:E
108:H
105:E
43:H
41:E
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