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37-585: The diagrams are named after Marcel Pourbaix (1904–1998), the Russian -born Belgian chemist who invented them. Pourbaix diagrams are also known as E H -pH diagrams due to the labeling of the two axes. The vertical axis is labeled E H for the voltage potential with respect to the standard hydrogen electrode (SHE) as calculated by the Nernst equation . The "H" stands for hydrogen, although other standards may be used, and they are for room temperature only. For

74-449: A red ) and the oxidized form (the oxidant , a ox ). Considering the 2 H / H 2 redox couple: at chemical equilibrium , the ratio Q r of the reaction products by the reagents is equal to the equilibrium constant K of the half-reaction: where More details on managing gas fugacity to get rid of the pressure unit in thermodynamic calculations can be found at thermodynamic activity#Gases . The followed approach

111-391: A linear relationship with the activity coefficient ( γ i {\displaystyle \gamma _{i}} ): The half-cell standard reduction potential E red ⊖ {\displaystyle E_{\text{red}}^{\ominus }} is given by where Δ G ⊖ {\displaystyle \Delta G^{\ominus }}

148-561: A metal corrosion potential estimation they have, however, some important limitations: The E h {\displaystyle E_{h}} and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram ( E h {\displaystyle E_{h}} – pH plot) . E h {\displaystyle E_{h}} explicitly denotes E red {\displaystyle E_{\text{red}}} expressed versus

185-406: A platinized platinum electrode. The electrode is immersed in the acidic solution and pure hydrogen gas is bubbled over its surface. The concentration of both the reduced and oxidised forms of hydrogen are maintained at unity. That implies that the pressure of hydrogen gas is 1 bar (100 kPa) and the activity coefficient of hydrogen ions in the solution is unity. The activity of hydrogen ions

222-491: A platinum electrode into a solution of 1  N strong acid and [bubbling] hydrogen gas through the solution at about 1 atm pressure". However, this electrode/solution interface was later changed. What replaced it was a theoretical electrode/solution interface, where the concentration of H was 1  M , but the H ions were assumed to have no interaction with other ions (a condition not physically attainable at those concentrations). To differentiate this new standard from

259-454: A platinum surface, and these also have to be avoided. Cations that can be reduced and deposited on the platinum can be source of interference: silver , mercury , copper , lead , cadmium and thallium . Substances that can inactivate ("poison") the catalytic sites include arsenic , sulfides and other sulfur compounds, colloidal substances, alkaloids , and material found in biological systems . The standard redox potential of

296-470: A reversible redox reaction described by the following chemical equilibrium : With the corresponding equilibrium constant K : The Nernst equation is: sometimes formulated as: or, more simply directly expressed numerically as: where: The horizontal axis is labeled pH for the −log function of the H ion activity. The lines in the Pourbaix diagram show the equilibrium conditions, that is, where

333-500: A similar function such as the palladium-hydrogen electrode . Because of the high adsorption activity of the platinized platinum electrode , it's very important to protect electrode surface and solution from the presence of organic substances as well as from atmospheric oxygen . Inorganic ions that can be reduced to a lower valency state at the electrode also have to be avoided (e.g., Fe , CrO 4 ). A number of organic substances are also reduced by hydrogen on

370-425: A specific environment. Immunity means that the metal is not attacked, while corrosion shows that general attack will occur. Passivation 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 aluminium because of the alumina layer formed on its surface when exposed to air. While such diagrams can be drawn for any chemical system, it

407-435: Is important to note that the addition of a metal binding agent ( ligand ) will often modify the diagram. For instance, carbonate ( CO 2− 3 ) 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. Even though Pourbaix diagrams are useful for

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444-487: Is not affected by the electrode potential. In this case, the reaction is a classical acid-base reaction involving only protonation /deprotonation of dissolved species. The boundary line will be a vertical line at a particular value of pH. The reaction equation may be written: and the energy balance is written as Δ G ∘ = − R T ln ⁡ K {\displaystyle \Delta G^{\circ }=-RT\ln K} , where K

481-556: Is observed for the reduction of O 2 into H 2 O, or OH, and for reduction of H into H 2 . E red {\displaystyle E_{\text{red}}} is then often noted as E h {\displaystyle E_{h}} to indicate that it refers to the standard hydrogen electrode (SHE) whose E red {\displaystyle E_{\text{red}}} = 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P gas = 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0). When

518-493: Is the equilibrium constant : Thus: or, in base-10 logarithms, which may be solved for the particular value of pH. For example consider the iron and water system, and the equilibrium line between the ferric ion Fe ion and hematite Fe 2 O 3 . The reaction equation is: which has Δ G ∘ = − 8242.5 J / m o l {\displaystyle \Delta G^{\circ }=-8242.5\,\mathrm {J/mol} } . The pH of

555-562: Is the same as for chemical activity and molar concentration of solutes in solution. In the SHE, pure hydrogen gas ( x H 2 = 1 {\displaystyle x_{\mathrm {H_{2}} }=1} ) at the standard pressure p {\displaystyle p} of 1 bar is engaged in the system. Meanwhile the general SHE equation can also be applied to other thermodynamic systems with different mole fraction or total pressure of hydrogen. This redox reaction occurs at

592-452: Is the standard Gibbs free energy change, z is the number of electrons involved, and F is the Faraday's constant . The Nernst equation relates pH and E h {\displaystyle E_{h}} as follows: In the following, the Nernst slope (or thermal voltage ) ⁠ V T = R T / F {\displaystyle V_{T}=RT/F} ⁠

629-717: Is their effective concentration, which is equal to the formal concentration times the activity coefficient . These unit-less activity coefficients are close to 1.00 for very dilute water solutions, but usually lower for more concentrated solutions. As the general form of the Nernst equation at equilibrium is the following: E cell = E cell ⊖ − R T z F ln ⁡ K {\displaystyle E_{\text{cell}}=E_{\text{cell}}^{\ominus }-{\frac {RT}{zF}}\ln K} and as E cell ⊖ = 0 {\displaystyle E_{\text{cell}}^{\ominus }=0} by definition in

666-475: Is thus written: As, the standard Gibbs free energy Δ G ∘ = − R T ln ⁡ K {\displaystyle \Delta G^{\circ }=-RT\ln K} : Using the definition of the electrode potential ∆G = -zFE , where F is the Faraday constant , this may be rewritten as a Nernst equation: or, using base-10 logarithms: For the equilibrium Fe / Fe , taken as example here, considering

703-616: Is used, which has a value of 0.02569... V at STP . When base-10 logarithms are used, V T λ = 0.05916... V at STP where λ = ln[10] = 2.3026. This equation is the equation of a straight line for E red {\displaystyle E_{\text{red}}} as a function of pH with a slope of − 0.05916 ( h z ) {\displaystyle -0.05916\,\left({\frac {h}{z}}\right)} volt (pH has no units). This equation predicts lower E red {\displaystyle E_{\text{red}}} at higher pH values. This

740-587: The Fe and Fe ions: For both ionic species at the same concentration (e.g., 10 − 6 M {\displaystyle 10^{-6}\mathrm {M} } ) at STP, log 1 = 0, so, E h = E ∘ = 0.771 V {\displaystyle E_{h}=E^{\circ }=0.771\,\mathrm {V} } , and the boundary will be a horizontal line at E h = 0.771 volts. The potential will vary with temperature. In this case, both electrons and H ions are involved and

777-469: The activity coefficients , and the stoichiometric coefficients are shown as exponents. 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 ( a i {\displaystyle a_{i}} ) can be related to the measurable concentration ( C i {\displaystyle C_{i}} ) by

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814-442: The standard hydrogen electrode (SHE). For a half cell equation, conventionally written as a reduction reaction ( i.e. , electrons accepted by an oxidant on the left side): The equilibrium constant K of this reduction reaction is: where curly braces { } indicate activities ( a ), rectangle braces [ ] denote molar or molal concentrations ( C ), γ {\displaystyle \gamma } represent

851-420: The thermodynamic scale of oxidation-reduction potentials . Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential ( E ° ) is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at

888-487: The Nernst equation implicitly takes into account the Henry's law for gas dissolution. Therefore, there is no need to independently consider the gas dissolution process in the system, as it is already de facto included. During the early development of electrochemistry, researchers used the normal hydrogen electrode as their standard for zero potential. This was convenient because it could actually be constructed by "[immersing]

925-481: The Wikimedia System Administrators, please include the details below. Request from 172.68.168.226 via cp1108 cp1108, Varnish XID 768385768 Upstream caches: cp1108 int Error: 429, Too Many Requests at Fri, 29 Nov 2024 05:52:54 GMT Standard hydrogen electrode In electrochemistry , the standard hydrogen electrode (abbreviated SHE ), is a redox electrode which forms the basis of

962-406: The activities ( a i {\displaystyle a_{i}} ) can be considered as equal to the molar , or the molal , concentrations ( C i {\displaystyle C_{i}} ) at sufficiently diluted concentrations when the activity coefficients ( γ i {\displaystyle \gamma _{i}} ) tend to one, the term regrouping all

999-494: 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. 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 used for all species present in

1036-439: The activity coefficients is equal to one, and the Nernst equation can be written simply with the concentrations ( C i {\displaystyle C_{i}} ) denoted here with square braces [ ]: There are three types of line boundaries in a Pourbaix diagram: Vertical, horizontal, and sloped. When no electrons are exchanged ( z = 0), the equilibrium between A , B , C , and D only depends on [H] and

1073-419: The boundary line between Fe and Fe, the half-reaction equation is: Since H ions are not involved in this redox reaction, it is independent of pH. E = 0.771 V with only one electron involved in the redox reaction. The potential E h is a function of temperature via the thermal voltage V T {\displaystyle V_{T}} and directly depends on the ratio of the concentrations of

1110-740: The case of the SHE, The Nernst equation for the SHE becomes: Simply neglecting the pressure unit present in p H 2 {\displaystyle p_{\mathrm {H_{2}} }} , this last equation can often be directly written as: And by solving the numerical values for the term the practical formula commonly used in the calculations of this Nernst equation is: As under standard conditions p H 2 = 1  bar, {\displaystyle p_{\mathrm {H_{2}} }=1{\text{ bar,}}} log ⁡ p H 2 = log ⁡ 1 = 0 , {\displaystyle \log p_{\mathrm {H_{2}} }=\log 1=0,}

1147-424: The electrode potential is a function of pH. The reaction equation may be written: Using the expressions for the free energy in terms of potentials, the energy balance is given by a Nernst equation: For the iron and water example, considering the boundary line between the ferrous ion Fe and hematite Fe 2 O 3 , the reaction equation is: Marcel Pourbaix Too Many Requests If you report this error to

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1184-431: The equation simplifies to: This last equation describes the straight line with a negative slope of -0.0591 volt/ pH unit delimiting the lower stability region of water in a Pourbaix diagram where gaseous hydrogen is evolving because of water decomposition. where: Note : as the system is at chemical equilibrium , hydrogen gas, H 2 (g) , is also in equilibrium with dissolved hydrogen, H 2 (aq) , and

1221-407: The equilibrium lines in accordance with the Nernst equation. 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. 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

1258-511: The previous one, it was given the name 'standard hydrogen electrode'. Finally, there are also reversible hydrogen electrodes (RHEs), which are practical hydrogen electrodes whose potential depends on the pH of the solution. In summary, The choice of platinum for the hydrogen electrode is due to several factors: The surface of platinum is platinized (i.e., covered with a layer of fine powdered platinum also known as platinum black ) to: Other metals can be used for fabricating electrodes with

1295-406: The same temperature. The hydrogen electrode is based on the redox half cell corresponding to the reduction of two hydrated protons , 2H (aq) , into one gaseous hydrogen molecule, H 2(g) . General equation for a reduction reaction: The reaction quotient ( Q r ) of the half-reaction is the ratio between the chemical activities ( a ) of the reduced form (the reductant ,

1332-512: The system. For soluble species, the lines are often drawn for concentrations of 1 M or 10 M. Sometimes additional lines are drawn for other concentrations. If the diagram involves the equilibrium between a dissolved species and a gas, the pressure is usually set to P = 1 atm = 101 325  Pa , the minimum pressure required for gas evolution from an aqueous solution at standard conditions. In addition, changes in temperature and concentration of solvated ions in solution will shift

1369-450: The vertical line on the Pourbaix diagram can then be calculated: Because the activities (or the concentrations) of the solid phases and water are equal to unity: [Fe 2 O 3 ] = [H 2 O] = 1, the pH only depends on the concentration in dissolved Fe : At STP, for [Fe] = 10, this yields pH = 1.76. When H and OH ions are not involved in the reaction, the boundary line is horizontal and independent of pH. The reaction equation

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