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Absolute electrode potential

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Absolute electrode potential, in <a href="Electrochemistry" title="Electrochemistry">electrochemistry</a>, according to an <a href="IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a> definition,<a href="#cite_note-1">[1]</a> is the <a href="Electrode_potential" title="Electrode potential">electrode potential</a> of a <a href="Metal" title="Metal">metal</a> measured with respect to a universal reference system (without any additional metal–solution interface).

<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>

According to a more specific definition presented by Trasatti,<a href="#cite_note-2">[2]</a> the absolute electrode potential is the difference in electronic energy between a point inside the metal (<a href="Fermi_level" title="Fermi level">Fermi level</a>) of an <a href="Electrode" title="Electrode">electrode</a> and a point outside the <a href="Electrolyte" title="Electrolyte">electrolyte</a> in which the electrode is submerged (an electron at rest in vacuum just above the electrolyte surface).

This potential is difficult to determine accurately. For this reason, a <a href="Standard_hydrogen_electrode" title="Standard hydrogen electrode">standard hydrogen electrode</a> is typically used for reference potential. The absolute potential of the SHE is 4.44 ± 0.02 <a href="Volt" title="Volt">V</a> at 25 <a href="%C2%B0C" class="mw-redirect" title="°C">°C</a>. Therefore, for any electrode at 25 °C:

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<annotation encoding="application/x-tex">{\displaystyle E_{\rm {(abs)}}^{M}=E_{\rm {(SHE)}}^{M}+(4.44\pm 0.02)\ {\mathrm {V} }}</annotation>

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</math><img src="./b3d61985cbb47811e938d1391777883262997cb7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:33.284ex; height:3.676ex;" alt="{\displaystyle E_{\rm {(abs)}}^{M}=E_{\rm {(SHE)}}^{M}+(4.44\pm 0.02)\ {\mathrm {V} }}" loading="lazy"></dd></dl>

where:

<dl><dd>E is electrode potential</dd>

<dd>M denotes the electrode made of metal M</dd>

<dd>(abs) denotes the absolute potential</dd>

<dd>(SHE) denotes the electrode potential relative to the standard hydrogen electrode.</dd></dl>

A different definition for the absolute electrode potential (also known as absolute half-cell potential and single electrode potential) has also been discussed in the literature.<a href="#cite_note-3">[3]</a> In this approach, one first defines an isothermal absolute single-electrode process (or absolute half-cell process.) For example, in the case of a generic metal being oxidized to form a solution-phase ion, the process would be

<dl><dd>M(metal) → M+(solution) + <a href="Electron" title="Electron">e− </a>(gas)</dd></dl>

For the <a href="Hydrogen" title="Hydrogen">hydrogen</a> electrode, the absolute half-cell process would be

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</style>⁠1/2⁠H2 (gas) → <a href="Hydron_(chemistry)" class="mw-redirect" title="Hydron (chemistry)">H+</a>(solution) + e− (gas)</dd></dl>

Other types of absolute electrode reactions would be defined analogously.

In this approach, all three species taking part in the reaction, including the electron, must be placed in thermodynamically well-defined states. All species, including the electron, are at the same temperature, and appropriate standard states for all species, including the electron, must be fully defined. The absolute electrode potential is then defined as the <a href="Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> for the absolute electrode process. To express this in volts one divides the Gibbs free energy by the negative of Faraday's constant.

Rockwood's approach to absolute-electrode thermodynamics is easily expendable to other thermodynamic functions. For example, the absolute half-cell entropy has been defined as the entropy of the absolute half-cell process defined above.<a href="#cite_note-4">[4]</a> An alternative definition of the absolute half-cell entropy has recently been published by Fang et al.<a href="#cite_note-5">[5]</a> who define it as the entropy of the following reaction (using the hydrogen electrode as an example):

<dl><dd>⁠1/2⁠H2 (gas) → H+(solution) + e− (metal)</dd></dl>

This approach differs from the approach described by Rockwood in the treatment of the electron, i.e. whether it is placed in the gas phase or the metal. The electron can also be in another state, that of a <a href="Solvated_electron" title="Solvated electron">solvated electron</a> in solution, as studied by <a href="Alexander_Frumkin" title="Alexander Frumkin">Alexander Frumkin</a> and B. Damaskin<a href="#cite_note-6">[6]</a> and others.

<div class="mw-heading mw-heading2"><h2 id="Determination">Determination</h2></div>

The basis for determination of the absolute electrode potential under the Trasatti definition is given by the equation:

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<annotation encoding="application/x-tex">{\displaystyle E^{M}{\rm {(abs)}}=\phi ^{M}+\Delta _{S}^{M}\psi }</annotation>

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</math><img src="./6f4c84251bf2aa8a19bee8bde59ebb45d6d963cb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.625ex; height:3.343ex;" alt="{\displaystyle E^{M}{\rm {(abs)}}=\phi ^{M}+\Delta _{S}^{M}\psi }" loading="lazy"></dd></dl>

where:

<dl><dd>EM(abs) is the absolute potential of the electrode made of metal M</dd>

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<annotation encoding="application/x-tex">{\displaystyle \phi ^{M}}</annotation>

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</math><img src="./3bc243370b3c02a558b372e87e74384da29dbcf4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.345ex; height:3.009ex;" alt="{\displaystyle \phi ^{M}}" loading="lazy"> is the electron <a href="Work_function" title="Work function">work function</a> of metal M</dd>

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<annotation encoding="application/x-tex">{\displaystyle \Delta _{S}^{M}\psi }</annotation>

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</math><img src="./6d3b2c0689e228e560f1d472ac6e2fe67732da8a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.408ex; height:3.176ex;" alt="{\displaystyle \Delta _{S}^{M}\psi }" loading="lazy"> is the <a href="Volta_potential" title="Volta potential">contact (Volta) potential</a> difference at the metal(M)–solution(S) interface.</dd></dl>

For practical purposes, the value of the absolute electrode potential of the standard hydrogen electrode is best determined with the utility of data for an <a href="Ideal_electrode" title="Ideal electrode">ideally-polarizable</a> <a href="Mercury_(element)" title="Mercury (element)">mercury</a> (Hg) electrode:

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<annotation encoding="application/x-tex">{\displaystyle E^{\ominus }{\rm {(H^{+}/H_{2})(abs)}}=\phi ^{\rm {Hg}}+\Delta _{S}^{\rm {Hg}}\psi _{\sigma =0}^{\ominus }-E_{\sigma =0}^{\rm {Hg}}{\rm {(SHE)}}}</annotation>

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</math><img src="./dff891177af9655d1842aba13a076ae33c900331.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:50.385ex; height:3.509ex;" alt="{\displaystyle E^{\ominus }{\rm {(H^{+}/H_{2})(abs)}}=\phi ^{\rm {Hg}}+\Delta _{S}^{\rm {Hg}}\psi _{\sigma =0}^{\ominus }-E_{\sigma =0}^{\rm {Hg}}{\rm {(SHE)}}}" loading="lazy"></dd></dl>

where:

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<annotation encoding="application/x-tex">{\displaystyle E^{\ominus }{\rm {(H^{+}/H_{2})(abs)}}}</annotation>

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</math><img src="./201d8d84246580ced61df64e63408860d9fb119c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.508ex; height:3.009ex;" alt="{\displaystyle E^{\ominus }{\rm {(H^{+}/H_{2})(abs)}}}" loading="lazy"> is the absolute standard potential of the hydrogen electrode</dd>

<dd>σ = 0 denotes the condition of the <a href="Point_of_zero_charge" title="Point of zero charge">point of zero charge</a> at the interface.</dd></dl>

The types of physical measurements required under the Rockwood definition are similar to those required under the Trasatti definition, but they are used in a different way, e.g. in Rockwood's approach they are used to calculate the equilibrium <a href="Vapor_pressure" title="Vapor pressure">vapour pressure</a> of the electron gas. The numerical value for the absolute potential of the standard hydrogen electrode one would calculate under the Rockwood definition is sometimes fortuitously close to the value one would obtain under the Trasatti definition. This near-agreement in the numerical value depends on the choice of ambient temperature and standard states, and is the result of the near-cancellation of certain terms in the expressions. For example, if a standard state of one atmosphere ideal gas is chosen for the electron gas then the cancellation of terms occurs at a temperature of 296 K, and the two definitions give an equal numerical result. At 298.15 K a near-cancellation of terms would apply and the two approaches would produce nearly the same numerical values. However, there is no fundamental significance to this near agreement because it depends on arbitrary choices, such as temperature and definitions of standard states.

<ul><li><a href="Electrochemical_potential" title="Electrochemical potential">Electrochemical potential</a></li>

<li><a href="Galvani_potential" title="Galvani potential">Galvani potential</a></li>

<li><a href="Standard_electrode_potential" title="Standard electrode potential">Standard electrode potential</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a rel="nofollow" class="external text" href="http://goldbook.iupac.org/A00022.html">IUPAC Gold Book – absolute electrode potential</a>

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<li id="cite_note-2"><a href="#cite_ref-2">^</a> Sergio Trasatti, "The Absolute Electrode Potential: an Explanatory Note (Recommendations 1986)", International Union of Pure and Applied Chemistry,

Pure & AppL Chem., Vol. 58, No. 7, pp. 955–66, 1986. <a rel="nofollow" class="external free" href="http://www.iupac.org/publications/pac/1986/pdf/5807x0955.pdf">http://www.iupac.org/publications/pac/1986/pdf/5807x0955.pdf</a> (pdf)

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</style><cite id="CITEREFRockwood1986" class="citation journal cs1">Rockwood, Alan L. (January 1, 1986). "Absolute half-cell thermodynamics: Electrode potential". Physical Review A. 33 (1). American Physical Society (APS): 554–559. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986PhRvA..33..554R">1986PhRvA..33..554R</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysreva.33.554">10.1103/physreva.33.554</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0556-2791">0556-2791</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9896642">9896642</a>.</cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite id="CITEREFRockwood1987" class="citation journal cs1">Rockwood, Alan L. (August 1, 1987). "Absolute half-cell entropy". Physical Review A. 36 (3). American Physical Society (APS): 1525–1526. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1987PhRvA..36.1525R">1987PhRvA..36.1525R</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysreva.36.1525">10.1103/physreva.36.1525</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0556-2791">0556-2791</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9899031">9899031</a>.</cite>

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<li id="cite_note-5"><a href="#cite_ref-5">^</a> <cite id="CITEREFFangWangZhangQiu2008" class="citation journal cs1">Fang, Zheng; Wang, Shaofen; Zhang, Zhenghua; Qiu, Guanzhou (2008). "The electrochemical Peltier heat of the standard hydrogen electrode reaction". Thermochimica Acta. 473 (1–2). Elsevier BV: 40–44. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008TcAc..473...40F">2008TcAc..473...40F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.tca.2008.04.002">10.1016/j.tca.2008.04.002</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0040-6031">0040-6031</a>.</cite>

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<li id="cite_note-6"><a href="#cite_ref-6">^</a> <a href="J._Electroanal._Chem." class="mw-redirect" title="J. Electroanal. Chem.">J. Electroanal. Chem.</a>, 79 (1977), 259-266

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