View source for Physics:Standard hydrogen electrode

{{Short description|Reference redox electrode used under standard conditions}}

In [[Chemistry:Electrochemistry|electrochemistry]], the '''standard hydrogen electrode''' (abbreviated '''SHE'''), is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its [[Chemistry:Absolute electrode potential|absolute electrode potential]] is estimated to be {{nowrap|4.44 ± 0.02 V}}<ref>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. http://www.iupac.org/publications/pac/1986/pdf/5807x0955.pdf (pdf)</ref> at 25&nbsp;°C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's [[Chemistry:Standard electrode potential|standard electrode potential]] ({{math|''E''°}}) is declared to be zero volts at any temperature.<ref>{{GoldBookRef|file=S05917|title=standard hydrogen electrode}}</ref> Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.

== Nernst equation for SHE ==
The hydrogen electrode is based on the redox half cell corresponding to the reduction of two hydrated protons, {{chem2|2H+_{(aq)},}} into one gaseous [[Chemistry:Hydrogen|hydrogen]] molecule, {{chem2|H_{2(g)}.}}

General equation for a reduction reaction: 
: <math chem>\underset{\text{ox}}{\text{(oxidant)}} + z\ce{e- <=>}\ \underset{\text{red}}{\text{(reductant)}}</math>

The [[Physics:Reaction quotient|reaction quotient]] ({{mvar|Q<sub>r</sub>}}) of the half-reaction is the ratio between the chemical activities ({{mvar|a}}) of the reduced form (the reductant, {{Math|''a''<sub>red</sub>}}) and the oxidized form (the oxidant, {{Math|''a''<sub>ox</sub>}}). 

: <math>Q_r = \frac{a_\text{red}}{a_\text{ox}}</math>

Considering the {{chem2|2 H+ / H2}} redox couple:

: <chem>2H_{(aq)}+ + 2e- <=> H2_{(g)}</chem>

at [[Chemistry:Chemical equilibrium|chemical equilibrium]], the ratio {{mvar|Q<sub>r</sub>}} of the reaction products by the reagents is equal to the [[Chemistry:Equilibrium constant|equilibrium constant]] {{mvar|K}} of the half-reaction: 

: <math>K = \frac{a_\text{red}}{a_\text{ox}} = \frac{a_\mathrm{H_2}}{a_\mathrm{H^+}^2} = \frac{p_\mathrm{H_2}/p^0}{a_\mathrm{H^+}^2} = \frac{x_\mathrm{H_2}p/p^0}{a_\mathrm{H^+}^2}</math>

where
*<math>a_\text{red}</math> and <math>a_\text{ox}</math> correspond to the chemical activities of the reduced and oxidized species involved in the redox reaction
*<math>a_\mathrm{H^+}</math> represents the activity of {{chem|H|+}}. 
*<math>a_\mathrm{H_2}</math> denotes the chemical activity of gaseous hydrogen ({{chem|H|2}}), which is approximated here by its [[Physics:Fugacity|fugacity]] <math>p_{\mathrm{H_2}}.</math>
*<math>p_\mathrm{H_2}</math> denotes the [[Physics:Partial pressure|partial pressure]] of gaseous hydrogen, expressed without unit; <math>p_{\mathrm{H_2}} = x_{\mathrm{H_2}} \cdot p,</math> where
**<math>x_{\mathrm{H_2}}</math> is the {{chem|H|2}} [[Chemistry:Mole fraction|mole fraction]] 
**<math>p</math> is the total gas pressure in the system 
*{{math|''p''<sup>0</sup>}} is the standard pressure (1 bar = 10{{sup|5}} pascal) introduced here simply to overcome the pressure unit and to obtain an [[Chemistry:Equilibrium constant|equilibrium constant]] without unit. 
More details on managing gas fugacity to get rid of pressure unit in thermodynamic calculations can be found at [[Chemistry:Thermodynamic activity#Gases|thermodynamic activity#Gases]]. The followed approach is the same as for chemical activity and [[Physics:Molar concentration|molar concentration]] of solutes in solution. In the SHE, pure hydrogen gas (<math>x_{\mathrm{H_2}} = 1</math>) at the standard pressure <math>p</math> of {{nowrap|1 [[Bar (unit)|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 a platinized [[Chemistry:Platinum|platinum]] electrode.
The electrode is dipped in an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced form and oxidised form is maintained at unity. That implies that the pressure of hydrogen gas is 1&nbsp;bar (100&nbsp;kPa) and the activity coefficient of hydrogen ions in the solution is unity. The activity of hydrogen ions is their effective concentration, which is equal to the formal concentration times the [[Chemistry:Activity coefficient|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 [[Physics:Nernst equation|Nernst equation]] at equilibrium is the following: 

<math display="block">E_\text{cell} = E^\ominus_\text{cell} - \frac{RT}{zF} \ln K</math>

and as <math>E^\ominus_\text{cell} = 0</math> by definition in the case of the SHE, 

The [[Physics:Nernst equation|Nernst equation]] for the SHE becomes:

:<math>E=0-{RT \over 2F}\ln \frac{{p_\mathrm{H_2}/p^0}}{a_\mathrm{H^+}^2}</math>

:<math>E=-2.303\,{RT \over F} \left( \mathrm{pH} + \frac{1}{2} \log \frac{p_\mathrm{H_2}}{p^0} \right) </math>

Simply neglecting the pressure unit present in <math>p_\mathrm{H_2}</math>, this last equation can often be directly written as: 

:<math>E=-2.303\,{RT \over F} \left( \mathrm{pH} + \frac{1}{2} \log p_\mathrm{H_2} \right) </math>

And by solving the numerical values for the term 
:<math>-2.303\,{RT \over F} = -2.303 \left( \frac{8.314 \times 298.15}{96,485} \right) = -0.0591 \ \mathrm{volts,}</math>
the practical formula commonly used in the calculations of this Nernst equation is:
:<math>E=-0.0591 \left( \mathrm{pH} + \frac{1}{2} \log p_\mathrm{H_2} \right)</math> (unit: [[Volt|volt]])

As under standard conditions <math>p_\mathrm{H_2} = 1 \text{ bar,}</math> <math>\log p_\mathrm{H_2} = \log 1 = 0,</math> the equation simplifies to: 

:<math>E=-0.0591 \ \mathrm{pH}</math> (unit: [[Volt|volt]])

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 [[Chemistry:Pourbaix diagram|Pourbaix diagram]] where gaseous hydrogen is evolving because of water decomposition. 

where:
* {{tmath|a_\mathrm{H^+} }} is the activity of the hydrogen ions (H<sup>+</sup>) in [[Chemistry:Aqueous solution|aqueous solution]], <math>a_\mathrm{H^+} = \gamma_\mathrm{H^+} \tfrac{C_\mathrm{H^+}}{C^0}</math> <br />with:
** {{tmath|\gamma_\mathrm{H^+} }} is the [[Chemistry:Activity coefficient|activity coefficient]] of hydrogen ions (H<sup>+</sup>) in aqueous solution
** {{tmath|C_\mathrm{H^+} }} is the [[Physics:Molar concentration|molar concentration]] of hydrogen ions (H<sup>+</sup>) in aqueous solution
** {{math|''C''<sup>0</sup>}} is the standard concentration (1 M) used to overcome concentration unit
* {{tmath|p_\mathrm{H_2} }} is the [[Physics:Partial pressure|partial pressure]] of the [[Chemistry:Hydrogen|hydrogen]] gas, in [[Bar (unit)|bar]] ({{nowrap|1 bar {{=}} 10{{sup|5}} Pa}})
* {{mvar|R}} is the universal gas constant: {{val|8.3144}} [[Joule|J]]⋅[[Kelvin|K]]<sup>−1</sup>⋅[[Mole (unit)|mol]]<sup>−1</sup> (rounded here to 4 decimal)
* {{mvar|T}} is the [[Physics:Absolute temperature|absolute temperature]], in [[Kelvin|kelvin]] (at 25 °C: 298.15 K)
* {{mvar|F}} is the [[Physics:Faraday constant|Faraday constant]] (the charge per mole of electrons), equal to {{nowrap|96,485.3 coulomb·mol<sup>−1</sup>}}
* {{math|''p''<sup>0</sup>}} is the standard pressure: {{nowrap|1 bar {{=}} 10{{sup|5}} Pa}}

{{underlined|Note}}: as the system is at [[Chemistry:Chemical equilibrium|chemical equilibrium]], hydrogen gas, {{chem2|H2_{(g)},}} is also in equilibrium with dissolved hydrogen, {{chem2|H2_{(aq)},}} and the Nernst equation implicitly takes into account the [[Physics:Henry's law|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.

==SHE vs NHE vs RHE==
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] a platinum electrode into a solution of 1&nbsp;N strong acid and [bubbling] hydrogen gas through the solution at about 1&nbsp;atm pressure".  However, this electrode/solution interface was later changed.  What replaced it was a theoretical electrode/solution interface, where the concentration of H<sup>+</sup> was 1&nbsp;M, but the H<sup>+</sup> ions were assumed to have no interaction with other ions (a condition not physically attainable at those concentrations).  To differentiate this new standard from the previous one, it was given the name 'standard hydrogen electrode'.
<ref>{{cite journal|last1=Ramette|first1=R. W.|title=Outmoded terminology: The normal hydrogen electrode|journal=Journal of Chemical Education|date=October 1987|volume=64|issue=10|page=885|doi=10.1021/ed064p885|bibcode=1987JChEd..64..885R}}
</ref> Finally, there are also reversible hydrogen electrodes (RHEs), which are practical hydrogen electrodes whose potential depends on the pH of the solution.<ref>[https://www.researchgate.net/post/Can_anyone_please_explain_me_the_difference_between_NHE_RHE_and_SHE_in_a_simple_way https://www.researchgate.net/post/Can_anyone_please_explain_me_the_difference_between_NHE_RHE_and_SHE_in_a_simple_way]</ref>


In summary,

:'''NHE''' (normal hydrogen electrode): potential of a platinum electrode in 1&nbsp;M acid solution

:'''SHE''' (standard hydrogen electrode):  potential of a platinum electrode in a theoretical [[Physics:Ideal solution|ideal solution]] (the current ''standard'' for zero potential for all temperatures)

:'''RHE''' ([[Physics:Reversible hydrogen electrode|reversible hydrogen electrode]]): a practical hydrogen electrode whose potential depends on the pH of the solution

==Choice of platinum==
The choice of platinum for the hydrogen electrode is due to several factors:
* inertness of platinum (it does not corrode)
* the capability of platinum to catalyze the reaction of proton reduction
* a high intrinsic [[Chemistry:Exchange current density|exchange current density]] for proton reduction on platinum
* excellent reproducibility of the potential (bias of less than 10&nbsp;μV when two well-made hydrogen electrodes are compared with one another)<ref name="Sawyer">{{cite book|first1=D. T. |last1=Sawyer |first2=A. |last2=Sobkowiak |first3=J. L. Jr. |last3=Roberts |title=Electrochemistry for Chemists |edition=2nd |publisher=John Wiley and Sons |date=1995}}</ref>
The surface of platinum is platinized (i.e., covered with a layer of fine powdered platinum also known as [[Physics:Platinum black|platinum black]])  to:
* Increase total surface area. This improves reaction kinetics and maximum possible current
* Use a surface material that [[Chemistry:Adsorption|adsorbs]] hydrogen well at its interface. This also improves reaction kinetics

Other metals can be used for fabricating electrodes with a similar function such as the [[Physics:Palladium-hydrogen electrode|palladium-hydrogen electrode]].

==Interference==
Because of the high [[Chemistry:Adsorption|adsorption]] activity of the [[Physics:Platinum black|platinized]] platinum [[Physics:Electrode|electrode]], it's very important to protect electrode surface and solution from the presence of [[Chemistry:Organic compound|organic substances]] as well as from [[Earth:Atmospheric chemistry|atmospheric oxygen]]. Inorganic ions that can be [[Chemistry:Redox|reduced]] to a lower [[Chemistry:Valence|valency state]] at the electrode also have to be avoided (e.g., {{chem|link=ferric ion|Fe|3+}}, {{chem|link=Monochromate|CrO|4|2−}}). A number of organic substances are also reduced by hydrogen on a platinum surface, and these also have to be avoided.

[[Physics:Ion|Cations]] that can be reduced and deposited on the platinum can be source of interference: [[Chemistry:Silver|silver]], [[Chemistry:Mercury (element)|mercury]], [[Chemistry:Copper|copper]], [[Chemistry:Lead|lead]], [[Chemistry:Cadmium|cadmium]] and [[Chemistry:Thallium|thallium]].

Substances that can inactivate ("poison") the [[Chemistry:Catalysis|catalytic]] sites include [[Chemistry:Arsenic|arsenic]], [[Chemistry:Sulfide|sulfide]]s and other [[Chemistry:Sulfur|sulfur]] compounds, [[Physics:Colloid|colloidal]] substances, [[Chemistry:Alkaloid|alkaloid]]s, and material found in [[Biology:Biological system|biological system]]s.<ref>{{cite book|first1=D. J. G. |last1=Ives |first2=G. J. |last2=Janz |title=Reference Electrodes: Theory and Practice |publisher=Academic Press |date=1961}}</ref>

==Isotopic effect==
The standard redox potential of the [[Physics:Deuterium|deuterium]] couple is slightly different from that of the proton couple (ca. −0.0044&nbsp;V vs SHE). Various values in this range have been obtained: −0.0061&nbsp;V,<ref>{{cite journal|last1=Znamirovschi|first1=V.|title=Isotopic Equilibrium at the Normal Hydrogen Electrode|journal=Isotopenpraxis Isotopes in Environmental and Health Studies|date=January 1970|volume=6|issue=1|pages=29–31|doi=10.1080/10256017008621700}}</ref> −0.00431&nbsp;V,<ref>{{cite journal|last1=Gary|first1=Robert|last2=Bates|first2=Roger G.|last3=Robinson|first3=R. A.|title=Thermodynamics of Solutions of Deuterium Chloride in Heavy Water from 5 to 50°|journal=The Journal of Physical Chemistry|date=May 1964|volume=68|issue=5|pages=1186–1190|doi=10.1021/j100787a037}}</ref> −0.0074&nbsp;V.

:<chem>2 D_{(aq)}+ + 2 e- -> D2_{(g)}</chem>

Also difference occurs when [[Chemistry:Hydrogen deuteride|hydrogen deuteride]] (HD, or deuterated hydrogen, DH) is used instead of hydrogen in the electrode.<ref>{{cite journal|last1=Wakao|first1=S.|last2=Yonemura|first2=Y.|title=Anodic polarization behaviour of hydride-deuteride electrodes|journal=Journal of the Less Common Metals|date=February 1983|volume=89|issue=2|pages=481–488|doi=10.1016/0022-5088(83)90359-4}}</ref>

==Experimental setup==
[[Image:Standard hydrogen electrode 2009-02-06.svg|thumb|Scheme of the standard hydrogen electrode]]

The scheme of the standard hydrogen electrode:

# [[Physics:Platinum black|platinized]] platinum electrode
# hydrogen gas
# solution of the acid with activity of H<sup>+</sup> = 1&nbsp;mol&nbsp;dm<sup>−3</sup>
# hydroseal for preventing oxygen interference
# reservoir through which the second half-element of the galvanic cell should be attached. The connection can be direct, through a narrow tube to reduce mixing, or through a [[Chemistry:Salt bridge|salt bridge]], depending on the other  electrode and solution. This creates an ionically conductive path to the working electrode of interest.

==See also==
{{Commons|Standard hydrogen electrode}}
* Table of standard electrode potentials
* [[Physics:Reversible hydrogen electrode|Reversible hydrogen electrode]]
* [[Physics:Palladium-hydrogen electrode|Palladium-hydrogen electrode]]
* [[Physics:Reference electrode|Reference electrode]]
* [[Physics:Dynamic hydrogen electrode|Dynamic hydrogen electrode]]
* [[Physics:Quinhydrone electrode|Quinhydrone electrode]]
* [[Chemistry:Thermodynamic activity|Thermodynamic activity]]
* [[Physics:Standard state|Standard state]]

==References==
{{reflist}}

==External links==
* {{cite journal|last1=Palibroda|first1=Evelina|title=Note sur l'activation anodique de la surface du métal support de l'électrode à hydrogène|journal=Journal of Electroanalytical Chemistry and Interfacial Electrochemistry|date=January 1967|volume=15|pages=92–95|doi=10.1016/0022-0728(67)85013-7}}

{{DEFAULTSORT:Standard Hydrogen Electrode}}
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{{Sourceattribution|Standard hydrogen electrode}}