Editing Electromotive force (section)

===Chemical sources===
{{Main|Electrochemical cell}}

[[File:Reaction path.JPG|thumb|380px|A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann ''et al.''<ref name=Bergmann>{{cite book |title=Constituents of Matter: Atoms, Molecules, Nuclei, and Particles |first=Nikolaus|last=Risch |chapter=Molecules - bonds and reactions |editor=L Bergmann |display-editors=etal |isbn=978-0-8493-1202-1  |year=2002 |publisher=CRC Press |chapter-url=https://books.google.com/books?id=mGj1y1WYflMC}}</ref> and [[Transition state]].]]

[[Image:Galvanic cell labeled.svg|thumb|380px|[[Galvanic cell]] using a [[salt bridge]]]]

The question of how batteries (galvanic cells) generate an emf occupied scientists for most of the 19th century. The "seat of the electromotive force" was eventually determined in 1889 by [[Walther Nernst]]<ref>{{cite journal |last1=Nernst |first1=Walter |title=Die elektromotorische Wirksamkeit der Ionen |journal=[[Z. Phys. Chem.]] |date=1889 |volume=4 |page=129}}</ref> to be primarily at the interfaces between the [[electrode]]s and the [[electrolyte]].<ref name=cajori>{{cite book
 | title = A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories
 | first = Florian|last=Cajori
 | publisher = The Macmillan Company
 | year = 1899
 | pages = [https://archive.org/details/ahistoryphysics03cajogoog/page/n232 218]–219
 | url = https://archive.org/details/ahistoryphysics03cajogoog
 | quote = seat of electromotive force.
 }}</ref>

Atoms in molecules or solids are held together by [[chemical bond]]ing, which stabilizes the molecule or solid (i.e. [[Minimum total potential energy principle|reduces its energy]]). When molecules or solids of relatively high energy are brought together, a spontaneous chemical reaction can occur that rearranges the bonding and reduces the (free) energy of the system.<ref name=reconfigure>
The brave reader can find an extensive discussion for organic electrochemistry in {{cite book |title=Organic electrochemistry |edition=4 |year=2000 |publisher=CRC Press |isbn=978-0-8247-0430-8 |editor1=Henning Lund |editor2=Ole Hammerich |chapter-url=https://books.google.com/books?id=tBxxZclgKyMC&pg=PA23 |first=Christian| last=Amatore |chapter=Basic concepts}}
</ref> In batteries, coupled half-reactions, often involving metals and their ions, occur in tandem, with a gain of electrons (termed "reduction") by one conductive electrode and loss of electrons (termed "oxidation") by another (reduction-oxidation or [[redox|redox reactions]]). The spontaneous overall reaction can only occur if electrons move through an external wire between the electrodes. The electrical energy given off is the free energy lost by the chemical reaction system.

As an example, a [[Daniell cell]] consists of a zinc anode (an electron collector) that is oxidized as it dissolves into a zinc sulfate solution. The dissolving zinc leaving behind its electrons in the electrode according to the oxidation reaction (''s'' = solid electrode; ''aq'' = aqueous solution):

:<math>\mathrm{Zn_{(s)} \rightarrow Zn^{2+}_{(aq)} + 2  e ^- \ } </math>

The zinc sulfate is the [[electrolyte]] in that half cell. It is a solution which contains zinc cations <math>\mathrm{Zn}^{2+}</math>, and sulfate anions <math>\mathrm{SO}_4^{2-} </math> with charges that balance to zero.

In the other half cell, the copper cations in a copper sulfate electrolyte move to the copper cathode to which they attach themselves as they adopt electrons from the copper electrode by the reduction reaction:

:<math> \mathrm{Cu^{2+}_{(aq)} + 2 e^- \rightarrow Cu_{(s)}\ } </math>

which leaves a deficit of electrons on the copper cathode. The difference of excess electrons on the anode and deficit of electrons on the cathode creates an electrical potential between the two electrodes. (A detailed discussion of the microscopic process of electron transfer between an electrode and the ions in an electrolyte may be found in Conway.)<ref name=Conway>
{{cite book |title=Electrochemical supercapacitors |first=BE|last=Conway |chapter=Energy factors in relation to electrode potential |page=37 |chapter-url=https://books.google.com/books?id=8yvzlr9TqI0C&pg=PA37 |isbn=978-0-306-45736-4 |year=1999 |publisher=Springer}}
</ref> The electrical energy released by this reaction (213 kJ per 65.4 g of zinc) can be attributed mostly due to the 207 kJ weaker bonding (smaller magnitude of the cohesive energy) of zinc, which has filled 3d- and 4s-orbitals, compared to copper, which has an unfilled orbital available for bonding.

If the cathode and anode are connected by an external conductor, electrons pass through that external circuit (light bulb in figure), while ions pass through the [[salt bridge]] to maintain charge balance until the anode and cathode reach electrical equilibrium of zero volts as chemical equilibrium is reached in the cell. In the process the zinc anode is dissolved while the copper electrode is plated with copper.<ref name= Tilley>{{cite book |title=Understanding Solids |url=https://archive.org/details/understandingsol0000till |url-access=registration |page=[https://archive.org/details/understandingsol0000till/page/267 267] |first=R. J. D.|last=Tilley |isbn=978-0-470-85275-0 |year=2004 |publisher=Wiley}}</ref> The salt bridge has to close the electrical circuit while preventing the copper ions from moving to the zinc electrode and being reduced there without generating an external current. It is not made of salt but of material able to wick [[cations and anions]] (a dissociated salt) into the solutions. The flow of positively charged cations along the bridge is equivalent to the same number of negative charges flowing in the opposite direction.

If the light bulb is removed (open circuit) the emf between the electrodes is opposed by the electric field due to the charge separation, and the reactions stop.

For this particular cell chemistry, at 298 K (room temperature), the emf <math>\mathcal{E}</math> = 1.0934 V, with a temperature coefficient of <math>d\mathcal{E}/dT</math>&nbsp;= −4.53×10<sup>−4</sup> V/K.<ref name= Finn>{{cite book |title=Thermal Physics |first=Colin B P|last=Finn |page=163 |url=https://books.google.com/books?id=BTMPThGxXQ0C&pg=PA162 |isbn=978-0-7487-4379-7 |year=1992 |publisher=CRC Press}}</ref>

====Voltaic cells====
Volta developed the voltaic cell about 1792, and presented his work March 20, 1800.<ref name=Mottelay>{{cite book |title=Bibliographical History of Electricity and Magnetism |first=Paul Fleury|last=Mottelay |page=247 |url=https://books.google.com/books?id=9vzti90Q8i0C&pg=RA1-PA247 |isbn=978-1-4437-2844-7 |publisher=Read Books |year=2008 |edition=Reprint of 1892}}</ref> Volta correctly identified the role of dissimilar electrodes in producing the voltage, but incorrectly dismissed any role for the electrolyte.<ref name=Kragh>{{cite journal
 |journal     = Nuova Voltiana:Studies on Volta and His Times
 |publisher   = Università degli studi di Pavia
 |year        = 2000
 |url         = http://ppp.unipv.it/Collana/Pages/Libri/Saggi/NuovaVoltiana_PDF/sei.pdf
 |title       = Confusion and Controversy: Nineteenth-century theories of the voltaic pile
 |first = Helge|last=Kragh
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20090320064922/http://ppp.unipv.it/Collana/Pages/Libri/Saggi/NuovaVoltiana_PDF/sei.pdf
 |archive-date = 2009-03-20
}}</ref> Volta ordered the metals in a 'tension series', "that is to say in an order such that any one in the list becomes positive when in contact with any one that succeeds, but negative by contact with any one that precedes it."<ref name=Cumming>{{cite book |title=An Introduction to the Theory of Electricity |first=Linnaus|last=Cumming |url=https://books.google.com/books?id=Nrb8723u4WEC&pg=PA118 |page=118 |isbn=978-0-559-20742-6 |publisher=BiblioBazaar |year=2008 |edition=Reprint of 1885}}</ref> A typical symbolic convention in a schematic of this circuit ( –<big>|</big>'''<small>|</small>'''– ) would have a long electrode 1 and a short electrode 2, to indicate that electrode 1 dominates.  Volta's law about opposing electrode emfs implies that, given ten electrodes (for example, zinc and nine other materials), 45 unique combinations of voltaic cells (10 × 9/2) can be created.

====Typical values====
The electromotive force produced by primary (single-use) and secondary (rechargeable) cells is usually of the order of a few volts. The figures quoted below are nominal, because emf varies according to the size of the load and the state of exhaustion of the cell.

{| class=wikitable

! rowspan="2" | EMF
! colspan="3" | Cell chemistry
! rowspan="2" | Common name
|-
! Anode
! Solvent, electrolyte
! Cathode 
|-
| 1.2&nbsp;V || Cadmium || Water, potassium hydroxide || NiO(OH) || [[Nickel–cadmium battery|nickel-cadmium]]
|-
| 1.2&nbsp;V || [[Mischmetal]] (hydrogen absorbing) || Water, potassium hydroxide || Nickel|| [[Nickel–metal hydride battery|nickel–metal hydride]]
|-
| 1.5&nbsp;V || Zinc || Water, ammonium or zinc chloride || Carbon, manganese dioxide|| [[zinc–carbon battery|Zinc carbon]]
|-
| 2.1&nbsp;V || Lead || Water, sulfuric acid || Lead dioxide || [[Lead–acid battery|Lead–acid]]
|-
| 3.6&nbsp;V to 3.7&nbsp;V || Graphite || Organic solvent, Li salts || LiCoO<sub>2</sub> || [[lithium-ion battery|Lithium-ion]]
|-
| 1.35&nbsp;V || Zinc || Water, sodium or potassium hydroxide || HgO || [[Mercury cell]]
|-
|}

==== Other chemical sources ====
Other chemical sources include [[fuel cell]]s.