Complete Heyting algebra: Difference between revisions

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{{distinguish|Electrochemical series}}
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In introductory [[chemistry]], the '''reactivity series ''' or '''activity series''' is an empirical series of [[metal]]s, in order of "reactivity" from highest to lowest.<ref>{{citation | url = http://www.gcsescience.com/r1-reactivity-series-metals.htm | title = The Reactivity Series of Metals | first = Colin | last = France | year = 2008}}</ref><ref>{{citation | title = Science in Focus, Chemistry for GCE 'O' Level | first = J. G. R. | last = Briggs | page = 172 | publisher = Pearson Education | year = 2005}}</ref><ref>{{citation | unused_data = Longman Pocket Study Guide 'O' Level Science-Chemistry | author = Lim Eng Wah | page = 190 | publisher = Pearson Education | year = 2005}}</ref> It is used to summarize information about the reactions of metals with [[acid (chemistry)|acids]] and [[water (molecule)|water]], [[single displacement reaction]]s and the extraction of metals from their [[ore]]s.
 
{| class = "wikitable"
|-
! Metal !! Ion !! Reactivity !! Extraction
|-
| bgcolor=#FA8072 | [[Caesium|Cs]]
| bgcolor=#FA8072 | Cs<sup>+</sup>
| rowspan=9 bgcolor=#FA8072 align=center | reacts with [[water]]
| rowspan=11 bgcolor=#FA8072 align=center| [[electrolysis]]
|-
| bgcolor=#FA8072 | [[Rubidium|Rb]]
| bgcolor=#FA8072 | Rb<sup>+</sup>
|-
| bgcolor=#FA8072 | [[Potassium|K]]
| bgcolor=#FA8072 | K<sup>+</sup>
|-
| bgcolor=#FA8072 | [[Sodium|Na]]
| bgcolor=#FA8072 | Na<sup>+</sup>
|-
| bgcolor=#FA8072 | [[Lithium|Li]]
| bgcolor=#FA8072 | Li<sup>+</sup>
|-
| bgcolor=#FA8072 | [[Radium|Ra]]
| bgcolor=#FA8072 | Ra<sup>2+</sup>
|-
| bgcolor=#FA8072 | [[Barium|Ba]]
| bgcolor=#FA8072 | Ba<sup>2+</sup>
|-
| bgcolor=#FA8072 | [[Strontium|Sr]]
| bgcolor=#FA8072 | Sr<sup>2+</sup>
|-
| bgcolor=#FA8072 | [[Calcium|Ca]]
| bgcolor=#FA8072 | Ca<sup>2+</sup>
|-
| bgcolor=yellow | [[Magnesium|Mg]]
| bgcolor=yellow | Mg<sup>2+</sup>
| rowspan=2 bgcolor=yellow align=center | reacts with [[acid]]s
|-
| bgcolor=yellow | [[Aluminium|Al]]
| bgcolor=yellow | Al<sup>3+</sup>
|-
| bgcolor=orange | [[Titanium|Ti]]
| bgcolor=orange | Ti<sup>4+</sup>
| rowspan=1 bgcolor=orange align=center | reacts with concentrated [[mineral acids]]
| rowspan=1 bgcolor=orange align=center | [[Pyrometallurgical]] extraction using [[magnesium]], or less commonly other [[alkali metals]], [[hydrogen]] or [[calcium]] in the [[Kroll process]]
|-
| bgcolor=yellow | [[Manganese|Mn]]
| bgcolor=yellow | Mn<sup>2+</sup>
| rowspan=9 bgcolor=yellow align=center | reacts with [[acid]]s
| rowspan=9 bgcolor=yellow align=center | [[smelting]] with [[coke (fuel)|coke]]
|-
| bgcolor=yellow | [[Zinc|Zn]]
| bgcolor=yellow | Zn<sup>2+</sup>
|-
| bgcolor=yellow | [[Chromium|Cr]]
| bgcolor=yellow | Cr<sup>3+</sup>
|-
| bgcolor=yellow | [[Iron|Fe]]
| bgcolor=yellow | Fe<sup>2+</sup>
|-
| bgcolor=yellow | [[Cadmium|Cd]]
| bgcolor=yellow | Cd<sup>2+</sup>
|-
| bgcolor=yellow | [[Cobalt|Co]]
| bgcolor=yellow | Co<sup>2+</sup>
|-
| bgcolor=yellow | [[Nickel|Ni]]
| bgcolor=yellow | Ni<sup>2+</sup>
|-
| bgcolor=yellow | [[Tin|Sn]]
| bgcolor=yellow | Sn<sup>2+</sup>
|-
| bgcolor=yellow | [[Lead|Pb]]
| bgcolor=yellow | Pb<sup>2+</sup>
|-
| bgcolor=#cdcdcd | [[Antimony|Sb]]
| bgcolor=#cdcdcd | Sb<sup>3+</sup>
| rowspan=8 bgcolor=#cdcdcd align=center | may react with some strong [[oxidizing acid]]s
| rowspan=8 bgcolor=#cdcdcd align=center | heat or<br/>physical extraction
|-
| bgcolor=#cdcdcd | [[Bismuth|Bi]]
| bgcolor=#cdcdcd | Bi<sup>3+</sup>
|-
| bgcolor=#cdcdcd | [[Copper|Cu]]
| bgcolor=#cdcdcd | Cu<sup>2+</sup>
|-
| bgcolor=cdcdcd  | [[Tungsten|W]]
| bgcolor=#cdcdcd | W<sup>3+</sup>
|-
| bgcolor=#cdcdcd | [[Mercury (element)|Hg]]
| bgcolor=#cdcdcd | Hg<sup>2+</sup>
|-
| bgcolor=#cdcdcd | [[Silver|Ag]]
| bgcolor=#cdcdcd | Ag<sup>+</sup>
|-
| bgcolor="#cdcdcd" | [[Platinum|Pt]]
| bgcolor="#cdcdcd" | Pt<sup>2+</sup>
|-
| bgcolor="#cdcdcd" | [[Gold|Au]]
| bgcolor="#cdcdcd" | Au<sup>3+</sup>
|}
 
Going from bottom to top the metals:
*increase in reactivity;
*lose electrons more readily to form positive ions;
*corrode or tarnish more readily;
*require more energy (and different methods) to be separated from their ores;
*become stronger [[reducing agent]]s ([[electron]] donors).
 
== Defining reactions ==
 
There is no unique and fully consistent way to define the reactivity series, but it is common to use the three types of reaction listed below, many of which can be performed in a high-school laboratory (at least as demonstrations).{{Citation needed|date=September 2011}}
 
=== Reaction with water and acids ===
 
The most reactive metals, such as [[sodium]], will react with cold water to produce [[hydrogen]] and the metal [[hydroxide]]:
 
:2 Na (s) + 2 H<sub>2</sub>O (l) →2 NaOH (aq) + H<sub>2</sub> (g)
 
Metals in the middle of the reactivity series, such as [[iron]], will react with acids such as [[sulfuric acid]] (but not water at normal temperatures) to give hydrogen and a metal [[salt (chemistry)|salt]], such as [[iron(II) sulfate]]:
 
:Fe (s) + H<sub>2</sub>SO<sub>4</sub> (l) → FeSO<sub>4</sub> (aq) + H<sub>2</sub> (g)
 
There is some ambiguity at the borderlines between the groups. [[Magnesium]], [[aluminium]] and [[zinc]] ''can'' react with water, but the reaction is usually very slow unless the metal samples are specially prepared to remove the surface layer of oxide which protects the rest of the metal. [[Copper]] and [[silver]] will react with [[nitric acid]]; but because nitric acid is an [[oxidizing acid]], the oxidizing agent is not the H<sup>+</sup> ion as in normal acids, but the NO<sub>3</sub><sup>−</sup> ion.
 
=== Single displacement reactions ===
 
An iron nail placed in a solution of [[copper sulfate]] will quickly change colour as metallic copper is deposited and the iron is converted into [[iron(II) sulfate]]:
 
:Fe (s) + CuSO<sub>4</sub> (aq) → Cu (s) + FeSO<sub>4</sub> (aq)
 
In general, a metal can displace any of the metals which are lower in the reactivity series: the higher metal [[Reduction (chemistry)|reduces]] the ions of the lower metal. This is used in the [[thermite reaction]] for preparing small quantities of metallic iron, and in the [[Kroll process]] for preparing [[titanium]] (Ti comes at about the same level as Al in the reactivity series). For example, aluminium will reduce [[iron(III) oxide]] to iron, becoming [[aluminium oxide]] in the process:
 
:Al (s) + Fe<sub>2</sub>O<sub>3</sub> (s) → Fe (s) + Al<sub>2</sub>O<sub>3</sub> (s)
 
Similarly, [[magnesium]] can be used to extract [[titanium]] from [[titanium tetrachloride]], forming [[magnesium chloride]] in the process:
 
:2 Mg (s) + TiCl<sub>4</sub> (l) → Ti (s) + 2 MgCl<sub>2</sub> (s)
 
However, other factors can come into play, such as in the preparation of metallic [[potassium]] by the reduction of [[potassium chloride]] with sodium at 850&nbsp;°C. Although sodium is lower than potassium in the reactivity series, the reaction can proceed because potassium is more volatile, and is distilled off from the mixture.
 
:Na (g) + KCl (l) → K (g) + NaCl (l)
 
== Comparison with standard electrode potentials ==
The reactivity series is sometimes quoted in the strict reverse order of [[standard electrode potential]]s, when it is also known as the "electrochemical series":
:Li > K > Sr > Ca > Na > Mg > Al > Zn > Cr > Fe > Cd > Co > Ni > Sn > Pb > H > Cu > Ag > Hg > Pt > Au
The positions of [[lithium]] and [[sodium]] are changed on such a series; gold and platinum are also inverted, although this has little practical significance as both metals are highly unreactive.
 
Standard electrode potentials offer a quantitative measure of the power of a reducing agent, rather than the qualitative considerations of other reactivity series. However, they are only valid for ''standard'' conditions: in particular, they only apply to reactions in aqueous solution. Even with this proviso, the electrode potentials of lithium and sodium – and hence their positions in the electrochemical series – appear anomalous. The order of reactivity, as shown by the vigour of the reaction with water or the speed at which the metal surface tarnishes in air, appears to be
:potassium > sodium > lithium > alkaline earth metals,
the same as the reverse order of the (gas-phase) [[Ionization energy|ionization energies]]. This is borne out by the extraction of metallic lithium by the electrolysis of a [[eutectic]] mixture of [[lithium chloride]] and [[potassium chloride]]: lithium metal is formed at the cathode, not potassium.<ref name="G&E">{{Greenwood&Earnshaw1st|pages=82–87}}</ref>
 
=== Anomalous electrode potential of lithium ===
The standard electrode potential of a reaction ''E''<sup><s>o</s></sup> is related to the [[Gibbs free energy]] change Δ''G''<sup><s>o</s></sup> and the [[enthalpy]] change Δ''H''<sup><s>o</s></sup> by
:<math>\Delta G^\ominus = -nFE^\ominus = \Delta H^\ominus - T\Delta S^\ominus\,</math>
{| class="wikitable" align="right" style="margin-left:1em"
|+ M(s) &rarr; M<sup>+</sup>(aq) + e<sup>–</sup>
|-
! align=left | M =
! Li
! Na
! K
|-
| Δ<sub>at</sub>''H''<sup><s>o</s></sup> / kJ&thinsp;mol<sup>&minus;1</sup> || +162 || +110 || +90
|-
| ''E''<sub>i</sub> / kJ&thinsp;mol<sup>&minus;1</sup> || +520 || +496 || +419
|-
| Δ<sub>hydr</sub>''H''<sup><s>o</s></sup> / kJ&thinsp;mol<sup>&minus;1</sup> || –960 || –846 || –761
|-
| Δ<sub>f</sub>''H''<sup><s>o</s></sup> / kJ&thinsp;mol<sup>&minus;1</sup> || –278 || –240 || –252
|-
| Δ<sub>f</sub>''S''<sup><s>o</s></sup> / J&thinsp;K<sup>&minus;1</sup>&thinsp;mol<sup>&minus;1</sup> || +51 || +73 || +104
|-
| Δ<sub>f</sub>''G''<sup><s>o</s></sup> / kJ&thinsp;mol<sup>&minus;1</sup> || –293 || –261 || –283
|-
| ''E''<sup><s>o</s></sup> / V || +3.04 || +2.71 || +2.93
|-
| colspan=4 | <small>''Sources'': Jolly (1991),<ref name="Jolly">{{Jolly2nd|pages=586–87}}</ref> Greenwood &<br/>Earnshaw (1984).<ref name="G&E" /><ref>The values for the enthalpy changes of hydration of Li<sup>+</sup> (&minus;520&nbsp;kJ/mol) and Na<sup>+</sup> (&minus;405&nbsp;kJ/mol) given in Greenwood & Earnshaw (1984) are inconsistent with the other data quoted in the same source and certainly far too low. The enthalpy changes for the ''gas-phase'' reactions Li<sup>+</sup>(g) + 6H<sub>2</sub>O &rarr; [Li(H<sub>2</sub>O)<sub>6</sub>]<sup>+</sup> and Na<sup>+</sup>(g) + 5H<sub>2</sub>O &rarr; [Na(H<sub>2</sub>O)<sub>5</sub>]<sup>+</sup> have been measured as &minus;529(16)&nbsp;kJ/mol and &minus;347(14)&nbsp;kJ/mol respectively: {{citation | last1 = Rodgers | first1 = M. T. | last2 = Armentrout | first2 = P. B. | title = Noncovalent Metal-Ligand Bond Energies as Studied by Threshold Collision-Induced Dissociation | journal = Mass Spectrom. Rev. | year = 2000 | volume = 19 | pages = 215 | pmid = 10986693 | issue = 4 | doi = 10.1002/1098-2787(200007)19:4<215::AID-MAS2>3.0.CO;2-X}}. The enthalpy changes of hydration quoted in the table have been calculated from the enthalpy changes of formation of the ions in solution.</ref></small>
|}
The same relation can be applied to the half-reactions of tabulated standard electrode potentials, as the energy associated with the electron(s) will cancel whenever a full reaction is considered and so can be ignored. The enthalpy change of the half-reaction can be further analyzed as a [[Born–Haber cycle]], and shown to be equal to the [[enthalpy change of atomisation]] Δ<sub>at</sub>''H''<sup><s>o</s></sup> plus the [[ionization energy]] ''E''<sub>i</sub> plus the [[enthalpy change of hydration]] Δ<sub>hydr</sub>''H''<sup><s>o</s></sup> of the gaseous ions. There is a further contribution from the [[entropy]] change of the half-reaction, Δ''S''<sup><s>o</s></sup>. Values of these quantities for lithium, sodium and potassium are given in the table (note that the reaction is shown for the formation of M<sup>+</sup>, which is the reverse of the reduction reaction for which standard electrode potentials are  conventionally quoted).
 
The high electrode potential of the Li/Li<sup>+</sup> couple can be seen to be entirely due to the unusually large enthalpy change of hydration of the gaseous Li<sup>+</sup> ion, which overrides the other three factors. The lithium ion is small and highly [[Polarizability|polarising]], and so binds the [[Coordinate covalent bond|coordinated]] water molecules very tightly. This can also be seen in the relatively low positive entropy change for the formation of Li<sup>+</sup>(aq): the presence of lithium ions in solution creates more order in the solvent (water) than for either sodium or potassium ions.
 
The reaction of metallic lithium with water is more exothermic than any other alkali metal (many times more exothermic for a given mass or volume), but it is less vigorous for kinetic reasons. The enthalpy change of atomisation is twice as high for lithium than for potassium, indicating stronger bonding in the metal (both metals have the same [[body-centered cubic structure]]). Another way to measure an element's reactivity relative to other elements, is to look at its electronegativity. This is most useful when looking at how anions might replace other anions in a reaction. Anions with greater electronegativity values are more reactive and will replace anions with lower electronegativity values.
 
==See also==
* [[Reactivity (chemistry)]], which discusses the inconsistent way that the term 'reactivity' is used in chemistry.
 
==References==
{{reflist}}
 
==External links==
* [http://web.archive.org/web/20040508085524/http://www.sciencenet.org.uk/database/chem/industrial/c00109b.html Science Line Chemistry]
 
[[Category:Inorganic chemistry]]

Latest revision as of 03:32, 16 June 2014

Im Kristine and was born on 28 November 1981. My hobbies are Basketball and Herpetoculture.

Feel free to surf to my web blog Bookbyte Coupon Code 2014