Encyclopedia of Geochemistry: A Comprehensive Reference Source on the Chemistry of the Earth

1013 Pages·43.201 MB·English

by  William M. White (eds.)

P
Polonium convert Po2+ to Po4+. Polonium has a relatively high vapor
pressure for a solid element as about half of a sample of
MonicaVasiliuandDavidA.Dixon poloniumwillevaporatewithin3days.Poloniumhaschem-
DepartmentofChemistry,TheUniversityofAlabama, icalpropertiessimilartoseleniumandtellurium.Mostofthe
Tuscaloosa,USA interestinPoisduetoitsradioactivity.Thehalf-lifeof209Po,
which is not observed naturally, is 105 y. The half-lives of
210Po,211Po,216Po,and218Poare138.4d,0.52s,0.15s,and
3.11m,respectively.Thus,thecommonisotope210Poisonly
found in trace amounts in uranium ore as it is a daughter
ElementData
productfromthedecayof238U.
Atomicsymbol:Po.
Atomicnumber:84.
Atomicweight:(209).
HistoryandUse
Isotopesandabundances:tracesof210Po,211Po,216Po,
218Po.
After Becquerel’s discovery in 1898 of radiation from the
1atmmeltingpoint:527K.
uranium ore pitchblende (uranium oxide, U O ), Marie and
1atmboilingpoint:1235K. 3 8
Commonvalences:+6,+4,+2,(cid:1)2. Pierre Curie studied pitchblende to determine the source of
Ionicradii:(+IV)65,((cid:1)II)230ppm. theradiation.Theyknewthaturaniumwasonesourceofthe
Paulingelectronegativity:2.0. radiation, but the amount of radiation could not come only
Firstionizationpotential:8.41eV. fromtheuranium.Aftermonthsofworkofpurifyingtonsof
Chondritic(CI)abundance: pitchblende, they isolated a new element, and Marie Curie
SilicateEarthabundance: nameditpoloniuminhonorofherhomeland,Poland.Polo-
Crustalabundance:tracesinuraniumores. nium is hundreds of times more radioactive than uranium.
Seawaterabundance: TheexistenceofpoloniumhadbeenpredictedbyMendeleev
Coreabundance: in 1891 on the basis of his periodic table. He realized that
there should be an element following bismuth that would
resembletelluriumandpredictedthatitwouldhaveanatomic
weightof212.
Properties Poloniumisana-emitterandisusuallyusedasathinfilm
onastainlesssteelforantistaticdevices.Poloniumwasused
Polonium is a reactive, silvery-gray, extremely rare radioac- in textile mills to eliminate static charges and in brushes to
tive semimetal (Emsley, 1991, 2001). It dissolves in dilute remove the accumulated dust in the manufacture of photo-
acids but is only slightly soluble in alkaline solutions. The graphicplates.Onegramofpoloniumreachesatemperature
solution formed by dissolving polonium in acids has a pink of500(cid:3)Casaresultofa-radiationemissionandisusedasa
color,thecolorofthePo2+ion,anditrapidlyturnsyellowas sourceofheatforspaceequipment.Poloniumcanbemixedor
a-radiation forms oxidizing species in aqueous solution that
#SpringerInternationalPublishingAG2017
W.M.White(ed.),EncyclopediaofGeochemistry,
DOI10.1007/978-3-319-39193-9_1-1
2 Polonium
alloyedwithberylliumtoprovideasourceofneutronswhich elementjustabovepoloniumintheperiodictable.Polonium
normallyonlyaccesstoanuclearreactorcanprovide. isconsideredtobemorethan1011timesmoredangerousthan
hydrogen cyanide. 210Po was used to assassinate Alexander
Litvinenko,aRussiandissidentresidinginLondonin2006.
GeochemicalBehavior 210Po has recently been found in the tobacco used in
cigarettesandotherproducts.210Poissolubleandcirculates
Polonium occurs rarely in nature in uranium ores and has through the body to every tissue and cell and has been
so few uses that it is extracted from natural ores only for detected in the blood and urine of smokers. The circulating
research purposes. All of the commercially produced polo- 210Po causes genetic damage and early death from liver and
nium in the world is from Russia. About 100 g/year of bladdercancers,stomachulcers,leukemia,cirrhosisofliver,
poloniumisproducedbybombardingbismuthwithneutrons andcardiovasculardiseases.
inanuclearreactor.
The radioactive disequilibrium between 210Po and 210Pb
hasbeenusedasachronometertodateglassyeruptionflows Cross-References
inmid-oceanridges,whicharedifficulttoaccess(Rubinetal.
1994).Theshorthalf-lifeof210Poof138.4dmeansthatitcan ▶Metalloids
only be used to determine if an event has occurred very ▶Radioactivity
recently.Theuseofthischronometerisbasedonthevolatil- ▶Selenium
ization of Po in volcanic emissions above 400 (cid:3)C likely as ▶Tellurium
halides and its return to its equilibrium values. This method ▶UraniumDecaySeries
wasusedtodeterminewhenandforhowlongtheridgeat9(cid:3)
500 NontheEastPacificRiseeruptedintheearly1990s.
References
BiologicalUtilizationandToxicity EmsleyJ(1991)Theelements,2ndedn.ClarendonPress,Oxford
EmsleyJ(2001)Nature’sbuildingblocksanA-Zguidetotheelements.
OxfordUniversityPress,Oxford
Poloniumhasnobiological roleandisextremelydangerous Rubin KH, Macdougall JD, Perfit MR (1994) 210Po-210Pb dating of
because of its intense radioactivity (a-emitter) which over- recentvolcaniceruptionsontheseafloor.Nature368:841–844
rides the toxicity concerns of tellurium, the noxious
C
Chemical Bonds dependstronglyonthedetailsoftheredistribution(Gillespie
andPopelier,2001).Thesedetailswillbediscussedherewith
BarryR.BickmoreandMatthewC.F.Wander reference to the electronegativity of the participating atoms.
DepartmentofGeologicalSciences,BrighamYoung (Electronegativity is a single-parameter summary of the
University,Provo,UT,USA electron-attractingpowerofatoms.)
Ionic bonds form between atoms with widely different
electronegativity values (metals with nonmetals). In these
Definition bonds, molecular orbitals concentrate most of the bonding
electron density around the more electronegative atoms,
LinusPaulingfamouslydescribedachemicalbondas“what- resulting in some atoms with a net negative charge (anions)
ever is convenient to the chemist to define as a bond” and others with a net positive charge (cations), which if
(Pauling, 1960). In the simplest terms, a chemical bond is sufficientlylargecanbehaveasseparateions.Anidealionic
merelyanattractionbetweenatomsinasubstancecontaining bondwouldinvolveacationandanionthatcanbetreatedas
an aggregation of two or more atoms. However, while all twopointcharges,butinrealionicsystems,somesharingof
bondsarebasedontheattractionbetweenpositivelycharged valenceelectronsoccurs,themolecularorbitalsarenotfully
protonsandnegatively chargedelectrons, quantum mechan- sphericallysymmetricalabouttheatomiccenters,andthereis
icaleffectsgoverningthespatialdistributionofelectronsgive alwayssomeorbitaloverlap,orsharing,ofelectrons.There-
rise to a wide range of bond properties and a continuum of fore, even bonds between atoms with the most disparate
bond types. The standard types include covalent, metallic, electronegativity values are not considered fully ionic
ionic, hydrogen, and van der Waals bonds (Gillespie and (Rohrer,2001).
Popelier,2001). Covalent bonds form between atoms with similar, high
electronegativityvalues(nonmetals).Heremolecularorbitals
distribute,orshare,thebondingelectrondensitymoreorless
TraditionalValenceBonds evenlybetweentheatomsinvolved,withanaccumulationof
electrondensityintheoverlapregionbetweenatomiccenters
Thestrongestchemicalbonds(covalent,metallic,andionic) (Popelier, 2000). Although fully ionic bonds do not exist,
are sometimes called “valence bonds,” due to the fact that fully covalent bonds do exist between atoms of the same
theyareformedwhenpartiallyfilledvalenceatomicorbitals element. Given that covalent bonds involve atoms that tend
combine to create molecular orbitals (Albright et al., 2013). to hold tightly to their valence electrons, the molecular
The average spatial distribution of electrons (the electron orbitals form with their associated electron density concen-
probability density or electron density) around a free atom tratedverylocally,aroundneighboringatoms.Thismakesthe
can be described in terms of atomic orbitals, which form bondsverylocalizedanddirectional,i.e.,theanglesbetween
three-dimensionalstandingwavepatternsaboutthenucleus. bonds to a given atom are relatively tightly constrained
Asatomsapproachoneanother,theiratomicorbitalsmixto (GillespieandHargittai,1991).
create molecular orbitals, which form three-dimensional Metallic bonds form between atoms with similar, low
standing wave patterns about multiple nuclei. The resulting electronegativityvalues(metals).Theseatomsholdrelatively
redistribution of the bonding electron density causes a net weaklytotheirvalenceelectrons,andthemolecularorbitals
attractionbetweentheatomiccenters,butthebondproperties formed spread out to encompass a very large number of
#SpringerInternationalPublishingSwitzerland2016
W.M.White(ed.),EncyclopediaofGeochemistry,
DOI10.1007/978-3-319-39193-9_4-1
2 ChemicalBonds
atoms.Thus,metallicallybondedsystemsareoftendescribed toahalf-filledorbitalontheF,creatinganionicbondwitha
as positively charged atoms (nuclei + core electrons) held bondorderof1.Theordersofbondsincidenttoagivenatom
together by a “sea” of valence electrons shared between all in a stable substance must sum to the atomic valence of the
the atoms. When so many atomic orbitals combine, a large atom. The atomic valence is equivalent to the number of
number of closely spaced (in terms of energy) molecular H atoms to which it can bond. Given that bond lengths are
orbitals becomeavailable,witharelativelysmallgap(or no highly correlated with bond orders (Brown, 2002), this cre-
gap) between the filled and unfilled levels. This leads to the atesstringentconstraintsregardingthecombinationsofbond
highthermalandelectricalconductivityofmetals,becausea lengthsthatarepossibleinastablestructure.Althoughatomic
relativelysmallexcitationofabondingelectrontakesitinto valencevaluesarenecessarilyintegers,bondorderscanhave
molecular orbitals that are comparatively empty and extend non-integer values, especially in condensed phases with
throughout thesubstance. The delocalization ofthebonding extendednetworksofvalencebonds.Forexample,incorun-
electrons also results in considerably less directionality and dum(a-Al O )Alhasavalenceof3,whileOhasavalenceof
2 3
forceinthebonds,whichexplainsthemalleabilityofmetallic 2.TheAl-Obondshavebondordersof~0.5,sothateachAlis
solids(Burdett,1997;Rohrer,2001). bondedtosixOatoms,andeachOisbondedtofourAlatoms.
Thedifferenttypesofvalencebondsformacontinuum,in Non-integerordersforindividualbondsarepossiblebecause
whichthedegreeofionicitycanberoughlyestimatedinterms molecularorbitals,whichmustcontainanintegralnumberof
of electronegativity differences between atoms, and cova- electrons, can encompass multiple atoms (Brown, 2002;
lency/metallicity can be roughly estimated in terms of the Albrightetal.,2013).
average electronegativity of the bonded atoms (Rohrer, At least for covalent bonds with integer bond orders, the
2001).Figure1showsavanArkel–Ketelaartriangle, which force constants used to describe bond vibrations are propor-
schematically illustrates this point. However, bonding char- tional to the bond order (Johnston, 1966). This gives rise to
acter can also be affected by factors such as pressure and anotherdefiningattributeofbonds,i.e.,theinverserelation-
temperature(Burdett,1997;BatsanovandBatsanov,2012). shipbetweenbondlengthandstrength.
One defining attribute of valence bonds is bond order. Bonds can also profitably be characterized in terms of
Bond order refers to the number of valence electron pairs bond energy (E ), which is the average energy per mole
bond
involvedinanindividualbond,whethersharedortransferred of bonds released when molecules are separated into their
(IUPAC, 1997; Brown, 2002). (In cases where antibonding constituent atoms. A similar quantity can be obtained from
electronpairsexist,thesearesubtractedfromthebondorder.) dividingtheatomizationenergiesofsolidsbythenumberof
ThebondinanF molecule,forexample,hasabondorder bonds per formula unit (Sanderson, 1976). For a bond
2(g)
of1,becausetheelectronsfromtwohalf-filledatomicorbitals between two given elements, of a given bond order, E
bond
are shared in one bonding molecular orbital. The electrons values are relatively transferable. Therefore, it is possible to
fromthreehalf-filledatomicorbitalsaresharedinN mol- roughly estimate enthalpies of formation by summing bond
2(g)
ecules, so the bond order is 3. In a CsF molecule, an energies.Itisimportanttonotethat,forthesamebondorder,
(g)
electron from a half-filled atomic orbital in Cs is transferred E can vary by hundreds of kJ/mol for bonds between
bond
ChemicalBonds,
Figure1 Avan
Arkel–Ketelaartriangle,
illustratingthecontinuum
ofbondtypesbetweenthe
ionic,covalent,andmetallic
limits.Thex-axisrepresents
themeanelectronegativity
(w )ofthetwoatoms
mean
involvedinthebondsin
eachofthesubstances
plotted.They-axis
representsthedifferencein
thetwoelectronegativity
values(w –w ).
1 2
ChemicalBonds 3
different elements. For example, the bond energy for the instant this may not be the case, creating a small dipole
singlebondinF is158.67kJ/mol,whereasthatforCs moment. As atoms approach one another, their oscillations
2(g) 2(g)
is 43.919 kJ/mol and that for CsF is 517.1 kJ/mol (Luo, synchronize to maximize attraction. This oscillation is cor-
(g)
2007).However,bondenergiesarenotstrictlyproportionalto rectlyaccountedforwithelectroncorrelationcalculationsand
bondorder,althoughthereisarelationshipbetweenthetwo. is in itself a type of standing wave behavior. A very weak
molecularstateiscreatedinthesecases,whichexplainswhy
an attraction between filled shells is possible (Housden and
HydrogenBondsasValenceBonds Pyper,2007;Krapp andFrenking,2007).This iswhy noble
gases, with filled valence shells, can condense into liquid at
Hydrogen bonds (H-bonds) are the weaker of conjugate verylowtemperatures.
bondsformedbetweenHandtwoormorehighlyelectroneg-
ativeatomssuchasN,O,orFandareusuallydesignatedas
X–H...X, where X represents the more electronegative BondsandtheDistributionofElements
atoms, the solid line represents a strong, polar covalent
bond,andthedottedlinerepresentsanH-bond.Theelectron A number of factors contribute to the distribution of the
densityinvolvedinthestrongbondisshiftedtowardthemore elements in the Earth, as described by the traditional
electronegative atom, creating a dipole between the two Goldschmidtclassification(Faure,1998),butonesuchfactor
atoms, resulting in a relatively weak electrostatic attraction has to do with bond energies. As noted above, bonds of the
betweenthepositivelychargedHandanyotherelectronega- same order can vary widely in bond energy with the bond
tive atoms in the vicinity. Thus, the H isbonded strongly to character.Elementswithverylowelectronegativity(e.g.,the
one comparatively electronegative atom and much more alkali and alkaliearth metals) favor highly ionic bonds with
weakly to one or more others. Due to the fact that H atoms fractional bond orders (i.e., bond order < 1), so they natu-
haveonlyoneelectron,alongwiththeirsmallsize,shiftingits rallybondeasilytoOinnetworksolids.Oxygenisthemost
electron densitytoward theanion results inarelativelyhigh abundant element in the Earth and the second-most electro-
positivechargedensity. negative, and some of the more electronegative elements,
Hydrogen bonds are often treated as simple electrostatic suchasthehalogens,oftensubstituteforO.Therefore,these
dipole interactions, rather than valence bonds, but in fact, it elements are classified as lithophile and are enriched in the
has been shown that even weak hydrogen bonds have some crustandmantle.Someofthemoreelectronegativeelements,
covalent character, so there is no reason to treat them as such as C and N, favor covalent bonds with one another,
anything but weak valence bonds that may be assigned a havinghighbondorders(1orgreater).Thisresultsinfewer
bond order. In fact, when H-bonds are shorter, the adjacent bonds and discrete molecules rather than network solids.
stronger bonds become longer, as one would expect for a Anumberofelementswithmoderatelyhighelectronegativity
valencebond(SteinerandSaenger,1994;Steiner,2002). favorcovalentbondswithsimilarelementsandlowtomod-
ThetypicalasymmetryofX–H...Xbondsislikelytobea eratebondorders,sothesetendtocongregateinsulfides,and
productofthesmallsizeofHatoms.SymmetricH-bonds,in areclassifiedaschalcophile.Anumberofmetalswithmod-
whichthetwobondstoHhaveequalbondordersof0.5,do erately low electronegativity favor metallic bonds with one
exist. However, they are quite rare because bond order falls another, with low bond orders. These tend to form metallic
off exponentially with distance. Therefore, an X–H–X con- solids and are classified as siderophile, because they readily
figurationwithtwo0.5orderbondsdrawstheXatomscon- bondwithFeandareenrichedinthecore.
siderably closer to one another than would typically be the
casefornonbondedatoms,whereasanasymmetricX–H...X
configuration results in a considerably longer X–X distance SummaryandConclusions
(Brown,2002).However,symmetricH-bondsbecomemore
common at high pressure (Steiner, 2002), because X atoms Chemical bonds can usefully be characterized in terms of
areforcedtogetherbycompression. bond order, bond energy, and bond type. Bond orders con-
strainsuitablecombinationsofbondlengthsincidenttoatoms
in stable configurations, and bond energies for bonds of the
LondonDispersion(vanderWaals)Forces same order vary widely as a function of bond type. It is
impossible to classify a given chemical bond as exclusively
London dispersion (van der Waals) forces originate due to one type, however, because van der Waals interactions are
oscillationsintheinstantaneouselectron distributionaround present between all neighboring atoms, and even in cases
atoms. The average electron distribution is generally very where van der Waals interactions dominate (e.g., noble gas
symmetrically disposed about the nucleus, but at any given dimersandcondensedphases),molecularorbitalsplaysome
4 ChemicalBonds
role. This is why there isa continuum between the different Gillespie,R.J.,andHargittai,I.,1991.TheVSEPRModelofMolecular
bondtypes,basedontheaffinityforelectronsofthebonded Geometry.Boston:AllynandBacon,248p.
Gillespie, R. J., and Popelier, P. L. A., 2001. Chemical Bonding and
atoms. The relationships between bond order and bond
MolecularGeometry:FromLewisStructurestoElectronDensities.
energy for different atom pairs are one of the determining Oxford:OxfordUniversityPress,268p.
factorsaffectingthedistributionofelementsintheEarth. Housden,M.P.,andPyper,N.C.,2007.Thenoblegasdimersasaprobe
oftheenergeticcontributionsofdispersionandshort-rangeelectron
correlation in weakly-bound systems. Molecular Physics, 105,
2353–2361.
Cross-References
IUPAC,1997.CompendiumofChemicalTerminology.Oxford:Black-
wellScientificPublications,p.
▶AbInitioCalculations Johnston,V.H.S.,1966.GasPhaseReactionRateTheory.NewYork:
▶AtmophileElements RonaldPress,372p.
Krapp,A.,andFrenking,G.,2007.Isthisachemicalbond?Atheoretical
▶ChalcophileElements study of Ng @C (Ng=He, Ne, Ar, Kr, Xe). Chemistry
2 60
▶Electronegativity AEuropeanJournal,13,8256–8270.
▶LithophileElements Luo,Y.-R.,2007.ComprehensiveHandbookof ChemicalBondEner-
▶SiderophileElements gies.NewYork:CRCPress,1657p.
Pauling, L., 1960. The Nature of the Chemical Bond. Ithaca: Cornell
UniversityPress,644p.
Popelier,P.L.A.,2000.AtomsinMolecules:AnIntroduction.Essex:
References PearsonEducation,164p.
Rohrer, G. S., 2001. Structure and Bonding in Crystalline Materials.
Cambridge:CambridgeUniversityPress,540p.
Albright, T. A., Burdett, J. K., and Whangbo, M.-H., 2013. Orbital
Sanderson,R.T.,1976.ChemicalBondsandBondEnergy.NewYork:
InteractionsinChemistry.Hoboken:Wiley,819p.
Academic,218p.
Batsanov,S.S.,andBatsanov,A.S.,2012.IntroductiontoStructural
Steiner, T., 2002. The hydrogen bond in the solid state. Angewandte
Chemistry.Dordrecht:Springer,542p. ChemieInternationalEdition,41,48–76.
Brown,I.D., 2002.TheChemicalBondinInorganicChemistry: The Steiner, T., and Saenger, W., 1994. Lengthening of the covalent O–H
BondValenceModel.NewYork:OxfordUniversityPress,278p. bond in O–H...O hydrogen bonds re-examined from
Burdett, J. K., 1997. Chemical Bonds: A Dialog. Chichester: Wiley,
low-temperature neutron diffraction data of organic compounds.
166p. ActaCrystallographica,B50,348–357.
Faure, G., 1998. Principles and Applications of Geochemistry. Upper
SaddleRiver:PrenticeHall,600p.
C
Critical Points
variations in pressure and temperature because the relative
proportions of the two phases, liquid and vapor, fluctuate
WilliamH.Casey1andPeterA.Rock2 widely.
1DepartmentofChemistry,DepartmentofEarthand To illustrate the sensitivity of fluid properties near the
PlanetarySciences,UniversityofCalifornia,Davis,CA,USA critical point, considerthat thecritical point for pure CO is
2
2CollegeofMathandPhysicalSciences,Departmentof at 31.8 (cid:2)C and 72.9 atm, which are easily accessible in a
Chemistry,UniversityofCalifornia,Davis,CA,USA laboratory. At these conditions a change in pressure of
1 part in 50,000 causes the CO fluid density to increase by
2
10%.ThedensityofcriticalCO is0.5g/cm3sothat1torrof
2
Definition
CO corresponds to an inch-thick layer. This one-inch-thick
2
layerofCO exhibitsa10%greaterdensityatthebottomof
2
Thepointinphasespacewherethedistinctionbetweenliquid thecolumnthanatthetopsimplyduetotheweightofthegas.
andvapordisappears. Likewise,theenthalpyofvaporizationgoestozeroatthe
critical point, and it can be seen that the isothermal
compressibility
Elaboration
(cid:1) (cid:3)
1 @V
b(cid:3)(cid:4) (2)
If you heat water in a closed volume, the temperature and V @P
T
pressure are initially fixed by equilibrium between a liquid
andvapor.Beyondacertaintemperatureandpressure,how- becomes infinite at the critical point. Correspondingly, the
ever, the meniscus that separates the two phases disappears, heatcapacity,C ,forthesubstancereacheslargevaluesnear
p
and they become indistinguishable. If one draws a curve in the critical point. Near-critical fluids also exhibit curious
P-V space that identifies the region where both a liquid and properties, such as critical opalescence, where light scatters
vaporcoexist,thecriticalpointliesatthemaximumwherethe intoadazzlingdisplayasthefluidreachesacertainmolecular
slopeiszero: densitybecausethemolecularstructuresreachacharacteristic
(cid:1) (cid:3) (cid:1) (cid:3) length similar to the wavelength of visible light. Stated dif-
@P @2P ferently, the refractive index varies widely near the critical
¼0 and ¼0 (1)
@V @V2 pointalongwiththeotherbulkproperties.
T¼T T¼T
c c
Additionofothercomponents,suchasCO ,NaCl,orH ,
2 2
Asthispointisapproached,thetwophases,gasandliquid, toH2Odramaticallyaffectsthecriticalpointofthesolution.
begin to closely resemble one another on a molecular scale. Forthesesystems,acurveofcriticalpointsisdefinedinP-T-X
Thecriticalpointforpurewaterisat374.2(cid:2)Cand218.3atm. space(Xisacompositionvariable)thatisgenerallynonlinear.
Nearthecriticalpoint,thestructureofthesephasesisvery ThecriticalcurvefortheCO2-H2Osystem,forexample,isa
sensitive to small changes in temperature and pressure, and saddlewithtwomaximanearend-membercompositionsand
these changes are reflected in the macroscopic properties. a minimum at intermediate values. The critical point for a
Density, for example, changes considerably with small saturated NaCl-H2O mixture is at almost 600 (cid:2)C and
Prof.PeterA.Rockisdeceased
#SpringerInternationalPublishingAG2016
W.M.White(ed.),EncyclopediaofGeochemistry,
DOI10.1007/978-3-319-39193-9_10-1
2 CriticalPoints
approximately390barspressure,significantlyhigherthanthe Cross-References
valueforpureH O.
2
Understanding the thermodynamic properties of mixed ▶GeochemicalThermodynamics
volatilefluids(e.g.CO -H O;H -H O)isimportantforpre- ▶Hydrothermal
2 2 2 2
dictingphaseassemblagesinrocks,forinterpretingthecom- ▶PhaseEquilibria
positionsoffluidinclusionsinminerals,andforpredictingthe
effectofvolatilegasesonmagma.Establishingthesethermo-
References
dynamicpropertieshasbeenamajorsuccessingeochemistry
during the last 50 years, and thermodynamic models have
recentlybeen extended to 6.0 GPa and 1200 (cid:2)C based upon SverjenskyDA,HarrisonB,AzzoliniD(2014)Waterinthedeepearth:
thedielectricconstantandthesolubilitiesofquartzandcorundumto
molecular-dynamic estimates of the dielectric constant of
60kband1200(cid:2)C.GeochimCosmochimActa129:125–145
water(Sverjenskyetal.2014).
G
Geochemical Thermodynamics theprimarythermodynamicvariablesoftemperature,energy,
heat,work,andentropy.Herewedoboth:
WilliamH.Casey1andPeterA.Rock2 First law: It is impossible to construct a device that
1DepartmentofChemistry,DepartmentofEarthand operates in a cyclical manner and performs work without
PlanetarySciences,UniversityofCalifornia,Davis,CA,USA puttingenergyintothedevice.
2CollegeofMathandPhysicalSciences,Departmentof Secondlaw:Entropyincreasesintheuniverse.Or,stated
Chemistry,UniversityofCalifornia,Davis,CA,USA differently, it is impossible to construct a device that can
transferenergyasheatfromalow-temperaturereservoirtoa
higher-temperaturereservoirwithoutaddingenergyaswork.
Definition Itisimpossibletoconstructadevicethatoperatesinacyclical
mannerandtakesinenergyasheatfromahigh-temperature
Thetransferofenergybetweenusefulworkandheat. reservoir and performs work without, in some part of the
cycle, discharging energy as heat to a low-temperature
reservoir.
Introduction Thirdlaw:Itisimpossibletoconstructadevicecapableof
decreasingthetemperatureofanymacroscopicsystemtothe
Thermodynamics concerns the conversion of energy in the absolutezerooftemperature(0K).
Earth.LengthscalesandtimesscalesforEarthprocessesare Statedintermsoftheprimarythermodynamicfunctionsof
sovast,andthemineralassemblagesandfluidsinnatureare temperature,energy,andentropy,thelawsofthermodynam-
so complicated, that equilibrium thermodynamics is usually icscanbestatedsuccinctlyasfollows:
the starting point for any geochemical investigation. This First law: The total energy is conserved (i.e., remains
point was established in the earliest days of modern science unchanged).
by the renowned physical chemist Jacobus Van’t Hoff Secondlaw:Thetotalentropyincreases.
(1852–1911), who used the then newly established Gibbs Third law: The absolute (Kelvin) temperature remains
PhaseRuletoreconstructthecompositionofancientseawater above0(cid:1).
fromthemineralassemblagesfoundinevaporitedeposits(see Theselawsprovidegeochemistswith(i)theconditionsfor
Eugster1971). the establishment of equilibrium in a system that includes
chemical reactions, heat transfer, and mechanical strain;
(ii) criteria to eliminate impossible processes; (iii) equations
LawsofThermodynamics to convert thermodynamic data, such as the energy and
entropy changes, into an equilibrium constant; and
Thelawsofthermodynamicsdifferfrommostotherscientific (iv)equationstopredicttheeffectsofchangesintemperature,
lawsinthattheyareusuallystatedintermsoftheimpossibil- pressure,orcompositiononthisreactionequilibrium.
ityofachievingcertaintypesofenergytransfers.Thelawscan The starting point in exploring thermodynamic laws is
bestatedintermsoftheoperationofmachinesorintermsof with knowledge of the experimental and thermodynamic
properties of temperature, heat, work, energy, and entropy.
Understanding work and heat is not difficult, but an
PeterA.Rockisdeceased.
#SpringerInternationalPublishingAG2017
W.M.White(ed.),EncyclopediaofGeochemistry,
DOI10.1007/978-3-319-39193-9_11-1
2 GeochemicalThermodynamics
understanding of temperature, energy, and entropy requires Energy,Work,andHeat
moreeffort.
Energyisanabstractmathematicalconceptthatisquantified
intermsofanenergyfunction,U.Someotherthermodynamic
Temperature functions also are called energy functions (Gibbs energy,
Helmholtzenergy)andarechosen specificallyasstatefunc-
A device designed to measure temperature is called a ther- tionsthatyieldexactdifferentialsintermsofexperimentally
mometer,ofwhichthere aremany types. Familiar examples convenientvariablessuchatTandP.
are the liquid-in-glass capillary, thermocouples, and resis- Energy is not a thing. There are no meters capable of
tance thermometers such as platinum wires and thermistors. directly measuring energy, yet there are electric-current
Allofthesedeviceshaveapropertythatvariesmonotonically meters, gas-flow meters, volume meters, mass meters, pres-
with temperature. The most fundamental thermometer, for sure meters, length meters, time meters, and thermometers.
example, is the constant-volume, ideal-gas thermometer, These measureable properties are used to calculate energy
which is based on the fact that nonassociating gases obey changes. Determination of the amount of energy transferred
theideal-gasequation: fromonesystemtoanotheralwaysinvolvesmeasurementsof
theappropriatephysicalparametersfollowedbycalculations
PV ¼nRT (1)
involvingtheappropriateenergyformulae.
Themostsignificantmathematicalpropertyoftheenergy
inthelimitasP!0wherePisthepressureofthegas,Vis
function is that of conservation. The principle of energy
thevolume,nisthenumberofmolesofthegas,andRisthe
conservationamountstothestatementthat,foranyrealpro-
gas constant. With a constant-volume gas thermometer, we
cess,thetotalamountofenergyremainsexactlythesameat
measurethetemperatureofafixedreferencepoint,suchasthe
theendoftheprocessasitwasatthebeginning.Energycan
meltingpointoftinmetal,asfollows:
be transferred and transformed, but it cannot be created or
(cid:1) (cid:3)
P destroyed.Thisconservationrelatestothedefinitionofastate
T ¼ð273:16KÞ lim T
P273(cid:4):16K!0 P273:16K(cid:5) (2) function,whichisalsoindependentofpath.
nRT=V Work and heat are the only modes of energy transfer
¼ð273:16KÞ nR273:16=V between systems. The transfer of energy as work requires
the existence of an unbalanced force between a system and
its surroundings. The transfer of energy as heat requires the
We measure P , the pressure of n moles of the gas at
T
existenceofatemperaturedifferencebetweenthesystemand
temperature T for progressively smaller values of n. The
its surroundings. When a force F acts on a system and dis-
resulting calculated values of temperature are extrapolated
placesthesystembyadifferentialamountdx,thenthework
to zero pressure to obtain the thermodynamic temperature.
doneonthesystemisgivenbyclassicalmechanicsas
ThevalueofP isthecorrespondingmeasuredpressure
273.16K
ofthegaswhenthethermometerbulbisincontactwithwater
dw¼(cid:3)Fdx (4)
atitstriplepoint.Thetriplepointofwateristhesinglemost
important accessible reference point in thermometry and is
Ingeneral,theworkdoneonasystemdependsonthepath
assignedatemperatureofexactly273.16Ktopreserveclose
alongwhichtheprocessiscarriedoutandmustbespecified
numerical agreement with older temperature scales, such as
(herefromstates1!2):
theCelsiusscale.
ThetemperaturescaledefinedbyEquation2isanabsolute
ð2
scale where zero is the lowest possible temperature and all
w¼(cid:3) Fdx (5)
temperatures are positive. This scale is called the absolute
Kelvin temperaturescale,andtemperaturesareexpressed as 1
kelvins. Celsius temperatures are related to Kelvin tempera-
inordertocalculatework:w.TheminussigninEquation5
turesviatheequation
ischosentomakeworkdoneonthesystem(dx<0)apositive
t=(cid:1)C¼T=K(cid:3)273:16 (3) quantity.Whenthepathmustbespecifiedbeforetheintegral
in Equation 5 can be evaluated, then the integral is called a
Thetemperaturesoffixedreferencepointsobtainedinthe lineintegral.Iftheworkdoneisindependentofthepath,e.g.,
the work done in lifting a weight in a constant gravitational
manner outlined above are, in turn, used to calibrate other
field
moreconvenientthermometers.