Physics of Aquatic Systems II

Size: px

Start display at page:

Download "Physics of Aquatic Systems II"

Rhoda Morrison
5 years ago
Views:

1 Contents o ession 3 ysics o quatic ystems II 3. table Isotopes - Teory Werner escbac-hertig Institute o Environmental ysics University o Heidelberg Fundamentals o table Isotopes otation and deinitions Origin and description o ractionation Fractionating processes ayleig distillation Literature: Moo Vol. I, c. 3 and 4 Fundamentals o table Isotope Geocemistry table isotope geocemistry o te ligt elements: Mainly: Hydrogen, carbon, nitrogen, oxygen lso used: Boron, sulur, cloride and oters Te ligt elements ave: One igly abundant ligt isotope ( H, C, 4, 6 O) One or two rare eavy isotopes ( H, 3 C, 5, 7 O, 8 O) ome radioactive eavy isotopes ( 3 H, 4 C) table isotope geocemistry studies natural variations o te ratios between rare and abundant isotopes 3 Isotope atios abundance o rare isotope abundance o eavy isotope = abundance o common isotope abundance o ligt isotope Isotope "concentration" or mixing ratio: Fractional abundance o given isotope relative to all isotopes o te element (oten in %) Element Isotope mixing ratio (%) Isotope ratio Hydrogen H H.5 H/ H.5 Carbon C C. 3 C/ C. itrogen / O O.4 8 O/ 6 O. 6 O O.38 7 O/ 6 O otation table isotope ratios are measured and reported relative to a reerence material or. Deinition o (relative deviation o sample rom ): sample sample = ( ) 8 6 O O 8 sample e.g. O= 8 6 ( O O) ote -values are dimensionless, small numbers, usually reported in. We ollow te convention o Moo (), in wic te actor o (used to convert to ) does not occur in equations, i.e.: 8 O [ ] = 3 is equivalent to 8 O =.3 5 eerence Materials everal international reererence s are distributed by te IE in Vienna: VMOW = Vienna tandard Mean Ocean Water VDB = Vienna ee Dee Belemnite (a carbonate roc) Element atio tandard e. value Hydrogen H/ H VMOW Carbon 3 C/ C VDB itrogen 5 / 4 atmosperic O/ 6 O VMOW VDB Laboratories use internal s tat are calibrated against te international s 6

2 Isotope Fractionation Te pysical and cemical properties o dierent isotopes (or compounds containing dierent isotopes) are sligtly dierent: ligt variations o te isotope ratios in natural materials Mobility are eavy isotopes are sligtly less mobile tan te ligt isotopes eason: T = ½mv v ~ m -½ at given T Binding Energy Molecules containing te rare eavier isotope generally ave iger binding energies tan molecules o te ligt isotopes eason: lower zero point energy Heavy isotopes (compounds) diuse and react slower (usually) Fractionation decreases wit increasing temperature 7 Energy Levels o Isotopic Molecules (Isotopomers) Diatomic molecule: m m educed mass: µ = m+ m otation: E = B J( J + ) B = Θ rot Θ=µ Vibration: Evib = ( v+ ) ω ω = D µ Heavy Isotopomer (iger µ): -Lower E and E vib, E rot - Higer dissociation energy 8 ysical roperties o Isotopic Forms o Water roperty H O D O H 8 O Density at C [g cm -3 ] Melting point [ C] Boiling point [ C].4.4 ote: D O (eavy water) is rare in nature, only HDO is relevant Beaviour at pase transitions: Heavy species need iger temperatures (energy!) to melt/evaporate Heavy isotopic species usually enriced in condensed pase rocesses Leading to Fractionation Isotope ractionation occurs in pysical, cemical, or biological transitions/reactions between two pases or compounds and B. Equilibrium ractionation: reversible equilibrium reaction B at equilibrium: orward and bacward reaction rates equal E.g. cemical equilibrium, pase equilibrium Kinetic ractionation: irreversible, unidirectional inetic reaction B E.g. isolated reaction products, pase separation, diusion Matematical description analogous Kinetic eects usually stronger tan equilibrium ractionation 9 Matematical Description o Fractionation Te isotopic eect o a transition/reaction B or B is described by te ractionation actor : ( B) B = = ( ) expresses te isotope ratio in B relative to tat in Oten only used, sometimes or inetic ractionation actors Fractionation eects are usually small:. Oten, te deviation o rom is used, te ractionation or enricment actor : B = = s te -values, te 's are usually given in. ometimes 3. ln is tabulated, because: ln = ln ( + ) = = + ( ) st st elationsips between,,, B B st + B = = = + st + = = B B / B + / B= = or * = B = = = = + + ( : separation) / B / B

3 dditivity in te -otation Cange o isotopic composition in te process B: = B + B pproximately linear mixing o -values ( ) + wit = m m mix tot and are multiplicative, and are approximately additive Terminology > : Enricment (nreicerung) o te rare isotope < : Depletion (breicerung) o te rare isotope > B : is enriced in te rare (eavy) isotope relative to B, is "eavier" tan B. or: B is depleted relative to, B is ligter tan. ote: - is iger/more positive/eavier tan - 3 rom Moo, 4 Equilibrium ractionation in reversible processes One way reaction: Kinetic ractionation Equilibrium isotope excange reaction + B l l + B [ ] [ ] [ ] [ ] [ ][ ] [ ][ ] B l l eq = = = = B B Bl l B K: Equilibrium constant o te isotope excange reaction K B divides in l B l and B wit reaction rates r l = l [ l ] and r = [ ] ( i : reaction rate constants) Te isotope ratio o te (instantaneous) product B is: [ ] [ ] r = = = = B rl l l l Examples Water/vapour isotope excange: H O(liq) H O(vap) 8 O(liq) + H 6 O(vap) H 6 O(liq) + H 8 O(vap) Examples Evaporation wit removal o vapour: 6 O(liq) H 6 O(vap) and H 8 O(liq) H 8 O(vap) Water/CO isotope excange: H O + CO H CO 3 8 O + C 6 O H C 8 O 6 O H 6 O + C 8 O 6 O 5 Biologically mediated reactions 4O CH O + 5HCO 3- + H + + H O 6 elation between inetic and equilibrium ractionation B divides in B and B wit product ratios: ( ) = and ( ) = B B wit and t equilibrium reaction rates are equal: r = r ; r = r ( B) ( ) ( ) = = l l Bl B = = l Bl l B rr l eq = = = = B rr ( ) l l l 7 Fractionation by diusion Mean energy o molecules in a gas in termodynamic equilibrium m T = mv v D = Dl m di D = m > l For diusion o gas troug gas B, m as to be replaced by te reduced mass µ (inetic teory o gases): ml, mb m, mb µ l = ; µ = m + m m + m Diusivity in water [ -9 m s - ] l, B, B He e r Mass [amu] D = c m -/ Kr Xe 8

Temperature dependence o ractionation Te dependence o ractionation on temperature T (usually decrease) is oten described by: ln = at + bt + c Water-vapour eq. ractionation actors w/v Vapour-water eq.

4 Temperature dependence o ractionation Te dependence o ractionation on temperature T (usually decrease) is oten described by: ln = at + bt + c Water-vapour eq. ractionation actors w/v Vapour-water eq. ractionation v/w ules o tumb on ractionation Ligt elements ractionate stronger tan eavy elements H/ H: m/m l =, 8 O/ 6 O: m/m l = /8 ( H) ~ 8( 8 O) Multiple isotopes: Fractionation scales wit mass dierence ( 8 O) ~ ( 7 O), ( 4 C) ~ ( 3 C) Fractionation decreases wit temperature Heavy isotopes generally enriced in te denser pase ( solid > liquid > gas ) cemically more strongly bound orm compound wit iger molecular weigt rom Faure, 986: rinciples o Isotope Geology rom Moo, 9 Fractionation: Te ayleig rocess Cange o isotope ratio in a diminising reservoir (substrate) ayleig: Isotopic evolution o te product t every moment, te isotopic composition o te ormed compound is at equilibrium wit te substrate: = or + Mass balance or te eavy (rare) isotope: ( + d)( + d) d n = = d( ) d d + d d = ( ) Integration wit = at = yields: ( ) or = = + Te isotopic composition o te accumulating product is: Σ = d = d Σ = wit Σ = ( + ) ote or = : Σ = Σ = ayleig ractionation during evaporation Open and closed systems 4 3 remaining water instantaneously ormed vapour accumulated vapour ( ) = + Open or closed wit respect to te product: Open: removal o product Closed: substrate and product always in equilibrium 8 O [ ] = v/w =.99 v/w = - = + Open or closed wit respect to te substrate: Open: continuous supply o substrate (ininite reservoir) Closed: inite substrate reservoir a Σ = ( + ). = / 3 O/C C/C O/O C/O 4

5 Wic system did we discuss (ayleig)? ayleig: ystems closed or substrate Classical ayleig system: Open or product, closed or substrate Open or product (solid): : remaining water B: instantaneous vapour C: accumulated vapour Closed or product (dased): D: remaining water E: accumulated vapour O/C 5 rom Kendall & McDonnell, Kinetic ractionation: Open or product Closed or substrate (solid) Open or substrate (dased): - o cange in substrate - roduct separated by ummary Conventions and Deinitions atios o rare, eavy to common, ligt isotopes -notation: relative deviation rom in International isation Fractionation Heavy species diuse/evaporate/react slower Fract. expressed by actor or relative cange (in ) - notation: only approximately additive Equilibrium and inetic ractionation ayleig: Isotopic evolution o substrate and product rom Kendall & McDonnell,

Lecture 5. Introduction to Stable Isotopes

Lecture 5. Introduction to Stable Isotopes Lecture 5 Introduction to Stable Isotopes Stable Isotope Geochemistry Primarily concerned with the isotope ratios of H, C, N, O, and S Si and B often included and new instrumentation has opened up others