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Fractionation
A reaction or process which selects for
one of the stable isotopes of a particular
element If the process selects for the heavier
isotope, the reaction product is heavy, the
reactant remaining is light
Isotope fractionation occurs for isotopic
exchange reactions and mass-dependent
differences in the rates of chemical
reactions and physical processes
a
bba
a
b (!} HHEln103
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Temperature effects on
fractionation The fractionation factors, E, are affected
by T (recall that this affects EA) and
defined empirically:
T
hen,
As T increases, ( decreases at high T(
goes to zero
BT
Aab
v!
2
6
3 10ln10 EWhere A and B are constants
determined for particular reactions
and T is temp. in Kelvins
a
bbaa
b (!} HHEln103
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Equilibrium vs. Kinetic fractionation
Fractionation is a
reaction, but one in
which the free energy
differences are on theorder of 1000x smaller
than other types of
chemical reactions
Just like other chemical
reactions, we candescribe the proportion
of reactants and
products as an
equilibrium or as akinetic function
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FRACTIONATION DURING
PHYSICAL PROCESSES
Mass differences also give rise to
fractionation during physical processes
(diffusion, evaporation, freezing, etc.).
Fractionation during physical process is aresult of differences in the velocities of
isotopic molecules of the same compound.
Consider molecules in a gas. All molecules
have the same average kinetic energy, which
is a function of temperature.
2
21 mvE
kinetic !
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Because the kinetic energy for heavy and light
isotopes is the same, we can write:
In the case of
12
C
16
O and
13
C
16
O we have:
Regardless of the temperature, the velocity of12C16O is 1.0177 times that of13C16O, so thelighter molecule will diffuse faster and
evaporate faster.
L
H
H
L
m
m
v
v!
0177.1994915.27
99827.28!!
H
L
v
v
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Equilibrium Fractionation
For an exchange reaction:
C16O2 + H218O C18O2 + H2
16O
Write the equilibrium:
Where activity coefficients effectively cancel
out
For isotope reactions, K is always small,
usually 1.0xx (this K is 1.047 for example)
)()(
)()(
2
182
1
2
16
2
162
1
2
18
OHOC
OHOCK!
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WHY IS K DIFFERENTFROM
1.0?
Because 18O forms a stronger covalent bond
with C than does 16O.
The vibrational energy of a molecule is given by
the equations:
H
O
H
RhE lvibrationa 21!
m
k
TR
2
1! kxF !
Thus, the frequency of vibration depends
on the mass of the atoms, so the energy
of a molecule depends on its mass.
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The heavy isotope forms a lower energy
bond; it does not vibrate as violently.
Therefore, it forms a stronger bond in
the compound. The Rule of Bigeleisen (1965) - The
heavy isotope goes preferentially into
the compound with the strongest bonds.
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Equilibrium Fractionation II
For a mass-dependent reaction:
Ca2+ + C18O32- CaC18O3
Ca2+ + C16O32- CaC16O3
Measure H18O in calcite (H18Occ) and water
(H18Osw)
Assumes 18O/16O between H2O and CO32- at
some equilibrium
T C = 16.998 - 4.52 (H18Occ - H18Osw) + 0.028 (H
18Occ-H18Osw)
2
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Empirical Relationship between Temp. &
Oxygen Isotope Ratios in Carbonates
At lower temperatures, calcite
crystallization tends to incorporate a
relativelylarger proportion of18O
because the energylevel(vibration)of ions containing this heavier isotope
decreases by a greater amount than ions
containing 16O.
As temperatures drop, the energylevel
of18O declines progressively by anamount that this disproportionately
greater than that of the lighter16O.
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Distillation
2 varieties, Batch and Rayleigh distillationdependent on if the products stay in contact
and re-equilibrate with the reactants
Batch Distillation:Hf=Hi (1 F) 10
3lnECO2-Rock
where the isotope of the rock (Hi) depends on
its initial value (Hf) and the fractionation factor Rayleigh Distillation
Hf - Hi =103(F(E 1) 1)
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RAYLEIGH DISTILLATION
Isotopic fractionation that occurs duringcondensation in a moist air mass can be
described by Rayleigh Distillation. The equation
governing this process is:
where Rv = isotope ratio of remaining vapor, Rv =
isotope ratio in initial vapor, = the fraction of
vapor remaining and a = the isotopic
fractionation factor
1! EfRR ovv
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Effect of Rayleigh
distillation on the
H18
O value of watervapor remaining in
the air mass and of
meteoric precipitation
falling from it at a
constant temperatureof25C.
Complications:
1) Re-evaporation
2) Temperaturedependency ofE
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Using isotopes to get information on
physical and chemical processes Fractionation is due to some reaction,
different isotopes can have different
fractionation for the same reaction, anddifferent reactions have differentfractionations, as well as being different atdifferent temperatures and pressures
Use this to understand physical-chemicalprocesses, mass transfer, temperaturechanges, and other things
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Volatilization
calcite + quartz = wollastonite + carbon dioxideCaCO
3+ SiO
2= CaSiO
3+ CO
2
As the CO2
is produced, it is likely to be expelled
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Other volatilization reaction examples
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ISOTOPE FRACTIONATION IN THE
HYDROSPHERE
Evaporation of surface water in equatorial regions
causes formation of air masses with H2O vapor
depleted in 18O and D compared to seawater.
This moist air is forced into more northerly, cooler airin the northern hemisphere, where water
condenses, and this condensate is enriched in 18O
and D compared to the remaining vapor.
The relationship between the isotopic composition of
liquid and vapor is:
331818 1010 !v
l
vl HEH
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Assuming that H18Ov = -13.1 and Evl(O) =
1.0092 at 25C, then
and assuming HDv = -94.8 and Evl(H) = 1.074
at 25C, then
These equations give the isotopic composition
of the first bit of precipitation. As 18O and D
are removed from the vapor, the remaining
vapor becomes more and more depleted.
Thus, H18O and HD values become increasingly
negative with increasing geographic latititude
(and altitude.
0003318 0.410101.130092.1 !!lH
00033
8.2710108.94074.1 !!lDH
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Map of North
America
showing
contours of theapproximate
average HD
values of
meteoric surface
waters.
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Because both H and O occur together in water, H18O and HD
are highlycorrelated, yielding the meteoric waterline
(MWL
): HD} 8
H
18O
+10
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Deviation from MWL
Any additional fractionation process which
affects O and D differently, or one to the
exclusion of the other will skew a water
away from the MWL plot
These effects include:
Elevation effects - (HD -8/1000m, -4/C)
Temperature (E different!)
Evapotranspiration and steam loss
Water/rock interaction (little H in most rocks)
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Kinetic Fractionation
lighter isotopes form weaker bonds incompounds, so they are more easily
broken and hence react faster. Thus, in
reactions governed by kinetics, the lightisotopes are concentrated in the products.
Again, isotope reactions can be exchange
reactions or mass-dependent chemical orphysical reactions kinetic factors may affect
any of these!
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Kinetic fractionation I
SO4
2- reduction
SO42- + CH4 + 2 H
+ H2S + CO2 + 2 H2O
This reaction is chemically slow at low T,
bacteria utilize this for E in anoxic settings Isotope fractionation of S in sulfide generated
by microbes from this process generates
some of the biggest fractionations in the
environment (-120 for S)
THEN we need to think about exchange
reactions with H2S orFeS(aq) as it may
continue to interact with other S species
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S isotopes and microbes
The fractionation of H2S formed frombacterial sulfate reduction (BSR) is affected
by several processes:
Recycling and physical differentiation yields
excessively depleted H2S
Open systems H2S loss removes34S
Limited sulfate governed by Rayleigh process,
enriching34
S Different organisms and different organic
substrates yield very different experimental H34S
Ends up as a poor indicator of BSR vs. TSR
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IronIsotopesEarths Oceans 3 Ga had no
oxygen and lots ofFe2+,cyanobacteria evolved,
produced O2 which oxidized
the iron to form BIFs in time
the Fe2+ was more depleted
and the oceans were stratified,
then later become oxic as theyare today
This interpretation is largely based on ironisotopes in iron oxides and sulfide minerals
deposited at those times (Rouxel et al., 2005)
No one has yet bothered tomeasure how iron isotopes
change when iron sulfide
minerals precipitate thats
where we come in
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Mass-independent fractionation
Mass effects for 3 stable isotopes(such as 18O, 17O, and 16O) shouldhave a mass-dependent relationshipbetween each for any process
Deviation from this is mass-
independent and thought to beindicative of a nuclear process(radiogenic, nucleosynthetic,spallation) as opposed to a physico-chemical process
Found mainly associated withatmospheric chemistry, effect can bepreserved as many geochemicalreactions in water and rock are mass-dependent
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S-isotopic evidence of Archaen
atmosphere
Farquar et al., 2001; Mojzsis et al., 2003found MIF signal in S isotopes (32S, 33S,
34S) preserved in archaen pyritesprecipitated before 2.45 Ga
Interpreted to be signal from the photolysisof SO2 in that atmosphere the reaction
occurs at 190-220nm light, indicating lowO2 and O3 (which very effficiently absorbthat wavelength)