Lecture 11 Stable Isotopes
Isotopes of Elements
Chart of the Nuclides
Delta Notation
Isotope Fractionation
Equilibrium
Kinetic
Raleigh
See E & H Chpt. 5
When the universe was formed 15 billion years ago (the “Big Bang”)
light elements of H (99%), He (1%) and trace amounts of Li were formed.
Subsequent reactions during star formation created the remaining elements,
Isotopes of Elements
The chemical characteristic of an element is determined by the
number of protons in its nucleus.
Atomic Number = # Protons = define the chemistry
Different elements can have different numbers of neutrons and
thus atomic weights (the sum of protons plus neutrons).
Atomic Weight = protons + neutrons = referred to as isotopes
There are 92 naturally occurring elements
Some are stable; some are Radioactive
The chart of the nuclides (protons versus neutrons)
for elements 1 (Hydrogen) through 12 (Magnesium).
Valley of Stability
Most elements have more
than one stable isotope.
1:1 line
b decay X
X
a decay
Number of neutrons tends
to be greater than the
number of protons
Full Chart of the Nuclides
1:1 line
Examples for H, C, N and O:
Atomic Protons
Neutrons
Weight (Atomic Number)
Hydrogen H
1P
0N
D
1P
1N
Carbon 12C
6P
6N
13C
6P
7N
14C
6P
8N
Nitrogen 14N
7P
7N
15N
7P
8N
Oxygen 16O
8P
8N
17O
8P
9N
18O
8P
10N
% Abundance
(approximate)
99.99
0.01
98.89
1.11
10-10 1/2 = 5730 yr
99.6
0.4
99.76
0.024
0.20
All Isotopes of a given element have the same chemical properties, yet there are small differences
due to the fact that heavier isotopes typically form stronger bonds and diffuse slightly slower
% Abundance is for the average Earth’s crust, ocean and atmosphere
Mass Spectrometer – Basic Schematics
Gases accelerated
high vacuum
Magnetic field
deflects ion beam
Gases ionized
1. Input as gases
2. Gases Ionized
3. Gases accelerated
4. Gases Bent by
magnetic field
5. Gases detected
Detectors
Isotopes are measured as ratios of two isotopes by various kinds of detectors.
Standards are run frequently to correct for instrument stability
Nomenclature
Report Stable Isotope Abundance as ratio to Most Abundant Isotope (e.g. 13C/12C)
-Why? The Ratio of Isotopes is What is Measured Using a Mass Spectrometer
The Ratio Can Be Measured Very Precisely.
The isotope ratio of a sample is reported relative to a standard using d (“del”) notation –
usually with units of ‰ because the differences are typically small.
Define H = heavy L = light
 ( H / L) sample  ( H / L) std 
 Rsample  Rstd 

1000



 1000
(
H
/
L
)
std
Rstd




dH 
d (in ‰) = [(Rsample - Rstandard) / R standard ] x 1000
or
d 

1

R / Rstd = 
 if δ is in ‰

1000 
Example:
d13C (in %o)
=
[ (13C/12C)sample / (13C/12C) standard ] – 1
Example: If (13C/12C) sample = 1.02 (13C/12C) std
d 13C =
1.02 (13C/12C) std / (13C/12C) std - 1
= 0.02 x 1000 = 20 %o
x 1000
x 1000
Standards Vary
Isotopic Fractionation
The state of unequal stable isotope composition within different
materials linked by a reaction or process is called “isotope fractionation”
Fractionation Factor = a
aA-B = RA / RB where R = ratio of two isotopes in materials A or B
often
a = Rproducts / Rreactants
Two kinds of Isotope Fractionation Processes
1. Equilibrium Isotope effects
Equilibrium isotope fractionation is the partial separation of isotopes between two
or more substances in chemical equilibrium.
Usually applies to inorganic species. Usually not in organic compounds
Due to slightly different free energies for atoms of different atomic weight
Vibrational energy is the source of the fractionation. Equilibrium fractionation results
from the reduction in vibrational energy when a more massive isotope is
substituted for a less massive one. This leads to higher concentrations of the
heavier isotope in substances where the vibrational energy is most sensitive to
isotope fractionation (e.g., those with the highest bond force constants)
If molecules are able to spontaneous exchange isotopes they will exhibit slightly
different isotope abundances at thermodynamic equilibrium (their lowest energy state)
For example: exchange reactions between light = Al, Bl and heavy = Ah, Bh
aA1 + bBh ↔ aAh + bB1
The heavier isotope winds up in the compound in which it is bound more strongly.
Heavier isotopes form stronger bonds (e.g. think of like springs).
If α = 1 the isotopes are distributed evenly between the phases.
Example: equilibrium fractionation of oxygen isotopes in liquid water (l)
relative to water vapor (g).
H216O(l) + H218O(g) ↔ H218O(l) + H216O(g)
At 20ºC, the equilibrium fractionation factor for this reaction is:
α = (18O/16O)l / 18O/16O)g = 1.0098
Example:
The carbonate buffer system involving gaseous CO2(g), aqueous CO2 (aq),
aqueous bicarbonate HCO3- and carbonate CO32-.
An important system that can exhibit equilibrium isotope effects for both
carbon and oxygen isotopes
13CO (g)
2
+ H12CO3- ↔
12CO (g)
2
+ H13CO3-
The heavier isotope (13C) is preferentially concentrated in the chemical
compound with the strongest bonds. In this case 13C will be concentrated
in HCO3- as opposed to CO2(g).
For this reaction a has the form:
aH/L = (H/L)product / (H/L)reactants = (H13CO3- / H12CO3-) / (13CO2 / 12CO2)
aH/L = 1.0092 at 0ºC and 1.0068 at 30ºC
Example: Estimation of temperature in ancient ocean environments
CaCO3(s) + H218O  CaC18OO2 + H2O
The exchange of 18O between CaCO3 and H2O
The distribution is Temperature dependent
last
interglacial
Holocene
last glacial
d18O of planktonic and benthic foraminifera
from piston core V28-238 (160ºE 1ºN)
Planktonic and Benthic differ due to differences
in water temperature where they grow.
Planktonic forams measure sea surface T
Benthic forams measure benthic T
Assumptions:
1. Organism ppted CaCO3 in isotopic equilibrium
with dissolved CO322. The δ18O of the original water is known
3. The δ18O of the shell has remained unchanged
d18O in CaCO3 varies with Temperature
from lab experiments
E & H Fig 5.3
Complication: Changes in ice volume also influence d18O
More ice, thus higher salinity – more d18O left in the ocean
d18O increases with salinity
2. Kinetic Fractionation
Non-equilibrium – during irreversible reactions like photosynthesis
Occurs when the rate of chemical reaction is sensitive to atomic mass
Results from either differential rates of bond breaking or diffusion rates
Compounds move at different rates due to unequal masses.
Light are always faster.
For kinetic fractionation, the breaking of the chemical bonds is the
rate limiting step. Essentially all isotopic effects involved with formation /
destruction of organic matter are kinetic
There is always a preferential enrichment for the lighter isotope in the products.
12CO
mw = 44
13CO mw = 45
2
2
These must have the same kinetic energy (Ek = 1/2mv2)
so 12CO2 travels 12% faster than 13CO2.
All isotope effects involving organic matter are kinetic
Example:
12CO + H O = 12CH O + O
2
2
2
2 faster
13CO + H O = 13CH O + O slower
2
2
2
2
Thus organic matter gets enriched in 12C during photosynthesis (d13C becomes negative)
Carbon
Carbon has only two stable isotopes with the following
natural abundances:
12C
13C
98.89%o
1.11%o
Below are some typical d13C values on the PDB scale in %o.
Standard (CaCO3; PDB)
Atmospheric CO2
Ocean SCO2
Plankton CaCO3
Plankton organic carbon
Trees
Atmospheric CH4
Coal and Oil
0
-8 (was -6‰, getting lighter due to new CO2)
+2 (surface)
0 (deep)
+0 (same as seawater)
-20
-26
-47
-26
δ13C in different reservoirs
E & H Fig. 5.6
d13C of atmospheric CO2 versus time
Raleigh Fractionation A combination of both equilibrium and kinetic isotope effects
Kinetic when water molecules evaporate from sea surface
Equilibrium effect when water molecules condense from
vapor to liquid form
Any isotope reaction carried out so that products
are isolated immediately from the reactants will show
a characteristic trend in isotopic composition.
Example: Evaporation – Condensation Processes
d18O in cloud vapor and condensate (rain)
plotted versus the fraction of remaining vapor
for a Raleigh process. The isotopic composition
of the residual vapor is a function of the
fractionation factor between vapor and water
droplets. The drops are rich in 18O. The vapor
is progressively depleted.
Where Rvapor / R liquid = f (a-1)
where f = fraction of residual vapor
a = Rl/Rv
Fractionation increases with
decreasing temperature
Distillation of meteoric water – large kinetic fractionation occurs between
ocean and vapor. Then rain forming in clouds is in equilibrium with vapor
and is heavier that the vapor. Vapor becomes progressively lighter.
dD and d18O get lower with distance from source.
Water evaporation is a kinetic effect.
Vapor is lighter than liquid. At 20ºC the difference is 9‰ (see Raleigh plot).
The BP of H218O is higher than for H216O
Air masses transported to
higher latitudes where it is cooler.
water lost due to rain
raindrops are rich in 18O relative
to cloud.
Cloud gets lighter
d18O variation with time in Camp Century
ice core.
d18O was lower in Greenland snow
during last ice age
Effect of temperature
Effect of ocean salinity
15,000 years ago d18O = -40‰
10,000 to present d18O = -29‰
Reflects
1. d18O of precipitation
2. History of airmass – cumulative depletion of d18O
d13C in important geological materials
Influence of carbon source and kinetic fractionation on the average
isotopic composition of marine and terrestrial plants.
Vertical profiles of SCO2, d13C in DIC, O2 and d18O in O2
North Atlantic data
d18O in average rain versus
temperature
Meteoric Water Line
linear correlation between
dD and d18O in waters of
meteoric origin
Spatial distribution of deuterium excess in the US