Lecture 11 Stable Isotopes

Isotopes of ElementsChart of the NuclidesDelta NotationIsotope Fractionation Equilibrium Kinetic Raleigh

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,

See E & H Chpt. 5

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 elementsSome are stable; some are Radioactive

The chart of the nuclides (protons versus neutrons) for elements 1 (Hydrogen) through 12 (Magnesium).

Valley of Stability

X decay

X

decay

Most elements have more than one stable isotope.

Number of neutrons tendsto be greater than the number of protons

1:1 line

Full Chart of the Nuclides

1:1 line

Examples for H, C, N and O:

Atomic Protons Neutrons % AbundanceWeight (Atomic Number) (approximate)

Hydrogen H 1P 0N 99.99 D 1P 1N 0.01Carbon 12C 6P 6N 98.89

13C 6P 7N 1.1114C 6P 8N 10-10

Nitrogen 14N 7P 7N 99.615N 7P 8N 0.4

Oxygen 16O 8P 8N 99.7617O 8P 9N 0.02418O 8P 10N 0.20

All Isotopes of a given element have the same chemical properties, yet there are small differencesdue 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

1/2 = 5730 yr

Mass Spectrometer – Basic Schematics

Isotopes are measured as ratios of two isotopes by various kinds of detectors.Standards are run frequently to correct for instrument stability

Magnetic fielddeflects ion beam

Gases ionizedGases accelerated

Detectors

1. Input as gases2. Gases Ionized3. Gases accelerated4. Gases Bent by magnetic field5. Gases detected

high vacuum

NomenclatureReport 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 (“del”) notation – usually with units of ‰ because the differences are typically small.

(in ‰) = [(Rsample - Rstandard) / R standard ] x 1000or

R / Rstd = if δ is in ‰

( / ) ( / )1000 1000

( / )

H L sample H L std Rsample RstdH

H L std Rstd

Define H = heavy L = light

11000

Example:

13C (in %o) = [ (13C/12C)sample / (13C/12C) standard ] – 1 x 1000

Example: If (13C/12C) sample = 1.02 (13C/12C) std

13C = 1.02 (13C/12C) std / (13C/12C) std - 1 x 1000

= 0.02 x 1000 = 20 %o

Standards Vary

Isotopic Fractionation

Fractionation Factor = A-B = RA / RB where R = ratio of two isotopes in materials A or B

often

= Rproducts / Rreactants

The state of unequal stable isotope composition within differentmaterials linked by a reaction or process is called “isotope fractionation”

Two kinds of Isotope Fractionation Processes

1. Equilibrium Isotope effects

Equilibrium isotope fractionation is the partial separation of isotopes between twoor more substances in chemical equilibrium.

Usually applies to inorganic species. Usually not in organic compoundsDue 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 slightlydifferent 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) + H2

18O(g) ↔ H218O(l) + H2

16O(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 bothcarbon and oxygen isotopes

13CO2(g) + H12CO3- ↔ 12CO2(g) + 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 has the form:

H/L = (H/L)product / (H/L)reactants = (H13CO3- / H12CO3

-) / (13CO2 / 12CO2)

H/L = 1.0092 at 0ºC and 1.0068 at 30ºC

18O of planktonic and benthic foraminiferafrom piston core V28-238 (160ºE 1ºN)

Planktonic and Benthic differ due to differencesin water temperature where they grow.

Planktonic forams measure sea surface TBenthic forams measure benthic T

Example: Estimation of temperature in ancient ocean environments

CaCO3(s) + H218O CaC18OO2 + H2O

The exchange of 18O between CaCO3 and H2OThe distribution is Temperature dependent

Assumptions:1. Organism ppted CaCO3 in isotopic equilibrium with dissolved CO3

2-

2. The δ18O of the original water is known3. The δ18O of the shell has remained unchanged

last glacialHolocene

lastinterglacial

E & H Fig 5.3

18O in CaCO3 varies with Temperature

from lab experiments

18O increases with salinity

Complication: Changes in ice volume also influence 18OMore ice, thus higher salinity – more 18O left in the ocean

2. Kinetic FractionationNon-equilibrium – during irreversible reactions like photosynthesisOccurs 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.

12CO2 mw = 44 These must have the same kinetic energy (Ek = 1/2mv2)13CO2 mw = 45 so 12CO2 travels 12% faster than 13CO2.

All isotope effects involving organic matter are kineticExample:12CO2 + H2O = 12CH2O + O2 faster13CO2 + H2O = 13CH2O + O2 slowerThus organic matter gets enriched in 12C during photosynthesis (13C becomes negative)

Carbon

Carbon has only two stable isotopes with the following natural abundances:

12C 98.89%o13C 1.11%o

Below are some typical 13C values on the PDB scale in %o.

Standard (CaCO3; PDB) 0Atmospheric CO2 -8 (was -6‰, getting lighter due to new CO2)Ocean CO2 +2 (surface)

0 (deep)Plankton CaCO3 +0 (same as seawater)Plankton organic carbon -20Trees -26Atmospheric CH4 -47Coal and Oil -26

δ13C in different reservoirs E & H Fig. 5.6

13C of atmospheric CO2 versus time

ExampleEvaporation – Condensation Processes18O in cloud vapor and condensate (rain)plotted versus the fraction of remaining vaporfor a Raleigh process. The isotopic compositionof the residual vapor is a function of thefractionation factor between vapor and waterdroplets. The drops are rich in 18O. The vaporis progressively depleted.

Fractionation increases withdecreasing temperature

Raleigh Fractionation - A combination of both equilibrium and kinetic isotope effectsKinetic when water molecules evaporate from sea surfaceEquilibrium effect when water molecules condense from vapor to liquid form

Any isotope reaction carried out so that productsare isolated immediately from the reactants will showa characteristic trend in isotopic composition.

Where Rvapor / R liquid = f (-1)

where f = fraction of residual vapor = Rl/Rv

Distillation of meteoric water – large kinetic fractionation occurs betweenocean and vapor. Then rain forming in clouds is in equilibrium with vaporand is heavier that the vapor. Vapor becomes progressively lighter.D and 18O 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 H2

18O 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 relativeto cloud.

Cloud gets lighter

18O variation with time in Camp Centuryice core.

18O was lower in Greenland snow during last ice age

Effect of temperatureEffect of ocean salinity

15,000 years ago 18O = -40‰10,000 to present 18O = -29‰

Reflects 1. 18O of precipitation2. History of airmass – cumulative depletion of 18O

13C in important geological materials

Influence of carbon source and kinetic fractionation on the averageisotopic composition of marine and terrestrial plants.

Vertical profiles of CO2, 13C in DIC, O2 and 18O in O2

North Atlantic data

18O in average rain versustemperature

Meteoric Water Line

linear correlation betweenD and 18O in waters ofmeteoric origin

Spatial distribution of deuterium excess in the US