E2 KT E4 KT
3 (20) e


/ 4 (18)3 / 2 e
1
combine combine
1
4618 ( ) e 44 20
3 2
( E1 E2 )( E3 E4 ) KT ECO2 EH 2O KT
1
4618 ( ) e 44 20
The changes in isotopic ratios in these processes are called “isotopic fractionation”


Expression of isotopic fractionation

For a process from reactant to product, the isotopic fractionation factor α is defined as:

The exchange reactions involve breaking of old bonds and formation of new bonds The strength of bonds formed by the light vs. heavier isotopes is different, resulting in difference in reaction rates



Thermodynamic equilibrium of isotope fractionation

Fractionation can be regarded as an exchange of isotopes between two molecular species or phases that are participating in a reaction H218O+C16O16O H216O+C16O18O


What is isotopic fractionation?

Isotopes of an element have slightly different chemical and physical properties due to the mass difference In chemical, physical or biological processes, the reactants and products may have different isotopic ratios

Friedman: found δ18O and δD change in coordinated fashion in precipitation Harmon Craig: studied δ18O and δD partition in precipitation, established meteoric water line (1961)
At lower temperatures, ∆E plays a greater role in changing the Q, hence larger isotopic fractionation

Requirement of isotopic equilibrium

Chemical equilibrium, forward and backward reaction rates are equal Forward and backward reactions have proceeded enough times to mix the isotopes between reactants and products

This process needs to occur many times to ensure full exchange, sometimes stirring is necessary, the exchange also proceeds faster when pH<4.5

Pቤተ መጻሕፍቲ ባይዱrtition functions (Q)

Dissociation energy of a molecule is related to its partition function (Q), at vibrational frequency
Q = -1m3/2∑e-E/kT
where, = a symmetry value m = mass E = the energy state, from zero point energy to the energy of the dissociated molecule (J*mole-1) K = Boltzmann constant (gas constant per molecule)=n1.380658 10-23JK-1 T = thermodynamic temperature K


Temperature impact

At higher temperature, the influence of difference in E (zero point energy difference) on Q is smaller, hence the isotopic fractionation between different isotopic species is smaller



Objectives

Understand the fundamental theory of stable isotope fractionation Familiar with the types of isotopic fractionation
Familiar with different ways to describe fractionation (sometimes confusing)
1. Equilibrium constant = α
X + Y* X* + Y H2 + HDO HD + H2O
e.g.,
K = [X*][Y]/[X][Y*] = {[X*]/[X]}÷{[Y*]/[Y]} = Rx/Ry = α
Concentration ratio = ratio of Q


For example, dissolution of CO2 in H2O CO2 + H2O H2CO3
The equilibrium involves exchange of O atoms between CO2 and H2O H218O+C16O16O H216O+C16O18O
Rx = [X*]/[X] = Qx* / Qx
C16O2/C16O18O ↔ H216O/H218O

QC16O18O / QC16O QH 18O / QH 16O
2 2 2

3 2
(46) e
3/ 2 1 3/ 2
1 1

E1 KT E3 KT
/ 2 (44) e
3/ 2
1

Later work demonstrates how isotopes are partitioned through other systems, such as 13C in the carbon cycle


Types of isotope fractionation

Equilibrium isotope fractionation

The heavy isotope has a stronger bond and require greater energy to dissociate than a light isotope
Lighter nuclei react more quickly In a equilibrium reaction, stronger bonds survive longer, so that usually the heavy isotopic species are partitioned into the more condensed phase, e.g., liquid phase in vapor-liquid reactions
Kinetic (non-equilibrium) isotope fractionation Diffusive isotope fractionation (a special case of kinetic isotope fractionation) Non-mass dependent isotope fractionation
Equilibrium isotopic fractionation

Redistribution of isotopes of an element among various reactants and products At equilibrium, isotope ratios in each compound are constant
Stable Isotope Fractionation
Topics in this class

Why do isotopic ratios change (fractionate) in nature?
Types of stable isotope fractionation How do we express the isotopic fractionation in a quantitative manner? How could isotopic fractionation be used for environmental and geological research?