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Stable Isotopes – Terminology 1 2 Outline Key questions to answer after this lecture: Stable Isotopes – Terminology 1) Definitions and terminology Roland A. Werner What is an isotope ? Institut für Agrarwissenschaften, ETH Zürich 2) Properties and isotope fractionation What properties differ between isotopic variants ? How does this influence reaction rates ? 3) Calculating and describing isotope fractionation How can I calculate and describe isotope fractionation ? What pitfalls and approximation should I be aware of ? 15st January 2021, 2 1 2 Part 1 Definition Isotope . Greek isos = "equal", tópos = "site, place" Isotopes occupy the same position in the periodic table of elements . Isotopes of an element have nuclei with the same number of protons (atomic number) but different numbers of neutrons . Therefore, isotopes have different masses and different nuclear properties Mass number m Element Atomic number n E 15st January 2021, 3 15st January 2021, 4 3 4 1 Definition Isotope Definition Isotope . Same position in periodic table Atom Core Mass number . Same number of protons (atomic number) but 6- 6- Hull different numbers of neutrons 6+ 6+ . Therefore, isotopes have different masses (mass 6n 7n number) and different nuclear properties 6 protons and 6 protons and Atomic number 7 neutrons 6 neutrons 12 13 Atoms with a (higher) number of neutrons C C 13 6 6 C can be used (one or more) than protons for NMR Different atomic weight 6 protons 15st January 2021, 5 15st January 2021, 6 5 6 Definition Isotope Definition Stable / Radioactive Isotope Atom Core Stable isotope or radioactive isotope ? Mass number 6- 6- Hull If the ratio of protons to neutrons in the nuclide of an atom is unbalanced, the atom is instable and decays 6+ 6+ under emission of radiation. This phenomenon is 6n 7n called radioactivity or radioactive decay. Protium Stable isotope Atomic number Calotte model Deuterium Stable isotope Electronic structure of an atom determines its chemical behaviour Nucleus is responsible for physical properties of the atom Tritium Radioactive isotope 15st January 2021, 7 15st January 2021, 8 7 8 2 Chart of Nuclides 13C natural abundance: Rough calculation Stable Isotopes Monoisotopic Relative atomic mass in u element 12 13 p+: 1.007276466583 u n : 1.00866491588 u C C e- : 5.48579909070 x 10−4 u "Valley of nuclear 6 6 stability" 12C: 12 u per definition 12C: 12 u ~ 98.9 % 13 C: 13.003355 u 13C: 13.003… u ~ 1.1 % 12 u x 0.989 + 13.003… u x 0.011 = 12.011 u Data from wikipedia 15st January 2021, 9 15st January 2021, 10 9 10 Average abundances of the stable isotopes Definition Isotopologue / Isotopomer Element Isotope Atomic Mass [u] Abundance . Isotopologues are molecules that differ only in their isotopic Hydrogen 1H 1.007 825 0319(6) 99.98 85(70) composition: 2H 2.014 101 7779(6) 0.01 15 (70) 12C is used to define Carbon 12C 12 (exactly) 98.93(8) Different mass atomic mass units 13C 13.003 354 838(5) 1.07(8) . Isotopomers are molecules with the same number of each Nitrogen 14N 14.003 074 0074(18) 99.63 6(20) Heavier isotopes of isotopic atom but differing in their positions: 15N 15.000 108 973(12) 0.36 4(20) bioelements have lower natural abundance Oxygen 16O 15.994 914 6223(25) 99.75 7(16) 17O 16.999 131 50(22) 0.03 8(1) 17O, 33S, 36S interesting for specific 18O 17.999 160 4(9) 0.20 5(14) applications Same mass Sulfur 32S 31.972 070 73(15) 94.99(26) after NE Holden in Handbook of 33 S 32.971 458 54(15) 0.75(2) Chemistry and Physics 92nd Edition, 2011-2012 34S 33.967 866 87(14) 4.25(24) http://www.hbcpnetbase.com/ . What can we call all four isotopic variants of e.g N2O ? 36 S 35.967 080 88(25) 0.01(1) and Coplen et al. (2002) Isotopocules Toyoda et al. (2015): Mass Spectrom Rev DOI 10.1002/mas.21459 15st January 2021, 11 15st January 2021, 12 11 12 3 Definition Isotopologue / Isotopomer Definition Isotopologue Isotopologues: further examples How many isotopologues from water and 1 1 2 2 1 18 2 18 carbon dioxide are possible? H O, CO H2O, H HO, H2O, H2 O, H2 O … 2 2 Naturally occurring stable H- and O-isotopes: 1 2 16 17 18 Isotopomers: further examples H2O: H, H, O, O, O 12 13 13 12 With which masses ? CH3 CH2OH / CH3 CH2OH Naturally occurring stable C- and O-isotopes: 12 13 16 17 18 CO2: C, C, O, O, O With which masses ? 15st January 2021, 13 15st January 2021, 14 13 14 Definition Isotopologue Definition Clumped isotopic species How many isotopologues from water and Clumped isotopic species are very rare … carbon dioxide are possible? H2O, CO2 Mass Isotope Abundance CO2 9 different H2O isotopologues There will be a 1 16 2 18 short introduction with mass from 18 ( H2 O) to mass 22 ( H2 O) in "clumped isotopes" on next Friday 12 different CO2 isotopologues starting from 12 16 13 18 Estimated by PhD thesis mass 44 ( C O2) to mass 49 ( C O2) Jesper Olson (2006), University of Aarhus, DK 15st January 2021, 15 15st January 2021, 16 15 16 4 Definition Isotopomers Definition Isotopomers How many isotopomers are possible for How many isotopomers are possible for water and methane? H2O, CH4 ? water and methane? H2O, CH4 ? H2O: H2O: none No (chemical) differentiation possible between the two hydrogen atoms of the water molecule ! CH4: CH4: none ? 15st January 2021, 17 15st January 2021, 18 17 18 Definition Isotopomers Definition Isotopomers How many isotopomers are possible for CH ? Methylene -group 4 Ethanol H H 1H 2HC C1H O1H ? 2 2 Methyl 1 1 2 1 . Stable isotopes: 1H and 2H ? H C C OH H3C C H H O H -group Hydroxyl 1 1 2 H H H3C C H2 O H No Isotopomers -group Lewis structures of the constitutional isotopomers of EtOH . Including radioactive 3H ? A1H 2 H B 1 2 2 1 HS HR HS HR No Isotopomers ? 1 H C C O 1 H H C OH H C OH . With four different substituents 1 H 1 H 3 3 • No mirror plane possible • R- and S-form possible Isotopomers Fischer projections of the stereo-isotopomers of EtOH No isotopomers for isotopic methane !! 15st January 2021, 19 15st January 2021, 20 19 20 5 Part 1 Different properties of isotopes For the detection of isotopes measurable differences in properties of isotopes (isotopologue molecules) are necessary. • Nuclide-physical reactivity (radioactivity) • Nuclear magnetism (NMR) • Nuclear mass and volume different spectra • Nuclear mass -> Density, Diffusion, different properties in gravity fields etc. Further-on we will concentrate on Mass-dependent isotope effects 15st January 2021, 21 15st January 2021, 22 21 22 Why is it interesting to measure “isotopes” ? Isotopologues - Different physical properties . Isotopes of an element have the same number of protons and electrons and therefore same electronic structure . The chemical behaviour of an atom is largely determined by its electronic structure, therefore different isotopes exhibit: . Nearly identical chemical behaviour but … . Can have different physical properties. Analogously, two molecules which differ only in the isotopic nature of their atoms (isotopocules) will have: . Identical electronic structure, and therefore similar chemical properties. f . Can have different physical properties. gaer 15st January 2021, 23 15st January 2021, 24 23 24 6 Isotopologues - Different physical properties Isotopologues - Different physical properties . Differences in behaviour in a magnetic field between isotopic variants is the basis of isotope ratio mass spectrometry . Most commonly used technique Next Lecture ! 1 2 m U r = B e . I.e.: When all else is equal, the radius of deflection varies as the square root of the mass of the isotopologue. 15st January 2021, 25 15st January 2021, 26 25 26 Molecular vibrations of a diatomic molecule Potential energy and internuclear distance Molecule vibration = periodic motion of atoms in a molecule Analogy to a spring Repulsion --> tension / relaxation Diatomic molecule as a simple example Both atoms are moving Harmonic oscillator potential curve Diatomic molecules have one normal mode of vibration: X H y g Stretching (and compressing) of the chemical bond r e X H n E X-2H E Act between the atoms (here O2) l Dissociation limit a Molecular motion: i t 1 n Translation, rotation not influencing chemical EAct X- H e t Attraction bonds to the same extent as vibration. o P O2 Non-harmonic oscillator potential curve 1 1 0(X- H) ZPE X- H Model Should be the other 2 ZPE X-2H 0(X- H) ZPE = energy at way. The heavier HCl one should vibrate 1 2 rX- H rX- H 0 K Vibrations of a methylene group (-CH2-) 3 atoms Correct scenario? less frequent? https://en.wikipedia.org/wiki/Molecular_vibration#Vibrations_of_a_methylene_g Internuclear Distance https://en.wikipedia.org/wiki/Molecular_vi bration roup_(%E2%80%93CH2%E2%80%93)_in_a_molecule_for_illustration 15st January 2021, 27 15st January 2021, 28 27 28 7 Different zero point and activation energy Isotopes and reaction rates Summary: KIE: Transition State Reaction rate Product • Bonds with heavier atoms have a lower vibration frequency than lighter ones. • Thus: More energy is needed to break the bonds of heavier isotopologues. ZPED(GS) Ground State • Thus: Heavier atoms/molecules react more J Bigeleisen (1965): Science AJ Bennet (2012): Curr Opin Struct 147:463-471 Biol 16:472-478 slowly than the lighter ones, because the bond strength is higher. • Increasing mass lowers vibration • Reaction coordinate describes • This results in lower turnover rates, causing frequency progress through the reaction isotope fractionations, e.g.
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