Pique the Geek 20120422: The Isotope Effect

(9 pm. – promoted by ek hornbeck)

The germ of this piece came from an undertaking that I am considering.  That undertaking is to write a post for every chemical element.  The recent successes of my more technical pieces have made me decide to concentrate more on the harder part of science rather than less technical material.

The problem with that is that it would take over two years to cover all of the elements, and in reality even longer because there are topics out there that will surely be more topical.  I am not sure that this is feasible.  Maybe I could look at families, but then that gets way too general.  Any thoughts on how to approach (or even if I should) this huge array of subjects would be appreciated.

In any event, I would start with hydrogen and work my way to heavier elements.  One of the first things that came to mind was the isotope effect, because hydrogen has the largest isotope effect of any element.  Please stay with us!

First, let us define what an isotope is.  All of the elements are defined by the number of protons in the nucleus, also called that atomic number.  The letter Z is used as a shorthand for the atomic number.  Thus for hydrogen, Z = 1.  For uranium, Z = 92.

Z determines the number of electrons, and thus the chemical properties, of the neutral atom.  However, we have not yet considered neutrons, the other components of the nucleus that have no electrical charge but do contribute mass.  They also contribute stability to almost all nuclei (hydrogen being the sole exception) because of their interaction with protons and other neutrons via the strong force.

Think about it this way:  if the nucleus had only protons the electrostatic repulsion would make it fly apart.  There has to be an attractive force that overcomes that repulsion, and it is the strong force.  The strong force operates only over very tiny distances, whilst the electrostatic repulsion operates over distances tiny and huge.  However, the strong force is indeed strong.  Neutrons in a sense act not only to “dilute” the positive charges of the protons, but also act to allow the strong force to overcome the electrostatic repulsion, at least up to lead, Z = 82.  After that they are fighting a losing battle as electrostatic repulsion wins and the nuclei are unstable.

The sum of protons and neutrons in a given nucleus is called the mass number, symbolized by the letter A.  Except for the lightest elements (up to calcium, Z = 20), it takes more neutrons than protons to provide a stable nucleus, and for nuclei with an odd Z the heaviest one that is stable with equal numbers of protons and neutrons is nitrogen with Z = 7.  Odd Z nuclei almost always have fewer stable isotopes than even Z nuclei, and there are theoretical reasons for that.  As a matter of fact, two elements with Z less than 82 have no stable isotope.  Those are technetium (Z = 43) and promethium (Z = 61).

Z controls the electronic structure of all atoms, and these atomic orbitals can combine to form molecular orbitals when two or more atoms are covalently bonded.  Thus, regardless of whether one isotope of a given element or a different isotope is involved, the chemical properties are identical.  Let us take compounds of hydrogen as examples.

Hydrogen has three isotopes, and is the only element with unique names for its isotopes.  The most common isotope of hydrogen (remember, all three have Z = 1) has no neutron, so A = 1 as well.  It is called protium, and accounts for 99.985% of all hydrogen on earth.  The nucleus is simply a proton.  The second isotope has a neutron as well, so it has A = 2.  It is called deuterium, and the nucleus is called a deuteron.  Deuterium is often given the chemical symbol D.  The third isotope occurs only in trace quantities (unless made synthetically) and has two neutrons, so for tritium A = 3.  It is often given the chemical symbol T, and the nucleus is called a triton.  This nucleus is unstable with a half life of around 12.3 years.  This is the first example of a general trend that shows that it is possible to have too many neutrons with respect to protons to have a stable nucleus.

Incidentally, the neutron is an unstable particle unless bound to protons.  Obviously there is a sweet spot where the ratio of protons to neutrons stabilizes both the neutrons and the nucleus.  It is much more complex for that, but this is an OK zeroth order explanation.  By the way, the half life of a naked neutron is about 15 minutes, when it decays into a proton, and electron, and an electron antineutrino.

This background was necessary to define what isotopes are for folks who are not highly technical.  Now comes the fun stuff!  Remember, it is Z alone (to a rather extreme extent) that controls the chemical properties of atoms, and the interactions of those atoms’ electrons is also controlled by the respective Zs of the group.  Thus, A really does not have anything to do with the chemical properties of compounds, so it can be said that chemically H₂O is identical to D₂O.  (Technical folks, hear me out before you get your panties in a wad, please!)

To use the jargon, chemical reactions can be described by multidimensional models of potential energy surfaces (there can be many more than the four standard dimensions).  These surfaces are functions of Z and not of A.  The reaction coordinate is a curve that follows the contours of the surface, generally the lowest energy path.  (Nature prefers the lowest energy route for changes, usually.)  However, this takes into account only the electronic alterations involved in reactions.  There is more to it.

Let us consider the physical properties of ordinary water and deuterium oxide.  Here is a brief list of properties, with ordinary water next:

Freezing point:          0 degrees C; 3.8 degrees C

Boiling point:             100 degrees C; 101 degrees C

Density:                   1 g/ml; 1.107 g/ml

Dipole moment:          1.85 Debye; 1.87 Debye

These differences are completely due to the fact that deuterium has twice the mass of protium.  The dipole moment one might not be obvious, but to understand that we have to think of springs (the twisted metal ones, not sources of water).

In classical mechanics, the interaction betwixt a given spring is described by Hooke’s Law:

F = -kx, where

x is the position of one end of the spring (the other end assumed to be rigidly attached to a massive anchor),

k is a constant unique to the spring that defines its stiffness,  and

F is the restoring force that tries to push or pull the spring into its rest position.

Chemical bonds are very much like springs.  The strength of the bond is an analogue to the spring constant, and for oxygen/hydrogen bonds the bond dissociation energy is 460 kJ/mol.  It does not matter if it is protium or deuterium, because it is a function of Z.  However, since deuterium has twice the mass of protium, the molecular equivalent to the restoring force is different given identical xs.  In other words, the spring (chemical bond) requires a longer distance to give the same restoring force with protium than with deuterium because deuterium is more massive.  We shall get back to that in a moment.

The dipole moment of a molecule is just a measure of charge separation.  Molecules like the linear O₂ have a zero net dipole moment, but nonlinear molecules like water have a positive side and a negative side.  Molecules are always in a constant state of flux, and that is just like springs stretching and contracting.  The reason that deuterium oxide is just a little more polar than ordinary water is that the deuterons are held a bit more closely to the oxygen than the protons are, and closer means a greater dipole moment.

The point is that although the chemical properties of compounds may be identical, the physical ones can be quite different.  This is the key to how isotope effects work, and what they can teach us.

Isotope effects, more properly called kinetic isotope effects, are the result of differences in the rates of chemical reactions that vary with the mass of atoms either directly involved in the reaction or bonded to reacting atoms (sometimes bonded to another nearby atom).  The former are called primary isotope effects and the latter secondary isotope effects.  Primary ones are almost always greater than secondary ones.

The classic example of a primary isotope effect is the reaction betwixt hydrogen and chlorine to form hydrogen chloride.  At 0 degrees C, protium reacts 13.4 times faster than deuterium.  Here is how this is explained:

There is a concept in chemistry that involves the activated complex, which is a segment of the curve on the energy surface that involves breaking of existing bonds and the formation of new ones.  The point of highest energy along this curve is called the transition state, where the reactants can fall to products or to reactants.  Now, when bonds are being broken, normally heavier isotopes retard this process because the bonds, although of the same strength for either isotope, have a lower vibrational energy in the heavy isotope case.  Thus, just a bit more energy has to be added to break a deuterium/deuterium bond than a protium/protium bond.

I was not able to get the specifics about the formation of hydrogen chloride, but considering the temperature, it must have been a free radical process, probably of the two gases diluted with an inert gas and driven by irradiation with light.  In this process, a photon homolytically cleaves a chlorine molecule, each with a free electron.  Then a chlorine atom attacks a hydrogen molecule, taking one hydrogen atom from it to form hydrogen chloride and thus leaving a new hydrogen atom.  This process continues until all of the reactants are consumed.  Since deuterium is less probable to be cleaved than protium, the overall reaction is slower.

Secondary isotope effects are a little more difficult to understand, but they are often much more informative and are certainly more widespread.  Basically, the same changes to the zero point energy of a vibrational mode is affected as in primary isotope effects, just to a lesser extent because the bond being broken and/or formed is more remote from the different mass.

The most common nuclei involved in isotope effect studies are the isotopes of hydrogen, carbon, nitrogen, and oxygen.  This goes for the stable nuclei, although radioactive nuclei can also be used but handling precautions and the large expense of sensitive mass spectrometers limit the use of radioactive nuclei.  Natural carbon contains 1.1% of carbon-13, the rest being oxygen-16; natural nitrogen about  0.37% nitrogen -15, the rest being nitrogen-14, and natural oxygen about 0.20% oxygen-18, most of the rest being oxygen-16.

As said previously, hydrogen isotope effects are large because of the large mass differences betwixt the isotopes.  Carbon-13 is only 8.3% heavier than 12, N-15 only 7.1% heavier than N-14, but O-18 is 12.5% heavier than O-16.  All of these elements are important in organic chemistry and in biochemistry, so measuring isotope effects has traditionally been a tool for elucidating reaction mechanisms in the laboratory.  The magnitude of the isotope effect is a sensitive tool used to determine what is the transition state for a given reaction, and that knowledge is important information.  But there are also lots of more recent applications that are fascinating.

For example, it is easy to tell beet sugar from corn or cane sugar because of differences in how beets fix carbon dioxide from the atmosphere.  Beet sugar contains around 14 parts per thousand less carbon-13 than cane or corn sugar.  Isotopes of other elements show analogous trends, and it is possible to used the combined isotope ratios of hydrogen, carbon, and oxygen to tell whether fruit juice, for example, is really what it purports to be or if it is adulterated.

There was a famous case around 1985 or so when it was shown that the Beechnut Company was selling apple juice for babies that was essentially flavored sugar water, and isotopic fingerprints were what proved the point.  A former colleague of mine, Dr. Allan Brause, led that effort, and it ended up with Beechnut paying a large fine to the Treasury because of it.

Isotope ratios can also be used to tell what kind a diet people long dead ate.  It is possible to distinguish wheat eaters from corn eaters, for example, due to the carbon-13 ratios in bone.  Very different ratios in native Americans before and after the Spanish domination in the southwest US and northern Mexico show a shift away from American corn towards European wheat.

Oxygen isotope ratios can also be used to determine the temperature when precipitation fell in polar ice cores.  Oxygen isotope ratios can also be used to determine where crops were grown because water containing oxygen-18 is just a wee bit more apt to fall as precipitation since it just a little heavier than water with only O-16.  Maps have been developed that show the relative ratios of the two isotopes in rain and snowfall worldwide.

It is possible by examining the nitrogen isotope ratios to tell whether someone is a vegan or not, because meat eaters have relatively more N-15 than vegans because the heavier isotope concentrates in meat, and is amplified with each step along the food chain.  Hair, being rich in protein and thus in nitrogen, is an ideal sample for such analyses.  In flesh, there are differences in seafood signatures and land based meat signatures so hair samples can be used to track changes in diet from sea based to land based flesh, just like carbon can be used to track the movement away from corn.

These are just a few examples of how the isotope effect can be used.  My interest in this subject goes back to graduate school, when I was a student of Professor Arthur Fry at the University of Arkansas, one of the leading experts in this subject in the world at the time.

Well, you have done it again!  You have wasted many more einsteins of perfectly good photons reading this weighty piece.  I do not have time to come up with a joke , so I will just ask that you keep those comments, questions, corrections and other feedback coming.  My readers are the best, and the comments not only enhance the series, I always learn from them.

As for my wrist, I am still showing slow improvement.  I have a little more movement every day, but I really am ready for this to go ahead and heal.

Warmest regards,

Doc, aka Dr. David W. Smith

Crossposted at

The Stars Hollow Gazette,

Daily Kos, and

firefly-dreaming