Deduction of the Molecular Formula of a Hydrocarbon

MS

Figure 1.1 (Spec) A Mass Spectrometer

The 1 MV accelerator mass spectrometer at Lawrence Livermore National Laboratory http://bioams.llnl.gov/equipment.php ¹⁴C and tritium analyses of biomedical samples submitted by Resource users are conducted using this 1 MV system. The AMS spectrometer consists of a cesium sputter source, low-energy injection beam line, the high voltage collision cell (accelerator), a high-energy mass spectrometer and a particle detector for energy measurements (proceeding clockwise from lower left in the photograph).This image is a work of a United States Department of Energy (or predecessor organization) employee, taken or made as part of that person's official duties. As a work of the U.S. federal government, the image is in the public domain via Wikimedia Commons.

Simply put, a mass spectrum is a graph showing the masses and abundances of all the ions that result when you smash a molecule with a hammer. There are lots of places to read about the scales used to weigh the ions and the hammers used to smash the molecules but that discussion is left to others. Remember, we're cutting right to the chase and learning how to elucidate structures from spectra.

Oftentimes, but not always, and maybe not even usually, it's possible to get a molecular formula from the mass spectrum. One quick and dirty approach is to look at the highest mass region of the spectrum with the hopes of spotting what is called the peak group for the molecular ion, M^+•. For this quick and dirty trick to work you need to identify a pair of peaks in the M^+•. The taller and lighter mass peak is from the M^+• ion where all of the carbons are ¹²C. The peak next door is called the (M+1)^+•, or "isotopic peak." This isotopic peak comes from an ion which has one ¹³C instead of a ¹²C as in the base peak. This peak is called the M+1 isotopic peak. Nature has endowed the earth with 1.1 ¹³C atoms for every 100 C atoms. With this knowledge we can do some arithmetic.

• Normalize the base peak; i.e., multiply it's intensity by some number to make it 100.
• Multiply the intensity of the isotopic peak by this same normalization factor you applied to the base peak. This is called the "normalized isotopic peak" intensity.
• Divide the normalized isotopic peak's intensity by 1.1. This is the approximate number of carbons in the compound which must of course be an integer.
• Take the difference between the mass of the base peak and the number of carbons × 12. This is the number of hydrogens.

This quick and dirty approach will work 100% of the time for the spectra in our first several weeks of problems. But keep in mind, this is still tee-ball.

If you know the molecular formula, then you can calculate the number of rings + π bonds.

Equation 1-1 (Spec) Rings + Double Bonds formula (aka, Degree of Unsaturation or Index of Hydrogen Deficiency)

Credit: https://en.wikipedia.org/wiki/Degree_of_unsaturation

Where C = number of carbons, H = number of hydrogens, X= number of halogens and N = number of nitrogens. Divalent atoms like oxygen never contribute a term to this R + DB equation. It's easier to remember in words. Take the number of C atoms, subtract half the number of monovalent atoms, skip the divalent atoms, add half the number of trivalent atoms and then add 1. Remember, a hydrocarbon that has no rings or double bonds has 2n + 2 hydrogen atoms.

NMR

Figure 1.2 (Spec) An NMR Spectrometer

By Mike25 (Own work) [Public domain], via Wikimedia Commons

The NMR experiment distinguishes nuclei in molecules and gives a glimpse of their nuclear environment. Without getting into the quantum mechanics, suffice it to say that some nuclei are susceptible to having their spin flipped while other nuclei are not. It's this spin flipping that gives a signal in our NMR spectra. In this course we'll be flipping ¹³C nuclei and ¹H nuclei.

¹³C-NMR

We will use three types of ¹³C experiments for our spectra in this course.

• Distortionless Enhancement of Polarization Transfer (DEPT)
• Off-Resonance Proton Decoupled
• Broad Band Proton Decoupled

Broad Band Proton Decoupled: Great for counting equivalent carbons. Each carbon gives a singlet.

The placement of the signal on horizontal scale on the spectrum is called the chemical shift. This is a relative scale comparing the signal to that from a reference compound. Typical ¹³C chemical shifts are shown below in Table 1.2-3.

Table 1.1 (Spec) Some ¹³C chemical shifts adapted from http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/NMR%3A_Experimental/NMR%3A_Interpretation

¹H NMR

This technique uses the same instrument as shown in figure 1.1-3. Historically, the ¹H-NMR experiment came first; however, extracting structural information from ¹H-NMR spectra can be a little more complicated than it is from the ¹³C-NMR data. We'll only consider one ¹H-NMR experiment. Again, chemical shift, i.e., the position of the peaks on the horizontal axis is very informative. There are two other important bits of information we can get from a ¹H-NMR that are not considered for ¹³C-NMR. The area under the peaks can be integrated to quantify the number of hydrogens. This is called "integration." Also, the signals are split by the protons on neighboring carbon atoms. This is called "signal splitting pattern" So that's three pieces of information we need to extract from our ¹H NMR spectra-

• chemical shift
• integration
• signal splitting pattern

Chemical Shift

Table 1.2 (Spec) Some ¹H chemical shifts adapted from http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/NMR%3A_Experimental/NMR%3A_Interpretation

Integration

The area of the curve under each peak is often displayed as a line plotted above the spectrum. The height from one plateau to another gives the relative number of equivalent protons moving from left to right across the spectrum. Rather than an integration line, sometimes the number of protons is displayed above the peak group.