Question

Following are structural formulas for the cis isomers of \(1,2-1,3\)-, and 1,4 -dimethylcyclohexane and three sets of \({ }^{13} \mathrm{C}-\mathrm{NMR}\) spectral data. Assign each constitutional isomer its correct spectral data. $$ \begin{array}{|c|c|c|} \hline \text { Spectrum 1 } & \text { Spectrum 2 } & \text { Spectrum 3 } \\ \hline 31.35 & 34.20 & 44.60 \\ \hline 30.67 & 31.30 & 35.14 \\ \hline 20.85 & 23.56 & 32.88 \\ \hline & 15.97 & 26.54 \\ \hline & & 23.01 \\ \hline \end{array} $$

Short answer

Answer: The 1,3-dimethylcyclohexane isomer corresponds to Spectrum 2.

Step-by-step solution

Drawing the chair conformations of the cis isomers

Draw the chair conformations of the cis-isomers of 1,2-;1,3-; and 1,4-dimethylcyclohexane. Remember to draw all possible conformations for each isomer.

Analyzing the chemical shifts in conformations

Analyze the chemical shifts of carbons in all conformations drawn in Step 1. First, assign the expected values of chemical shifts for axial and equatorial carbons in the conformation. Then, compare these values to the chemical shifts provided for each spectrum.

Assigning the correct spectrum to each isomer

Based on the analysis and comparison of the expected chemical shifts of carbons in the conformations with the given spectra, assign the correct spectrum to each isomer as follows: - 1,2-dimethylcyclohexane: Spectrum 1 - 1,3-dimethylcyclohexane: Spectrum 2 - 1,4-dimethylcyclohexane: Spectrum 3 This completes the assignment of the correct \({}^{13}\mathrm{C}\)-\(\mathrm{NMR}\) spectral data to each isomer.

Key concepts

Cis Isomers

When it comes to organic chemistry, understanding the spatial arrangement of atoms in a molecule is crucial. Cis isomers are one such spatial configuration where two substituents are on the same side of a double bond or ring structure. Imagine sitting at a round dinner table with your friends: if you and your best friend sit next to each other, that's analogous to a cis configuration in chemistry. The closeness in space often affects the molecule's physical and chemical properties, such as boiling points, melting points, and reactivity.

Specifically applying this to cyclohexane rings, substituents can either be on the same side (cis) or opposite sides (trans) of the ring plane. A common challenge with cis and trans isomers is using spectroscopy techniques like 13C-NMR to distinguish them as their chemical environments cause different chemical shifts. This is especially true for isomers like 1,2-dimethylcyclohexane, where the two methyl groups are next to each other.

Dimethylcyclohexane

Diving deeper into a specific example, dimethylcyclohexane exists in several isomers depending on the positions of the methyl groups around the cyclohexane ring. The isomers discussed here are 1,2-, 1,3-, and 1,4-dimethylcyclohexane. What makes these isomers interesting is that the different positioning of the methyl groups creates unique interactions and chemical environments within the molecule.

When working through problems involving these isomers, as seen in the exercise, we focus on the 'cis' orientation where the methyl groups reside on the same side of the ring. Each isomer has its distinctive 13C-NMR chemical shifts which are fingerprints that identify those isomers. In educational contexts, exercises asking to match 13C-NMR spectra with the correct isomers are common for reinforcing the concepts of isomer identification and understanding molecular structure.

Chemical Shifts

Chemical shifts are the heart of NMR (Nuclear Magnetic Resonance) spectroscopy. Think of them as GPS coordinates that pinpoint where specific types of carbon atoms are located within a molecule. Every carbon atom in a molecule is affected by its electronic environment, which can shift its resonant frequency in the NMR spectrum. These shifts are measured in parts per million (ppm) and they provide insight into the structure of the molecule.

For instance, in carbon-13 NMR, different types of carbons (like those attached to a methyl group versus those part of a ring) will have different shifts. In the case of the dimethylcyclohexane isomers, we look for patterns in these shifts that match the various environments the carbons are in, which helps us assign the correct spectrum to each isomer, as done in the exercise. The exact values of chemical shifts are influenced by factors such as electronegativity of neighboring atoms and the carbon's location (whether it's in an axial or equatorial position on a chair conformation).

Chair Conformations

The chair conformation is a way to depict cyclohexane rings that are staggered, resembling the shape of a chair. This is a very stable and low-energy conformer due to minimal strain on the bonds. In chemistry visualization, imagine a cyclohexane molecule as a tiny hexagonal stool, where the 'legs' can point either up or down. These positions are referred to as axial (up and down) and equatorial (around the equator of the ring).

Using the chair conformation helps chemists deduce which positions on the ring are more likely to have different chemical shifts in an NMR spectrum. For dimethylcyclohexane isomers, the 1,2-, 1,3-, and 1,4-positions greatly affect where the methyl groups end up in the conformation, which in turn affects the chemical shifts observed in NMR. This concept is used in exercises, like the one provided, to correlate the 3D structure of the molecule with the observed 13C-NMR spectra, enabling students to interpret the data more accurately.