Problem 34 - Basic Principles of Organic Chemistry

Question

a. Show how the assignment of \(J_{A B}=J_{B C}=2 J_{A C}\) leads to the prediction of four equally spaced and equally intense lines for the methyl resonance of 2 -phenylpropene. b. What would the splittings of the alkenic and methyl protons look like for trans-1-phenylpropene if \(J_{A B}=16 \mathrm{~Hz}\), \(J_{A C}=4 \mathrm{~Hz}\), and \(J_{B C}=0 \mathrm{~Hz} ?\)

Step-by-Step Solution

Answer

For 2-phenylpropene: four equally spaced, equally intense lines; for trans-1-phenylpropene: alkenic protons doublet, methyl protons affected mainly by A-C coupling.

Step 1: Understand the Couplings Given

In the exercise, it's given that the coupling constants are assigned as follows: \( J_{AB} = J_{BC} = 2J_{AC} \). This implies that the value of \( J_{AC} \) is half of that of \( J_{AB} \) and \( J_{BC} \). If we let \( J_{AC} = x \), then \( J_{AB} = J_{BC} = 2x \). The relationship among these couplings affects the resulting NMR splitting pattern, particularly for the methyl resonance in 2-phenylpropene.

Step 2: Predicting the Splitting for Methyl Resonance

The methyl resonance arises from three equivalent hydrogens. Given the couplings \( J_{AB} = J_{BC} = 2J_{AC} \), the methyl group (denoted as A) interacts with the B and C protons. The effective splitting observed in NMR will have contributions primarily from these couplings leading to a multiplet structure. Since \( J_{AB} = J_{BC} = 2x \), four lines appear, and due to symmetry, they will be equally spaced and equally intense.

Step 3: Translate Couplings for trans-1-Phenylpropene

For trans-1-phenylpropene, given: \( J_{AB} = 16 \) Hz, \( J_{AC} = 4 \) Hz, and \( J_{BC} = 0 \) Hz, we can analyze the splitting pattern. These values suggest that the A-B coupling is strong, the A-C coupling is weaker, and there's no coupling between B and C.

Step 4: Determine the Alkenic Proton Splittings

For the alkenic protons, we analyze the effect of the given couplings. Proton A primarily couples with B with a large coupling constant (16 Hz) leading to a doublet for B. Since C doesn't couple with B, it does not split B further. A's coupling with C (4 Hz) results in a smaller doublet for C.

Step 5: Look at Splittings for Methyl Protons

Due to the A-C coupling, the methyl protons see A and C interaction predominantly. Given their \( J_{AC} = 4 \) Hz coupling interaction, and no additional interaction (\( J_{BC} = 0 \) Hz), methyl protons experience limited splitting from A and minimal influence from C, essentially generating a doublet pattern modified slightly by B due to its influence on A.

Key Concepts

Coupling Constants

Coupling constants in NMR spectroscopy are crucial as they tell us about the splitting patterns of signals. These constants, denoted by the letter J, reflect the interaction between neighboring nuclei, and their magnitudes are in hertz (Hz). They help reveal molecular connectivity.
For example, when given coupling constants such as \(J_{AB}, J_{BC},\) and \(J_{AC}\), we investigate how nuclei A, B, and C influence each other's magnetic environments. In the given problem, the conditions \(J_{AB} = J_{BC} = 2J_{AC}\) imply very specific splitting patterns, aiding in deducing the structure of complex molecules like 2-phenylpropene and trans-1-phenylpropene. Remember, the splitting observed in spectrum lines results from these coupling interactions, providing insights into molecular geometry.

Methyl Resonance

Methyl resonance in NMR pertains to the signal observed from the hydrogen atoms of a methyl group \((-CH_3)\). These hydrogens are equivalent, usually resulting in a unique and identifiable signal in the spectrum.
In the context of 2-phenylpropene and as described in the exercise, due to the specific coupling constants \(J_{AB} = J_{BC} = 2J_{AC}\), these methyl protons register a notable splitting pattern. They can generate four equally spaced signals. This pattern emerges due to their interaction with neighboring protons, displaying the methyl group's structural environment.

• Four lines, equally spaced, arise due to the symmetrical coupling
  
• Uniform intensity as the protons are identical

2-Phenylpropene

2-Phenylpropene is an organic compound featuring a phenyl group attached to a propenyl group. This structure infers certain NMR characteristics that help differentiate it from similar compounds.
In this molecule, how the coupling constants affect the hydrogens determines the NMR pattern. For instance, the specific relationship \(J_{AB} = J_{BC} = 2J_{AC}\) plays a pivotal role in interpreting the splitting pattern related to its methyl resonance.

• Methyl resonance shows a quartet pattern due to specific couplings
• These splitting patterns are diagnostic of particular chemical environments

Understanding such patterns further facilitates distinguishing 2-phenylpropene from other structural isomers.

trans-1-Phenylpropene

Trans-1-phenylpropene is an organic compound with distinct proton environments, measurable through NMR spectroscopy. The term "trans" refers to the geometry of the molecule, specifically the arrangement of substituents across a double bond.
In NMR, this trans-configuration results in unique coupling constants \(J_{AB}, J_{AC},\) and \(J_{BC}\), which are essential to understanding its spectrum. Given in the problem are \(J_{AB} = 16 \text{ Hz}, J_{AC} = 4 \text{ Hz},\) and \(J_{BC} = 0 \text{ Hz}\). The strong A-B coupling results in significant splitting, forming a doublet indicative of the structural alignment.

• Strong coupling (16 Hz) creates doublets for alkenic protons
• Weaker coupling (4 Hz) results in more subtle splitting patterns
• Lack of \(J_{BC}\) interaction simplifies the interpretation

Thus, trans-1-phenylpropene’s NMR spectrum corresponds directly to its defining structural features.