Draw the all six Newman projection formulas for 3-methylhexane for the rotation about C3- C4 bond and draw the potential energy diagram?(4 points) 2 3 4 5 ? H?C-CH?-CH-CH?-CH?-CH? CH? HH H UZHS HH H HSC2 HC2CH3 H CH H H2 H C?H? 13 C HEC2
The Correct Answer and Explanation is:
Of course. Here are the six Newman projections for 3-methylhexane rotating about the C3-C4 bond, along with the corresponding potential energy diagram and a detailed explanation.
Solution
First, we identify the groups attached to the front carbon (C3) and the back carbon (C4).
- C3 (Front Carbon): A hydrogen (H), a methyl group (CH₃), and an ethyl group (C₂H₅).
- C4 (Back Carbon): Two hydrogens (H) and an ethyl group (C₂H₅).
The six key conformations are generated by rotating the back carbon in 60° increments.
1. The Six Newman Projections
Here are the six conformations, starting with the most stable anti-conformation at a 0° dihedral angle.
- 0° (Staggered, Anti): The two largest groups, both ethyl (C₂H₅), are 180° apart. This minimizes steric strain, making it the most stable conformation (lowest energy).
- 60° (Eclipsed): The ethyl group on the back carbon eclipses the methyl group on the front carbon. This C₂H₅/CH₃ eclipsing interaction creates significant steric strain.
- 120° (Staggered, Gauche): The two ethyl groups are 60° apart (gauche). This C₂H₅/C₂H₅ gauche interaction is more destabilizing than the interaction in the 240° conformer.
- 180° (Eclipsed): The two largest groups (ethyl/ethyl) are eclipsed. This creates the most severe steric repulsion, making it the least stable conformation (highest energy).
- 240° (Staggered, Gauche): The back ethyl group is gauche to the front methyl group. The C₂H₅/CH₃ gauche interaction has less strain than the C₂H₅/C₂H₅ interaction at 120°.
- 300° (Eclipsed): The back ethyl group eclipses a hydrogen. This conformation is less strained than the other eclipsed forms because it lacks any bulky group-on-group eclipsing.
2. Potential Energy Diagram
The potential energy diagram plots the energy of the conformations against the dihedral angle of rotation.
Explanation
The analysis of 3-methylhexane’s conformations around the C3-C4 bond involves drawing Newman projections and evaluating their relative stabilities. The front carbon, C3, is bonded to a hydrogen (H), a methyl group (CH₃), and an ethyl group (C₂H₅). The back carbon, C4, is bonded to two hydrogens and an ethyl group. The stability of each conformation depends on steric and torsional strain.
Rotation around the single bond produces a continuous series of conformations, but we focus on the six staggered and eclipsed forms. Staggered conformations, where the dihedral angles between substituents are 60°, are energy minima (more stable). Eclipsed conformations, where substituents are aligned with a 0° dihedral angle, are energy maxima (less stable) due to increased electron cloud repulsion.
The relative energy levels are determined by the size of the interacting groups. Larger groups create more steric strain.
- Most Stable (0°): The conformation with the two largest groups (ethyl/ethyl) positioned 180° apart (anti) is the most stable due to minimized steric strain. This is the global energy minimum.
- Least Stable (180°): The conformation where the two ethyl groups are eclipsed creates the maximum possible steric repulsion. This is the least stable conformation and the global energy maximum.
- Other Conformations: The remaining conformations have intermediate energies. The staggered conformer at 240° (gauche C₂H₅/CH₃) is more stable than the one at 120° (gauche C₂H₅/C₂H₅), as the interaction between two ethyl groups is more destabilizing. Similarly, for the eclipsed forms, the conformation at 180° (eclipsed C₂H₅/C₂H₅) is the most unstable, followed by 60° (eclipsed C₂H₅/CH₃), and finally 300° (eclipsed C₂H₅/H), which is the most stable of the high-energy maxima.
The potential energy diagram graphically represents this relationship, with three unequal minima and three unequal maxima, reflecting the unique steric environment of each conformation.
