Problem 1 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

The synclinal conformation of 1,2 -dichloroethane is \(4.8 \mathrm{kJmol}^{-1}\) higher in energy than the anti-periplanar conformation. The two energy barriers for rotation about the C-C bond in 1,2 -dichloroethane are \(21.5 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(38.9 \mathrm{kJmol}^{-1}\) higher than the energy of the anti-periplanar conformation. (Section \(18.2)\) (a) Sketch a graph of energy versus angle of rotation about the C-C bond (dihedral angle) for 1,2 -dichloroethane. (b) What conformation of 1,2 -dichloroethane has the highest energy?

Step-by-Step Solution

Answer

The highest energy conformation is the eclipsed conformation at 0° with 38.9 kJ/mol above the anti-periplanar.

Step 1: Identify Energy Levels

First, identify the given energy differences for the conformations of 1,2-dichloroethane in relation to the anti-periplanar conformation, which is considered the reference with the lowest energy. The synclinal conformation is 4.8 kJ/mol higher, while two rotational barriers are specified as 21.5 kJ/mol and 38.9 kJ/mol respectively.

Step 2: Understand Conformation Types

Recognize that different conformations correspond to different dihedral angles: - Anti-periplanar (lowest energy) - Synclinal, also known as gauche (4.8 kJ/mol higher) - Eclipsed forms which have higher energy states (corresponding to the energy barriers of 21.5 kJ/mol and 38.9 kJ/mol).

Step 3: Sketch Energy Diagram

Draw a graph plotting energy on the y-axis and dihedral angle (degree of rotation) on the x-axis: - At 0°, an eclipsed conformation likely has the highest energy (38.9 kJ/mol above) - At 60° (synclinal), energy is 4.8 kJ/mol above the anti-periplanar - At 180°, the conformation returns to anti-periplanar (0 kJ/mol) - Another eclipsed conformation appears at 120° or 240° with 21.5 kJ/mol energy above.

Step 4: Identify Highest Energy Conformation

From the energy graph, the highest point is at the eclipsed conformation where energy is 38.9 kJ/mol above the anti-periplanar state at 0° dihedral angle.

Key Concepts

Synclinal Conformation

The synclinal conformation, also known as the gauche conformation, is a specific arrangement of atoms in a molecule. This conformation has a dihedral angle of approximately 60°. In the case of 1,2-dichloroethane, this synclinal conformation is about 4.8 kJ/mol higher in energy compared to the anti-periplanar conformation.
This increase in energy is mostly due to the increased steric hindrance; the chlorine atoms are closer together, causing repulsion. By understanding synclinal conformation, it's easier to predict molecular stability and reaction behavior in certain conditions.

• Occurs at 60° dihedral angle
• Involves steric hindrance
• Higher energy than anti-periplanar conformation

Anti-Periplanar Conformation

The anti-periplanar conformation is often considered the most stable due to its minimal steric interactions. This conformation appears when substituents are arranged in opposite directions around the central bond, resulting in a dihedral angle of 180°. For 1,2-dichloroethane, this is the reference point for measuring energy levels of other conformations.
Energy-wise, it is the lowest and serves as a baseline representing optimum separation of substituent groups.
This stability is why molecules naturally favor the anti-periplanar conformation in the absence of external rotational forces.

• Dihedral angle is 180°
• Least steric hindrance
• Lowest energy conformation

Energy Barriers

Energy barriers are key concept in discusses the required energy to overcome in transitioning from one molecular conformation to another. In 1,2-dichloroethane, these barriers are established as 21.5 kJ/mol and 38.9 kJ/mol. These two energy barriers correspond to different eclipsed conformations that require more energy due to atom crowding.
The higher the energy barrier, the more stable the conformation on either side is. These barriers are due to steric hindrance and other molecular forces that resist changes in structure. Understanding these barriers aids in comprehending the energetic landscape through which molecules transition.

• Indicate rotational resistance
• Stem from steric and electronic interactions
• Vary in height due to different conformational changes

Dihedral Angle

The dihedral angle is a measure of the angle between a set of three points (or atoms) that defines the spatial relationship between parts of a molecule. It substantially influences which conformation a molecule favors and which might be more stable.
In conformational analysis, understanding how the dihedral angle modulates the energy of various conformations of compounds like 1,2-dichloroethane reveals why some structures are more prevalent or how they might react. Specific dihedral angles correspond to particular conformations:

• 0° and 120° conflict with eclipse conformations
• 60° corresponds to synclinal conformation
• 180° indicates anti-periplanar conformation

The dihedral angle provides a straightforward representation of how far the molecules must rotate to switch conformations, highlighting their dynamic nature.