Barrier To Rotation: Videos & Practice Problems

In molecular chemistry, understanding the energy barriers associated with molecular rotation is crucial. The energy barrier, measured in kilojoules per mole, indicates the energy required to rotate around a bond. To effectively calculate these barriers, it is essential to memorize four common energy values associated with different molecular interactions.

The least energetic conformation is the anti conformation, while the most energetic is the eclipsed conformation. The eclipsed interactions can be categorized based on the substituents involved:

1. **Eclipsed Methyl-Methyl Interaction**: This is the highest energy interaction, where two methyl groups overlap perfectly, resulting in an energy cost of 11 kilojoules per mole. This significant energy barrier makes this conformation rare.

2. **Eclipsed Methyl-Hydrogen Interaction**: When a methyl group overlaps with a hydrogen atom, the energy cost is lower, at 6 kilojoules per mole. This interaction is still unfavorable but occurs more frequently than the methyl-methyl overlap.

3. **Eclipsed Hydrogen-Hydrogen Interaction**: The energy cost for two hydrogen atoms eclipsing each other is 4 kilojoules per mole. This is the least energetic of the eclipsed interactions, making it the most favorable among them.

4. **Gauche Interaction**: A notable gauche interaction occurs when two large groups, such as methyl groups, are staggered but still interact significantly. This interaction has an energy cost of approximately 3.8 kilojoules per mole, which is close to the energy cost of the eclipsed hydrogen-hydrogen interaction.

By memorizing these four key values—11, 6, 4, and 3.8 kilojoules per mole—you will be well-equipped to analyze and solve problems related to molecular rotation and energy barriers. Understanding these interactions not only aids in predicting molecular behavior but also enhances your grasp of steric effects and torsional strain in organic molecules.

In this example, we explore the concept of rotational barriers in molecular interactions, specifically focusing on the energy cost associated with eclipsing interactions between atoms. The total energy required to rotate a molecule from a staggered to an eclipsed conformation is given as 22 kilojoules per mole. This value represents the cumulative energy cost of various interactions occurring during this rotation.

To determine the specific energy cost of the eclipsing interaction between a bromine (Br) atom and a hydrogen (H) atom, we can break down the total energy into its constituent parts. The interactions involved include the eclipsing of hydrogen with hydrogen (H-H) and methyl with methyl (methyl-methyl). The known energy costs for these interactions are 4 kilojoules per mole for H-H and 11 kilojoules per mole for methyl-methyl.

By summing these known values, we can set up the equation:

4 (H-H) + 11 (methyl-methyl) + x (H-Br) = 22

Here, x represents the unknown energy cost of the H-Br eclipsing interaction. Simplifying the equation gives:

15 + x = 22

To isolate x, we subtract 15 from both sides:

x = 22 - 15

x = 7

This calculation reveals that the energy cost for the eclipsing interaction between H and Br is 7 kilojoules per mole. This method demonstrates how to utilize known values to deduce unknown interactions effectively, reinforcing the importance of memorizing key energy values for various atomic interactions.

As a next step, students are encouraged to practice this concept independently by drawing the Newman projection of a given compound and applying the same principles to calculate unknown energy costs associated with eclipsing interactions.