Alkane Reactions and Nomenclature

To determine the equilibrium percentage of two compounds, use the equation: $[\Delta G = -RT \ln K]$ , where $[\Delta G]$ is the Gibbs free energy, R is the gas constant, T is the temperature, and K is the equilibrium constant.
Solve for K to find the equilibrium constant.
Alternatively, estimate the equilibrium percentage using a provided graph that relates energy difference to equilibrium constant.
For example, an energy difference of 3.6 kilojoules per mole at room temperature (298 K) yields an equilibrium constant of 4.5, resulting in approximately 82% of the molecule in the more stable form and 18% in the less stable form.
A graph with red asterisks indicates that at 0.9 kcals, approximately 82% is in the more stable form and 18% in the less stable form.
If two compounds differ by 3 kcals per mole, the most stable conformer is approximately 99%.

To illustrate the concept of conformational stability, two methylbutane is used as an example, specifically looking at the bond between carbons two and three.
The task involves drawing the most stable, least stable, and second most stable Newman projections of two methylbutane.
The most stable conformation must be a staggered conformation.
In a Newman projection where carbon two is in the front and carbon three is in the back, carbon two has a CH3 group, another CH3 group, and a hydrogen attached to it. Carbon three has two hydrogens and a methyl group (carbon four).
For the least stable conformation, draw an eclipsed conformation.
The methyl group in the eclipsed conformation can eclipse either a hydrogen or another methyl group.
Based on slide 21, the energy cost of a methyl-methyl eclipsing interaction is 11 kilojoules, a hydrogen-hydrogen interaction costs 4, and a methyl-hydrogen interaction costs 6. The total energy for the least stable conformation adds up to 21.
Percentages beyond three kcals per mole are effectively 99% for the more stable and less than 1% for the less stable.

Homework assignments will involve drawing Newman projections for given molecules, identifying the most and least stable conformations, and calculating their energies.
The graph for estimating percentages will be provided during exams.
Practice is essential for mastering these concepts.

For simple cyclic structures, add the prefix "cyclo-" to the corresponding carbon chain name.
- For example, a six-carbon chain (hexane) becomes cyclohexane when it forms a ring.
If branching points or substitutions are present, numbering becomes more critical.
When substituents are on the same side, use the prefix "cis-"; when on opposite sides, use "trans-".
- For example, if a methyl and an ethyl group are both pointing towards the ceiling, it's cis.
Stereoisomers must be considered when naming cyclic alkanes.
Examples:
- Trans-1,2-dichloro cyclo butane.

Two compounds can be related as the same molecule, isomers, or not isomers.
If they are isomers, they can be constitutional, conformational, or steric isomers.

If cyclohexane exists with all carbon atoms in the same plane, it forms a perfect hexagon with bond angles that deviate from the ideal angle for sp3 carbons.
In this flat conformation, all hydrogens are eclipsed, leading to high energy due to torsional strain.
- Each H-H eclipsing interaction costs 4 kilojoules per mole, totaling 48 kilojoules per mole of strain
However, cyclohexane can rotate to a chair conformation where every bond angle is 109.5 degrees, and all bonds are perfectly staggered.
A six-membered ring (cyclohexane) has no strain energy compared to a normal six-carbon chain.

Types of strain in cyclic structures:
- Angle strain: Deviation from 109.5 degrees.
- Torsional strain: Eclipsing groups on the atoms.
Cyclopropane (three-membered ring) has the highest amount of ring strain and all H's are eclipsed.
Four-membered rings have a lot of ring strain, but some rotation can occur to reduce eclipsing.
Five-membered rings also allow some rotation to reduce eclipsing.
Six-membered rings (cyclohexane) can achieve a chair conformation with every bond angle at 109.5 degrees and perfectly staggered bonds.
This chair conformation is the focus, and substituents will be added to it.

In cyclohexane, substituents can occupy axial or equatorial positions.
Axial positions point straight up or straight down, along an axis perpendicular to the ring.
Equatorial positions are around the circumference of the cyclohexane ring.
Each carbon in the ring has one axial and one equatorial position.
A methyl group in the equatorial position has more space around it.
A methyl group in an axial position is in close proximity to other axial hydrogens, causing steric strain, which costs energy.
Putting a methyl group in an axial position costs 3.8 kilojoules per mole due to 1,3-diaxial interactions.
The most stable chair structure has substituents in equatorial positions.
1,3-diaxial interactions occur between the substituent at carbon 1 and the hydrogen at carbon 3, which points in the same direction.

A ring flip (chair to chair inversion) converts axial groups to equatorial and equatorial groups to axial.
The stability of chair conformations depends on the size and position of the substituents.
Example: If a yellow group (bromine) is in the axial position, it has a certain energy. After a ring flip, the bromine is in the equatorial position with less energy.
If bromine is axial, the 1,3-diaxial interaction costs 5.6 kilojoules.
Only 8% would be in the chair structure with the bigger group in the axial position.
The energy values for substituent-H interactions are provided.

It is necessary to take a drawing on paper and draw the two different chair structures, showing the ring flip, adding up their energies, and determining which one is more stable.