Question

Optically active 'P' has the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{12}\) and catalytic hydrogenation converts into achiral \(\mathrm{C}_{6} \mathrm{H}_{14}\). The structure of ' \(\mathrm{P}\) ' is

Short answer

The structure of the optically active 'P' with the molecular formula C6H12 is: \( \hspace{17.5mm}\big\downarrow \\ \mathrm{H}_{3}\mathrm{C}-\mathrm{C}=\mathrm{C}-\mathrm{C}(\mathrm{CH}_{3})_{2} \\ \phantom{----}\big\uparrow \\ \phantom{---}\mathrm{H} \\ \) It is an alkene with one double bond and a chiral center at the second carbon atom, which causes optical activity.

Step-by-step solution

Analyze the molecular formula of 'P'

Given that 'P' has the molecular formula C6H12, we can determine its degrees of unsaturation (DoU). DoU is a measure of the number of multiple bonds and/or rings present in the molecule. We can calculate the DoU using the formula: \(DoU = \frac{(2 * \mathrm{number\ of\ Carbons} + 2) - \mathrm{number\ of\ Hydrogens}}{2}\) For 'P': \(DoU = \frac{(2 * 6 + 2) - 12}{2} = \frac{14-12}{2} = 1\) The molecule has one degree of unsaturation, indicating that it has either one double bond or one ring present in its structure.

Hydrogenation converts 'P' into an achiral C6H14 molecule

Upon hydrogenation, 'P' loses its optical activity and gains two extra hydrogen atoms, resulting in a saturated alkane with the molecular formula C6H14. This indicates that the single degree of unsaturation in 'P' comes from a double bond rather than from a ring since hydrogenation removes double bonds by adding hydrogen atoms across them.

Determine the structure of 'P'

Since the optically active 'P' molecule has six carbons and one degree of unsaturation from a double bond, it must be a chiral alkene. To possess optical activity, the alkene must have a chirality center, meaning the double bond must be connected to a carbon with four distinct groups. Considering these criteria, the structure of 'P' is: \( \hspace{17.5mm}\big\downarrow \\ \mathrm{H}_{3}\mathrm{C}-\mathrm{C}=\mathrm{C}-\mathrm{C}(\mathrm{CH}_{3})_{2} \\ \phantom{----}\big\uparrow \\ \phantom{---}\mathrm{H} \\ \) This molecule has the double bond causing the unsaturation and a chiral center at the second carbon atom, leading to optical activity.

Key concepts

Degrees of Unsaturation

Understanding the degrees of unsaturation (DoU) is integral to grasping the makeup of hydrocarbons. DoU refers to the total number of pi bonds or rings in a compound that prevent it from being fully saturated with hydrogen atoms. The formula for calculating DoU is quite straightforward:

\[\begin{equation}DoU = \frac{(2 * \text{number of Carbons} + 2) - \text{number of Hydrogens}}{2}\right.\end{equation}\]For hydrocarbons like alkanes that are fully saturated, the DoU is zero. However, for hydrocarbons with double bonds or rings, the DoU would be higher. Each double bond or ring in the structure counts as one degree of unsaturation. For instance, a molecule with the formula C6H12 has one degree of unsaturation. This means there is either one double bond or one ring present. The essential idea here is that unsaturation is a clue about the structure of the molecule that can inform you about the presence of functional groups or rings, which then guides us to understanding their chemical behavior.

It's important to note that triple bonds count as two degrees of unsaturation because they can be thought of as having one pi bond and one sigma bond that could have been two sigma bonds if the molecule were fully saturated.

Catalytic Hydrogenation

Catalytic hydrogenation is a critical concept for comprehending transformations in organic chemistry. This process involves the addition of hydrogen (H2) to a molecule in the presence of a catalyst. It is commonly used to reduce double or triple bonds in hydrocarbons, thereby increasing their hydrogen content and making them more saturated. Take, for example, an alkene undergoing catalytic hydrogenation;
the added hydrogen atoms break the double bond and bond to the carbon atoms individually, resulting in an alkane. This conversion not only changes the molecule's structure but also its physical and chemical properties like reactivity and boiling point.

Catalysts like platinum, palladium, or nickel are used to speed up the hydrogenation process without being consumed by it. This process is widely applied in the food industry to convert vegetable oils into semi-solid fats, a process vital for creating margarine from plant oils. It also has deep implications for pharmaceuticals, where catalytic hydrogenation can be used to refine or alter drug compounds.

Chirality in Organic Molecules

Chirality is a geometric property of some molecules where the molecule and its mirror image are not superimposable, much like left and right hands. This is present in molecules that have an asymmetry element such as a carbon atom bonded to four different substituents, known as a chiral center.

A molecule with chiral centers is called optically active because it can rotate plane-polarized light, either to the left (levorotatory) or to the right (dextrorotatory). The presence of chirality in a molecule can profoundly affect its interaction with biological systems and can lead to different biological activities between two enantiomers (non-superimposable mirror images). Thus, understanding chirality is particularly important in the field of medicinal chemistry and drug design.

For instance, in our exercise, the optically active hydrocarbon 'P' must have at least one chiral center which aligns with the molecular changes observed during catalytic hydrogenation. These concepts of chirality and stereochemistry are not just academic; they are applied during the synthesis of many drugs to ensure that the active enantiomer is produced, ultimately influencing the efficacy and safety of the medication.