Question

Terpin, prepared commercially by the acid-catalyzed hydration of limonene, is used medicinally as an expectorant for coughs. C=C(C)C1CC=C(C)CC1 Limonene Terpin (a) Propose a structural formula for terpin and a mechanism for its formation. (b) How many cis, trans isomers are possible for the structural formula you propose?

Short answer

Answer: The structural formula of terpin is as follows:  There are 4 possible cis, trans isomers for the structural formula of terpin due to the presence of two asymmetric carbons bearing the hydroxyl group.

Step-by-step solution

Demonstrate the structure of limonene

Limonene is a terpene with the molecular formula C10H16. It has a cyclic structure with one double bond. The structure of limonene is: 

Propose a mechanism for the acid-catalyzed hydration of limonene

The hydration of limonene, catalyzed by an acid, consists of adding a molecule of water (H2O) to the double bond. The mechanism consists of three steps: 1. Protonation of the double bond 2. Nucleophilic attack by water 3. De-protonation The result is the addition of an -OH group and a -H group across the double bond to form a new molecule, which is terpin.

Propose a structural formula for terpin

Since the double bond has been broken and an -OH group has been added to one of the carbons involved in the double bond, terpin will have a hydroxyl group on one of the carbons. The structural formula for terpin is: 

Determine the number of cis, trans isomers possible

To find the number of cis, trans isomers possible for the structural formula of terpin, we need to consider the carbon atoms bearing the hydroxyl group. Due to the presence of asymmetric carbon atoms, there can be a cis-isomer (both hydrogens on the same side) and a trans-isomer (hydrogens on opposite sides) for each asymmetric carbon bearing the hydroxyl group. In the case of terpin, there are two asymmetric carbons bearing the hydroxyl group. Therefore, there are a total of 2^2 = 4 possible cis, trans isomers for the structural formula of terpin.

Key concepts

Chemical Mechanism

Chemical mechanisms detail the step-by-step process by which chemical reactions occur. An insightful example of this is the acid-catalyzed hydration of limonene, which leads to the formation of terpin. As we see in our step-by-step solution, the reaction begins with the protonation of the double bond. This makes limonene more reactive to the addition of water.

A water molecule, which acts as a nucleophile, attacks one of the positively charged carbons, adding an -OH group to that carbon atom. Finally, a de-protonation step occurs, where a hydrogen atom is lost, making the resulting compound neutral. This series of actions transforms the starting material, limonene, into terpin, which carries an additional hydroxyl group and a hydrogen atom across the former double bond.

Understanding this mechanism is critical since it depicts not just the changes to the molecular structure, but also the subtle intricacies of electron movements during the reaction. This can be crucial for predicting reaction outcomes and understanding how and why certain products, like terpin in this case, are formed.

Terpin Structure

When looking at the terpin structure proposed in the solution, it's important to appreciate the changes that occur during its formation. Initially, limonene has a single double bond, which is the site of reactivity during the hydration process.

The resulting terpin molecule contains no double bonds but includes a new hydroxyl (-OH) group. The presence of this functional group is evidence of the water molecule's addition during the hydration reaction. The structural formula proposed for terpin reveals two hydroxyl groups, which are indicative of an addition reaction on a symmetrical double bond of limonene.

Terpin's structure is critical in its role as an expectorant, a compound that helps clear mucus from the airways, aiding coughs. Its molecular geometry and the presence of specific functional groups account for its medicinal properties. Grasping the structure of terpin enables one to understand its physical and chemical properties, and by extension, its therapeutic potential.

Cis-Trans Isomerism

Cis-trans isomerism is a form of stereoisomerism characterized by the orientation of functional groups within a molecule. In cis isomers, functional groups are on the same side of a double bond or a cyclical structure, whereas in trans isomers, they are on opposite sides.

This is a key concept when considering the structural formula proposed for terpin and calculating the possible isomers. Terpin does not have a double bond, but it does have stereocenters - carbon atoms with four different substituents, giving rise to chirality.

Chirality and Its Consequences

Due to the presence of these stereocenters, terpin can have multiple chiral configurations, leading to different stereoisomers. The compound's spatial arrangement influences whether the isomer will be 'cis' or 'trans', though in a broad sense, since the classic definition involves double bonds.

According to the solution presented, terpin has two asymmetric carbon atoms, each capable of 'cis' or 'trans' positioning based on their hydroxyl groups' location, allowing for four different isomers, demonstrating the complexity and variability in organic compound structures.