Question

You have two bottles labeled "1, 2-Cyclopentanediol," one containing a compound of m.p. \(30^{\circ}\), the other a compound of m.p. \(55^{\circ}\); both compounds are optically inactive. How could you decide, beyond any doubt, which bottle should be labeled "cis" and which "trans"?

Short answer

The bottle containing the compound with a melting point of 30°C should be labeled "cis" as cis isomers typically have lower melting points, while the bottle with a melting point of 55°C should be labeled "trans" as trans isomers usually have higher melting points due to their more symmetrical structure and stronger intermolecular forces.

Step-by-step solution

Understand the difference between cis and trans isomers

Cis and trans isomers are geometric isomers that arise due to restricted rotation around a double bond or a single bond in a cyclic compound. In cis isomers, similar groups are on the same side of the double bond or the cyclic structure, whereas in trans isomers, similar groups are on opposite sides of the double bond or the cyclic structure. The difference in their spatial arrangement leads to differences in physical properties such as melting points.

Relate isomer structure to melting point

Typically, cis isomers have lower melting points compared to trans isomers. This is because the trans isomers have a more symmetrical structure and thus create better packing within solid-state which leads to stronger intermolecular forces, resulting in higher melting points.

Determine the isomers based on melting points

Given that we have two bottles containing 1,2-Cyclopentanediol with melting points of 30°C and 55°C, knowing that cis isomers usually have lower melting points while trans isomers have higher melting points: 1. The bottle containing the compound with a melting point of 30°C is more likely to be the cis isomer. 2. The bottle containing the compound with a melting point of 55°C is more likely to be the trans isomer.

Conclusion

Based on the difference in melting points and understanding of cis and trans isomers, you can label the bottle with a melting point of 30°C as "cis" and the bottle with a melting point of 55°C as "trans".

Key concepts

Geometric Isomerism

Geometric isomerism, a fascinating aspect of chemistry, occurs when two or more compounds have the same formula but different spatial arrangements. The concept is particularly relevant in cyclic compounds and compounds with double bonds, where the atoms cannot simply rotate to convert one isomer into another. This restriction of rotation leads to the formation of distinct isomers known as cis and trans.

In cis isomers, the identical or similar groups are adjacent to each other, on the same side, which often results in a more polar molecule and impacts its boiling point, solubility, and melting point. On the other hand, trans isomers have the groups on opposite sides of the central bond or ring, often leading to a more symmetrical shape and less polarity.

Melting Points

Melting point is a physical property that can provide insights into the purity and structure of a substance. The melting point of a compound is affected by the strength of intermolecular forces - the stronger the forces, the higher the melting point. For geometric isomers, trans configurations generally have higher melting points than cis configurations. This is due to the symmetrical shape of trans isomers allowing for better packing in the solid-state. In contrast, the cis isomers, with groups on the same side, can't pack as efficiently, leading to weaker Van der Waals forces between the molecules and, consequently, lower melting points.

Melting points are not only indicative of structural differences but are also used to determine the identity and purity of substances, making them a valuable characteristic in differentiating between isomers.

1,2-Cyclopentanediol

The molecule 1,2-Cyclopentanediol is an organic compound comprising a five-membered ring with two hydroxyl (OH) groups positioned on the first and second carbon atoms. The position of these two OH groups can result in two geometric isomers: cis and trans. The cis isomer has both OH groups on the same side of the ring, which can lead to hydrogen bonding between the groups, making it more polar and potentially impacting its solubility and boiling point. The trans isomer, with OH groups on opposite sides, is less polar and more symmetric. Due to differences in these properties, the cis isomer typically exhibits a lower melting point, while the trans isomer, with stronger intermolecular interactions due to its symmetry, normally has a higher melting point.

This distinction in physical properties, based on isomerism, can be used to determine the correct labeling of bottles containing 1,2-Cyclopentanediol, even in the absence of optical activity. The bottle with the compound that melts at 30°C, being the lower melting point of the two, should be labeled as cis-1,2-Cyclopentanediol, and the one with a melting point of 55°C should be labeled as trans-1,2-Cyclopentanediol, reflecting their structural differences and consistent with conventional melting point trends.