Question

Name and draw structural formulas for all cycloalkanes with molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10}\). Include cis and trans isomers as well as constitutional isomers.

Short answer

Question: List and draw all the structural formulas for cycloalkanes with the formula C5H10, including cis and trans isomers and any constitutional isomers. Answer: There are three different structural formulas for cycloalkanes with the molecular formula C5H10, including one unsubstituted cyclopentane and two conformations of 1-methylcyclopentane. The structural formulas are as follows: 1. Cyclopentane  2. 1-Methylcyclopentane - gauche conformation (similar to cis)  3. 1-Methylcyclopentane - anti conformation (similar to trans) 

Step-by-step solution

Draw the basic cycloalkane structure

First, draw a 5-membered carbon ring, which is a cyclopentane molecule, with all single bonds. This molecule has the formula \(\mathrm{C}_{5} \mathrm{H}_{10}\). So, cyclopentane is our base structure upon which we will build substituted and isomeric structures. 

Identify possible substituents

We could have one or more of the hydrogen atoms in the ring replaced by other groups or atoms. Considering only hydrogen and carbon atoms, the only possible substituent here is the methyl group, \(\mathrm{-CH}_{3}\).

Add substituents to the base structure

Add a methyl group to different carbons on the cyclopentane ring. This will generate constitutional isomers, changing the connectivity of the atoms in the molecule. You can connect a methyl group to any carbon in the cyclopentane ring. However, if it is added to the non-adjacent carbons, we'll get the same structure. Thus, we only consider adding the methyl group to one of adjacent carbons. 

Cis and trans isomers

Cyclopentane does not have double bonds, so we cannot directly bring cis and trans isomers into account. However, when you consider the high energy conformations of 1-methylcyclopentane, you can have a gauche conformation and an anti conformation. These two conformations can be considered similar to the cis and trans isomers in a planar molecule. However, strictly speaking, these conformations are better represented as rotamers rather than true cis and trans isomers.

Summarize the results

We have the following cycloalkanes with the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10}\): 1. Cyclopentane 2. 1-Methylcyclopentane - gauche conformation (similar to cis) 3. 1-Methylcyclopentane - anti conformation (similar to trans) Here are the structural formulas for these cycloalkanes: 1.  2.  3.  In total, we have three different structural formulas for cycloalkanes with the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10}\), including one unsubstituted cyclopentane and two conformations of 1-methylcyclopentane.

Key concepts

Understanding the Molecular Formula C5H10

The molecular formula C_{5}H_{10} indicates a family of hydrocarbons with five carbon atoms and ten hydrogen atoms. These compounds belong to the cycloalkane series, which are characterized by a ring structure made with carbon atoms. Due to the general formula for cycloalkanes being C_{n}H_{2n}, with C_{5}H_{10} we specifically look at cyclic structures with a single ring.

Since multiple arrangements of atoms are possible even with the same molecular formula, we encounter different isomers that have unique properties. Identifying the structural formulas for C_{5}H_{10} isomers involves considering both the ring size and the position of any substituents (e.g., methyl groups as -CH_{3}). This leads us to explore not just the base cyclopentane but also variations like substituted cycloalkanes such as methylcyclopentane.

Constitutional Isomers and Their Significance

Constitutional isomers, also known as structural isomers, are compounds with the same molecular formula but different structural formulas due to variations in the way atoms are connected. For C_{5}H_{10}, one can imagine the base structure as cyclopentane, a five-membered carbon ring. However, by substituting one hydrogen atom with a methyl group (-CH_{3}), we produce 1-methylcyclopentane, which is a constitutional isomer of cyclopentane.

Identifying all possible constitutional isomers requires us to consider various ways the atoms can be rearranged without altering the molecular formula. For example, if we substituted two hydrogens with two methyl groups, it would result in a different compound known as dimethylcyclopropane. The ability to comprehend and draw these isomers is a fundamental skill in organic chemistry as it extensively affects the physical and chemical properties of the compounds.

Cis and Trans Isomers in Cycloalkanes

In the case of cycloalkanes like C_{5}H_{10}, the concepts of cis and trans isomers are nuanced. Typically, 'cis' refers to two substituents being on the same side of a carbon-carbon double bond, while 'trans' indicates they are on opposite sides. However, cycloalkanes usually lack double bonds, so we look at the spatial arrangement of substituents around the ring.

In substituted cyclopentane, for example with 1-methylcyclopentane, the substituent can adopt different positions relative to other atoms or groups in the molecule. Though not true cis and trans isomers due to the lack of double bonds, the substituents may still be considered as being on the same side (gauche or pseudo-cis) or opposite sides (anti or pseudo-trans) of the ring, when viewed in a certain projection. Understanding this mimicry of cis and trans orientations in cycloalkanes helps in grasping the concept of stereochemistry in cyclic compounds.