Question

Write the condensed structural formulas for as many alkenes and alkynes as you can think of that have the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{10}\)

Short answer

The condensed structural formulas for alkenes and alkynes with the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{10}\) are as follows: 1. 1-Hexene: \(H_{2}C=CH-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 2. 2-Hexene: \(CH_{3}-CH=CH-CH_{2}-CH_{2}-CH_{3}\) 3. cis-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\) 4. trans-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\) 5. 1-Hexyne: \(HC \equiv C-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 6. 2-Hexyne: \(CH_{3}-C \equiv C-CH_{2}-CH_{2}-CH_{3}\) 7. 3-Hexyne: \(CH_{3}-CH_{2}-C \equiv C-CH_{2}-CH_{3}\) There are a total of 7 different isomers with the given molecular formula.

Step-by-step solution

Determine constitutional isomers with a double bond

To determine the alkenes, locate the double bond in different positions within the \(\mathrm{C}_{6}\) chain. These isomers include: 1. 1-Hexene: \(H_{2}C=CH-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 2. 2-Hexene: \(CH_{3}-CH=CH-CH_{2}-CH_{2}-CH_{3}\) There could also be additional isomers if a carbon-containing group were located on either side of the double bond.

Identify cis/trans isomers

Next, we must take into consideration the cis/trans isomers (also known as geometric isomers) of alkenes. These isomers involve different arrangements of atoms around the double bond. We can identify the following cis/trans isomers: 1. cis-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\) 2. trans-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\)

Determine constitutional isomers with a triple bond

Now, we will provide the condensed structural formulas for the alkynes, taking into account different triple bond positions in the \(\mathrm{C}_{6}\) chain. These isomers include: 1. 1-Hexyne: \(HC \equiv C-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 2. 2-Hexyne: \(CH_{3}-C \equiv C-CH_{2}-CH_{2}-CH_{3}\) 3. 3-Hexyne: \(CH_{3}-CH_{2}-C \equiv C-CH_{2}-CH_{3}\)

Combine all isomers

Now we can list all the isomers we have found: 1. 1-Hexene: \(H_{2}C=CH-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 2. 2-Hexene: \(CH_{3}-CH=CH-CH_{2}-CH_{2}-CH_{3}\) 3. cis-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\) 4. trans-3-Hexene: \(CH_{3}-CH_{2}-CH=CH-CH_{2}-CH_{3}\) 5. 1-Hexyne: \(HC \equiv C-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 6. 2-Hexyne: \(CH_{3}-C \equiv C-CH_{2}-CH_{2}-CH_{3}\) 7. 3-Hexyne: \(CH_{3}-CH_{2}-C \equiv C-CH_{2}-CH_{3}\) A total of 7 different isomers have the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{10}\), comprising both alkenes and alkynes.

Key concepts

Structural Isomerism

Structural isomerism, also known as constitutional isomerism, is a form of isomerism in which molecules with the same molecular formula have different connectivity of their atoms. This means that the atoms are bonded together in different orders. For example, considering the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{10}\), this formula could represent various alkenes and alkynes each with a distinct structure.
In the context of the exercise, various structural isomers for this formula include different locations for the double or triple bonds. Isomers like 1-hexene and 2-hexene have their double bond at varying points within the carbon chain, changing the molecules' physical and chemical properties even though their molecular formulas remain the same. When we consider triple bonds, we introduce alkynes such as 1-hexyne, 2-hexyne, and 3-hexyne, each with the triple bond at a different position along the chain. While the names might seem similar, their differing structures lead to unique characteristics for each compound.
Understanding structural isomerism is crucial because it explains why compounds with the same atoms can exhibit vastly different behaviors and reactivities, a key concept in organic chemistry.

Cis-Trans Isomerism

Cis-trans isomerism, also referred to as geometric isomerism, specifically occurs in alkenes due to the restricted rotation around the double bond. The two isomers differ in the positioning of substituents around the rigid bond. In 'cis' isomers, the substituents are on the same side of the double bond, giving rise to a certain physical and chemical property, whereas in 'trans' isomers, the substituents are on opposite sides, resulting in another set of properties.
Take, for instance, cis-3-Hexene and trans-3-Hexene from our exercise. They share the same molecular formula and structure except for the orientation around the double bond. This minor difference can lead to major changes; for example, cis isomers generally have higher polarity than their trans counterparts and often have different boiling and melting points. The identification of such isomers is vital for the synthesis and application of alkenes in industry and research. Recognizing these subtle variances helps students understand the importance of molecular geometry in chemical functionality and reaction outcomes.

Condensed Structural Formulas

Condensed structural formulas are a way of writing the structure of a molecule to show the specific arrangement of atoms without drawing out the full structural diagram. It's succinct yet contains the necessary information to understand the molecule's structure. For the series of hydrocarbons with the formula \(\mathrm{C}_{6} \mathrm{H}_{10}\), condensed structural formulas provide a quick and informative representation of each molecule's structure.
For instance, the condensed formula for 1-Hexene is \(H_{2}C=CH-CH_{2}-CH_{2}-CH_{2}-CH_{3}\). Each segment of the formula represents a piece of the molecule, with dash symbols indicating bonds between atoms. A double or triple bond is shown with equal signs (\(=\)) or triple lines (\(\equiv\)), respectively. While studying organic chemistry, students benefit immensely from understanding how to interpret and write condensed structural formulas. This skill enables them to recognize and compare molecular structures quickly, predict molecular properties, and understand reaction mechanisms more fundamentally. In essence, learning to work with condensed structural formulas bridges the gap between a molecule's abstract representation and its tangible reality.