Question

Draw line-angle formulas for the three constitutional isomers with the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{12^{*}}\).

Short answer

Question: Draw line-angle formulas for three constitutional isomers with the molecular formula C5H12. Answer: The three constitutional isomers with the molecular formula C5H12 and their line-angle formulas are: 1. n-Pentane: $$ \begin{array}{c} \boldsymbol{-} \mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C} \boldsymbol{-} \end{array} $$ 2. Isopentane: $$ \begin{array}{c} \mathrm{C}-(\mathrm{C}-\mathrm{C})-\mathrm{C}-\mathrm{C} \end{array} $$ 3. Neopentane: $$ \begin{array}{c} \mathrm{C}-(\mathrm{C}-(\mathrm{C}-\mathrm{C})-\mathrm{C}) \end{array} $$

Step-by-step solution

Understand Constitutional Isomers

Constitutional isomers, also known as structural isomers, are molecules with the same molecular formula but have different structural arrangements. In this case, all three isomers will have the molecular formula C5H12, but the carbon atoms will be connected differently.

Identify the Isomers

With a 5-carbon molecular formula, there are three possible structural arrangements: 1. A straight chain of 5 carbon atoms (n-pentane) 2. A chain of 4 carbon atoms with a 1-carbon branch (isopentane) 3. A chain of 3 carbon atoms with a 2-carbon branch (neopentane)

Draw Line-Angle Formulas for Each Isomer

For each isomer, we will draw the line-angle formulas, which are simplified Lewis structures that represent covalent single bonds as lines and assume that all carbon vertices have enough hydrogen atoms to complete their valence shells. 1. n-pentane: - Place five vertices in a straight line and connect them with single bonds. This represents five carbon atoms connected in a straight chain. 2. Isopentane: - Place four vertices in a straight line and connect them with single bonds. This represents four carbon atoms in a chain. - Add a fifth vertex connected to the second carbon in the chain. 3. Neopentane: - Place three vertices in a straight line and connect them with single bonds. This represents three carbon atoms in a chain. - Add two vertices connected to the middle carbon in the chain. The final line-angle formulas are: 1. n-Pentane: $$ \begin{array}{c} \boldsymbol{-} \mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C} \boldsymbol{-} \end{array} $$ 2. Isopentane: $$ \begin{array}{c} \mathrm{C}-(\mathrm{C}-\mathrm{C})-\mathrm{C}-\mathrm{C} \end{array} $$ 3. Neopentane: $$ \begin{array}{c} \mathrm{C}-(\mathrm{C}-(\mathrm{C}-\mathrm{C})-\mathrm{C}) \end{array} $$

Key concepts

Structural Isomers

When it comes to understanding compounds in organic chemistry, structural isomers are a fundamental concept. These are molecules that share the same molecular formula, meaning they possess an identical number of each type of atom, but their arrangement in space greatly differs. As a result, the isomers can exhibit very distinct physical and chemical properties, despite their similar compositions.

Imagine a set of building blocks with the same number, shapes, and types. Although you can build multiple different structures using the same blocks, each design can be unique in its own right—this is the essence of structural isomers.

Using the example of C₅H₁₂, despite all isomers containing five carbon atoms and twelve hydrogen atoms, they differ in the connectivity of these atoms, leading to different compounds: n-pentane with a straight chain, isopentane with a single branch, and neopentane with a more complex branching.

Line-Angle Formulas

The line-angle formulas, sometimes referred to as skeletal structures, are a simplified way of drawing organic molecules that help us visualize structural isomers without clutter. They capitalize on the fact that carbon atoms typically form four bonds and hydrogen atoms are not shown unless they are connected to something other than carbon.

A line represents a bond between two carbon atoms, and a vertex or bend in the line represents a carbon atom itself. Assuming that each carbon completes its four bonds, any absent atoms from the drawing are presumed to be hydrogen atoms.

For instance, the line-angle formula for n-pentane displays a straight line of five connected vertices with implied hydrogens completing the valence of each carbon atom. This method greatly streamlines organic structures, making them easier to read and compare, especially when assessing multiple isomers of the same molecule.

Molecular Formula C5H12

The molecular formula C₅H₁₂ represents a family of molecules known as pentanes, which are all alkanes—saturated hydrocarbons with only single bonds. This particular molecular formula indicates that every molecule in this category has five carbon atoms and twelve hydrogen atoms.

However, given the versatility in how we can arrange these atoms, there are three distinct structural isomers that fall under this formula:

• n-pentane: A linear chain of five carbon atoms, all single bonded in sequence.
• isopentane: Four carbon atoms in a row with one carbon branched off the second atom.
• neopentane: A central carbon atom with four carbon atoms single bonded around it, creating a more compact, branched structure.

Understanding the structure and naming conventions of these isomers is crucial for students as it lays the groundwork for more complex organic chemistry topics that involve larger and more varied molecules.