Question

Draw all the structural isomers for hydrocarbons having the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{10}\).

Short answer

There are two structural isomers: n-butane and isobutane.

Step-by-step solution

Understand the Molecular Formula

The molecular formula \(\mathrm{C}_{4}\mathrm{H}_{10}\) represents a hydrocarbon, specifically an alkane since all carbons are saturated with hydrogen. To find its isomers, we need to find all possible structures with this formula.

Identify Possible Carbon Chains

Determine different ways to arrange the four carbon atoms. For \(\mathrm{C}_{4}\mathrm{H}_{10}\), these can be linear or branched. Start by arranging them in a straight chain (n-butane) and then consider branching by forming a three-carbon chain with one methyl group attached (isobutane).

Draw Linear Isomer

Draw the structure for n-butane, which is a straight chain of four carbon atoms: \(\mathrm{CH}_{3} - \mathrm{CH}_{2} - \mathrm{CH}_{2} - \mathrm{CH}_{3}\). All carbons must be saturated with hydrogens, ensuring each carbon atom has four bonds.

Draw Branched Isomer

Draw the structure for isobutane, where three carbons form a chain and the fourth carbon forms a branch: \( \mathrm{CH}_{3} - \mathrm{CH}(\mathrm{CH}_{3}) - \mathrm{CH}_{3} \). This structure, also known as methylpropane, has a central carbon with one hydrogen and three connected carbons.

Verify Structure Completeness

Ensure the drawn structures are complete. Each carbon atom should form four bonds total, through connections with hydrogen atoms and other carbon atoms. Both n-butane and isobutane should satisfy the molecular formula \(\mathrm{C}_{4}\mathrm{H}_{10}\).

Key concepts

Alkanes

Alkanes are a simple class of hydrocarbons where all carbon atoms are connected by single bonds. This makes them saturated hydrocarbons, meaning they have the maximum number of hydrogen atoms attached to each carbon. Alkanes are sometimes called paraffins.
They follow a general formula of \(C_nH_{2n+2}\), where \(n\) is the number of carbon atoms. This formula ensures each carbon atom is bonded to four other atoms. Alkanes can vary in form, being either straight-chained or branched.

• **Simple Bonds:** Only single bonds between carbon atoms.
• **Saturated Hydrocarbons:** Maximum hydrogen atoms for each carbon.
• **Examples:** Methane (\(CH_4\)), Ethane (\(C_2H_6\)), Propane (\(C_3H_8\)).

Understanding alkanes is crucial in drawing and recognizing different isomers such as n-butane and isobutane.

n-butane

n-Butane is one of the structural isomers of the molecular formula \(C_4H_{10}\). It is the simplest arrangement with a straight chain of four carbon atoms. In the n-butane structure, all carbon atoms are connected in a continuous line, making it linear.
This isomer can be depicted as: \(CH_3 - CH_2 - CH_2 - CH_3\). Each carbon atom forms four bonds. This structure ensures each carbon atom meets the bonding requirement, as each has two or three hydrogen atoms depending on its placement in the chain.

• **Structure:** Linear, continuous chain.
• **Bonding:** Each carbon connected to 2 or 3 hydrogen atoms.
• **Properties:** Colorless gas at room temperature, used in fuel.

Recognizing n-butane involves identifying the longest continuous carbon chain without any branches.

isobutane

Isobutane, another isomer of \(C_4H_{10}\), showcases a branched structure. Unlike the linear n-butane, isobutane features a three-carbon chain with a methyl group (\(CH_3\)) attached to the central carbon. This gives it a different shape and physical properties compared to n-butane.
The isobutane structure is: \(CH_3 - CH(CH_3) - CH_3\). Central carbon connects with three other carbons and a single hydrogen atom, creating a more compact form. Often called methylpropane, it highlights how carbon chains can branch.

• **Structure:** Branched, central carbon with a methyl group.
• **Alternate Name:** Methylpropane.
• **Uses:** Commonly used as a refrigerant and in lighter fuels.

Understanding isobutane involves picturing how branches alter carbon chain arrangements and properties.

Molecular Formula

A molecular formula is a concise way to represent the number of each type of atom in a molecule. For alkanes, the formula specifically shows the exact number of carbon and hydrogen atoms.
For example, \(C_4H_{10}\) indicates this compound contains four carbon atoms and ten hydrogen atoms. These formulas are essential in identifying and differentiating between isomers, as they ensure both structures utilize the same total atoms while arranging them differently.

• **Indication:** Shows types and numbers of atoms.
• **Usefulness:** Helps in identifying possible isomer structures.
• **Consistency:** Regardless of structure, the total number of atoms remains constant.

Molecular formulas provide the foundation for sketching and identifying structural isomers, such as n-butane and isobutane.

Carbon Chains

Carbon chains form the backbone of many organic compounds, including alkanes. These chains consist of carbon atoms linked together, which can form different shapes depending on the arrangement.
For alkanes, these can be:

• **Linear Chains:** Like n-butane, where the carbon atoms are in a straight line.
• **Branched Chains:** Like isobutane, where at least one carbon atom connects to more than two other carbons, creating branches.

Carbon chains influence properties like boiling point and stability.
The more branched the chain, generally, the lower its boiling point due to decreased surface contact.
Understanding these chains is key to recognizing different isomer forms and determining their unique properties.