Problem 1 - General Chemistry: Principles and Modern Applications

Question

Write structural formulas corresponding to these condensed formulas. (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHBrCHBrCH}_{3}\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}_{2} \mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) (c) \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{CHCH}=\mathrm{CHCH}_{2} \mathrm{CH}_{3}\).

Step-by-Step Solution

Answer

The structural formulas for the given compounds are (a) \(\mathrm{CH_{3}-CH_{2}-CBr-CHBr-CH_{3}}\), (b) \((\mathrm{CH}_{3})_{3} \mathrm{C}- \mathrm{CH_{2}-C}- (\mathrm{CH}_{3})_{2} \mathrm{-CH_{2}-CH_{2}-CH_{3}}\), and (c) \((\mathrm{C}_{2} \mathrm{H}_{5})_{2} \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH_{2}-CH_{3}}\).

Step 1: Understand the condensed structural formula.

Condensed structural formulas show the hydrogen atoms right next to the carbon atoms to which they are bonded. The non-Carbon atoms (inorganic atoms like Br, Cl) are shown for each atom exactly as they appear.

Step 2: Draw the structural formula for (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHBrCHBrCH}_{3}\)

In this formula, presence of 5 carbons is indicated by 'CH'. Two of the carbons are attached to bromine atoms. Hence, the corresponding structural formula can be represented as: \(\mathrm{CH_{3}-CH_{2}-CBr-CHBr-CH_{3}}\). Each 'CH' represents a carbon atom together with the number of hydrogen atoms that carbon is bonded to.

Step 3: Draw the structural formula for \((\mathrm{CH}_{3})_{3} \mathrm{CCH}_{2}\mathrm{C}(\mathrm{CH}_{3})_{2} \mathrm{CH}_{2} \mathrm{CH}_{2}\mathrm{CH}_{3}\)

This molecule contains multiple branches, featuring carbon atoms bonded to 3 methyl groups, and carbon atoms bonded to two methyl groups. The structural formula can be represented as: \((\mathrm{CH}_{3})_{3} \mathrm{C}- \mathrm{CH_{2}-C}- (\mathrm{CH}_{3})_{2} \mathrm{-CH_{2}-CH_{2}-CH_{3}}\). The brackets indicate that the groups are branches i.e., they are bonded to the carbon in the main chain.

Step 4: Draw the structural formula for \((\mathrm{C}_{2} \mathrm{H}_{5})_{2}\mathrm{CHCH}=\mathrm{CHCH}_{2} \mathrm{CH}_{3}\)

This molecule contains ethyl groups, carbon atoms, and a double bond. The structural formula can be represented as: \((\mathrm{C}_{2} \mathrm{H}_{5})_{2} \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH_{2}-CH_{3}}\). The presence of '=' indicates a double bond between the carbon atoms.

Key Concepts

Condensed Structural Formula

Condensed structural formulas are a shorthand way of writing the molecular structure of a compound. Using this notation, chemists can summarize the arrangement of atoms within a molecule without drawing a full diagram. For example, the condensed formula CH_{3} CH_{2} CHBrCHBrCH_{3} represents a chain of carbon atoms where each carbon atom's associated hydrogen atoms are directly indicated next to it.

• The symbol CH_{3} indicates a carbon atom bonded to three hydrogen atoms.
• Groups like CH_{2} indicate a carbon with two hydrogens, and when an atom like bromine (Br) is present, it is written next to the carbon to which it's bonded, as in CHBr.

This compact way of writing structures is especially useful when dealing with complex organic molecules, allowing a clear glimpse into the molecule's makeup without requiring a detailed drawing.

Drawing Structural Formulas

Drawing structural formulas is an essential skill in organic chemistry, allowing one to visualize the specific connectivity of atoms. When converting a condensed formula to its structural form, each carbon atom is represented by a vertex or the end of a line, and the bonds between them are depicted as lines. The structural formula for(CH_{3})_{3} CCH_{2} C(CH_{3})_{2} CH_{2} CH_{2} CH_{3} uses lines and branches to show how the carbon atoms are bonded together and to represent the groups attached to the central chain.

Considerations When Drawing

• Single lines represent single bonds, while double lines represent double bonds.
• Branches off the main chain are indicated by lines leading to the attached groups.
• Groups that repeat, such as CH_{3}, can be drawn together to simplify the depiction.

In a complete structural diagram, the arrangement of atoms is presented, giving a clear and detailed view of the molecule's structure.

Organic Molecules Representation

Organic molecules can be complex, and their representation requires various types of structural formulas to convey the necessary information. In addition to condensed and full structural formulas, there are two other common representations:

• Skeletal formulas: This depicts the carbon skeleton where carbon atoms are implied at each vertex and end of the lines. Hydrogens bonded to carbon are usually not shown.
• Line-angle formulas: A simplified version of the skeletal formula where only lines are utilized to represent the carbon backbone, and the angles between them imply carbon atoms.

Each method of representation has its uses, depending on the complexity of the molecule and the context in which it's being discussed. For students starting out, it's important to become comfortable with all forms to understand and communicate the structures of organic compounds effectively.

Interpretation of Chemical Notation

Interpreting chemical notation accurately is crucial for understanding and communicating the composition and structure of molecules. The notation provides a wealth of information:

• Types of atoms involved are represented by their chemical symbols, like C for carbon and H for hydrogen.
• Quantities of atoms are indicated by subscript numbers, as in H_{2} for two hydrogen atoms.
• Bonding between atoms is shown using dashes for single bonds (-), double equal signs for double bonds (=), and triple lines for triple bonds (not shown in the above examples).

Understanding this notation allows you to move from a textual representation to a visual depiction of the molecule, unraveling the intricacies of its structure. Learning to read and write these formulas will enable students to excel in organic chemistry.