Write a condensed structural formula, such as \(\mathrm{CH}_{3} \mathrm{CH}_{3}\), and describe the molecular geometry at each carbon atom. (a) 2 -propanol (b) acetone (c) dimethyl ether (d) acetic acid (e) 3-methyl-1-hexene

Molecular geometry is a fundamental concept in chemistry that reveals the three-dimensional arrangement of atoms within a molecule. It is determined by the electron pairs, both bonding and nonbonding, that surround each atom. For instance, when a carbon atom forms four single bonds, as is typical in organic compounds, the geometry is described as tetrahedral. This is because the electrons repel each other and adopt a structure that minimizes this repulsion, resulting in a tetrahedron shape with bond angles close to 109.5 degrees.

In the case of molecules like acetone, the central carbon atom is connected to three groups and has one double bond, thus forming a trigonal planar geometry. The double bond counts as a region of electron density, affecting the geometry and creating bond angles of approximately 120 degrees around the central atom. Understanding molecular geometry not only helps predict the shape of the molecule but also its reactivity and properties.

Organic chemistry is the branch of chemistry that specializes in the study of carbon-containing compounds. Carbon is an incredibly versatile atom that can form strong covalent bonds with other carbon atoms or various elements such as hydrogen, oxygen, nitrogen, and more. This bonding ability allows for a vast array of organic molecules, ranging from simple structures like methane e (CH_4) to complex macromolecules like proteins and DNA.

The condensed structural formulas provided in the exercise, such as \(\mathrm{CH}_3CH(OH)CH_3\) for 2-propanol, represent just a small glimpse into the diversity of organic chemistry. Recognizing these formulas and understanding their implications in terms of molecular structure, physical and chemical properties, is a critical skill when exploring organic substances.

Chemical bonding is the force that holds atoms together in molecules. In organic compounds, this usually involves covalent bonding where atoms share electron pairs. A single covalent bond forms when two electrons are shared, a double bond with four, and a triple bond with six electrons shared between two atoms. For example, the carbon-carbon double bond in 3-methyl-1-hexene (e \(\mathrm{CH}_3CH_2C(CH_3)=CHCH_2CH_3\)) introduces rigidity and a specific geometry to the molecule—the trigonal planar arrangement around the carbons in the double bond.

Chemical bonding is not limited to the connections between atoms but also determines molecular geometry and properties. The spatial arrangement of different types of chemical bonds, including sigma (σ)) and pi (π)) bonds, influences the structural representation and behavior of a molecule in chemical reactions.

Structural representation of molecules is crucial for chemists to understand and communicate chemical structures. The condensed structural formula is a method of representing organic molecules in a simplified manner without drawing all atoms and bonds. It is used to convey information about the types of atoms present and their connectivity, focusing on the carbon skeleton and functional groups.

For example, dimethyl ether's condensed formula (\(\mathrm{CH}_3OCH_3\)) indicates that two methyl groups (\(\mathrm{CH}_3\)) are attached to an oxygen atom. Organic molecules can also be depicted using Lewis structures, skeletal formulas, or 3D models. Each method differs in information density and purpose, but they all serve the goal of providing clarity in molecular visualization and aiding in predicting reactivity and interactions with other molecules.