Problem 51 - Chemistry: Principles and Reactions

Question

Which of the following are expected to show bond angles of \(109.5^{\circ}\) ? \(120^{\circ} ? 180^{\circ} ?\) (a) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) (c) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\)

Step-by-Step Solution

Answer

Answer: The bond angle for H₃C-CH₃ is 109.5°, and the bond angle for H₃C-C≡C-CH₃ is 180°.

Step 1: Identify the Central Atom

In both molecules, the central atom is carbon.

Step 2: Determine the Hybridization of Central Atom in \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\)

To determine the hybridization of the central carbon atom in \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\), we need to find the electron domain of the atom. The central carbon atom is bonded to three hydrogen atoms and one carbon atom. So, it has four electron domains surrounding it. Since it has four electron domains, the hybridization of the central carbon atom in \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) is \(\mathrm{sp^{3}}\).

Step 3: Determine the Bond Angle for \(\mathrm{H}_{3}\mathrm{C}-\mathrm{CH}_{3}\)

Since the central carbon atom in \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) is \(\mathrm{sp^{3}}\) hybridized, the bond angle associated with it is \(109.5^{\circ}\). So, \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) has a bond angle of \(109.5^{\circ}\).

Step 4: Determine the Hybridization of Central Atom in \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\)

To determine the hybridization of the central carbon atom in the molecule \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\), we need to consider the carbon atom which is triple-bonded. This carbon atom is bonded to two other carbon atoms (one single bond and one triple bond). Therefore, it has two electron domains surrounding it. Since it has two electron domains, the hybridization of the triple-bonded carbon in this molecule is \(\mathrm{sp}\).

Step 5: Determine the Bond Angle for \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\)

Since the triple-bonded carbon is \(\mathrm{sp}\) hybridized, the bond angle associated with it is \(180^{\circ}\). Therefore, the molecule \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\) has a bond angle of \(180^{\circ}\). From our analysis, we can conclude that the molecule \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) has a bond angle of \(109.5^{\circ}\), while the molecule \(\mathrm{H}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{3}\) has a bond angle of \(180^{\circ}\). Neither molecule has a bond angle of \(120^{\circ}\).

Key Concepts

Hybridization

Hybridization is a fundamental concept in chemistry that helps us understand how atomic orbitals combine to form new hybrid orbitals. These hybrid orbitals are essential for the formation of chemical bonds in molecules. Whenever atoms bond, their atomic orbitals mix to create hybrid orbitals tailored to the molecular geometry.

• For example, sp³ hybridization occurs when one 's' orbital combines with three 'p' orbitals. This leads to the formation of four equivalent sp³ hybrid orbitals. These are oriented in a tetrahedral geometry, commonly associated with a bond angle of approximately 109.5°.
• In the case of sp hybridization, one 's' orbital combines with one 'p' orbital resulting in two sp hybrid orbitals. This hybridization results in a linear arrangement with bond angles of 180°.

By understanding hybridization, you can predict the shape and bond angles in molecules, offering valuable insights into the chemical behavior and properties of the compound.

Bond Angle

Bond angles are a key aspect of molecular geometry and directly relate to hybridization. They are the angles between adjacent bonds in a molecule.

• In an sp³ hybridized environment such as in ext{H}_{3} ext{C}- ext{CH}_{3}, the bond angles are roughly 109.5°. This reflects a tetrahedral arrangement, minimizing repulsion between the electron domains.
• When it comes to sp hybridized molecules like ext{H}_{3} ext{C}- ext{C} ext{C} ext{H}_{3}, the bond angles are linear at 180°.

Recognizing and understanding bond angles is essential as they affect molecular shape, chemical reactivity, and physical properties. Differences in bond angles can influence how molecules interact in chemical reactions and contribute to the unique properties of substances.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. It is crucial for understanding physical and chemical properties.

• The geometry depends on the hybridization and the number of electron domains involved in bonding. For sp³ hybridized carbon, as in ext{H}_{3} ext{C}- ext{CH}_{3}, the geometry is tetrahedral. This means the molecule is shaped like a pyramid with a triangular base, optimizing space between electrons.
• On the other hand, an sp hybridized system, such as in ext{H}_{3} ext{C}- ext{C} ext{C} ext{H}_{3}, the geometry is linear. This results in all atoms aligning in a straight line.

Understanding molecular geometry helps in predicting how molecules will grow and interact with each other. It is key in fields like pharmacology, nanotechnology, and materials science, where molecular shape determines the function and character of the material.