Problem 41 - Chemistry A Molecular Approach

Question

Determine the molecular geometry about each interior atom and sketch each molecule. a. \(\mathrm{C}_{2} \mathrm{H}_{2}\) (skeletal structure \(\mathrm{HCCH}\) ) b. \(\mathrm{C}_{2} \mathrm{H}_{4}\) (skeletal structure \(\mathrm{H}_{2} \mathrm{CCH}_{2}\) ) c. \(\mathrm{C}_{2} \mathrm{H}_{6}\) (skeletal structure \(\mathrm{H}_{3} \mathrm{CCH}_{3}\) )

Step-by-Step Solution

Answer

a. C2H2 has a linear molecular geometry. b. C2H4 has a trigonal planar molecular geometry around each carbon. c. C2H6 has a tetrahedral molecular geometry around each carbon.

Step 1: Determining the Molecular Geometry for C2H2

Each carbon in ethyne (C2H2) forms a triple bond with the other carbon and a single bond with hydrogen. Thus, they have a linear geometry due to the sp hybridization with bond angles of approximately 180 degrees.

Step 2: Sketching C2H2

The skeletal structure HC≡CH represents C2H2 as a straight line with two hydrogens bonded to the ends, signifying its linear molecular geometry.

Step 3: Determining the Molecular Geometry for C2H4

Each carbon in ethene (C2H4) forms a double bond with the other carbon and single bonds with two hydrogens. The hybridization of the carbons is sp2, which results in a trigonal planar geometry around each carbon with bond angles of approximately 120 degrees.

Step 4: Sketching C2H4

The skeletal structure H2C=CH2 represents C2H4 as two carbons connected by a double bond, each carbon also bonded to two hydrogens, arranged in a plane, reflecting its trigonal planar molecular geometry.

Step 5: Determining the Molecular Geometry for C2H6

Each carbon in ethane (C2H6) forms a single bond with the other carbon and three single bonds with hydrogen. The central atoms are sp3 hybridized leading to a tetrahedral geometry with bond angles close to 109.5 degrees around each of the carbons.

Step 6: Sketching C2H6

The skeletal structure H3C-CH3 represents C2H6 with two carbon atoms single-bonded to each other, each carbon also bonded to three hydrogen atoms evenly spaced, illustrating the tetrahedral molecular geometry.

Key Concepts

SP Hybridization

Understanding sp hybridization is essential to grasping the structure of certain organic molecules, such as ethyne (C₂H₂). In sp hybridization, an atom’s s-orbital mixes with one of its p-orbitals, creating two equivalent hybrid orbitals. This hybridization occurs in carbon atoms that are involved in a triple bond, typical for molecules like C₂H₂.

These two sp hybrid orbitals are arranged linearly, 180 degrees apart, which explains why such molecules have a linear geometry. When a carbon atom undergoes sp hybridization, like in ethyne, it can make very strong σ (sigma) bonds with other carbons or hydrogens, leaving two p-orbitals untouched. These unhybridized p-orbitals overlap side-to-side to form π (pi) bonds, which are essential for the triple bond's formation.

• Each carbon in C₂H₂ forms a σ bond through sp hybrid orbitals.
• The linear arrangement maximizes the distance between the bonded pairs, minimizing repulsion.
• The molecule exhibits a straight-line geometry, with bond angles at about 180 degrees.

Visualizing this linear arrangement can greatly simplify the understanding of complex organic molecules and predict their reactions.

Trigonal Planar Geometry

When examining molecules such as ethene (C₂H₄), one comes across the term trigonal planar geometry. This geometric arrangement is associated with sp² hybridization, where one s-orbital and two p-orbitals within an atom, such as carbon, hybridize to form three sp² hybrid orbitals.

These three orbitals lie in a single plane, separated by approximately 120 degrees. In ethene, each carbon atom forms three sigma bonds, two with hydrogen atoms and one with the other carbon atom, leading to this planar arrangement. Simultaneously, the remaining p-orbital that is not involved in hybridization forms a pi bond with the other carbon atom.

• The trigonal planar shape describes a flat, three-pointed shape where bond angles are about 120 degrees.
• In C₂H₄, the double bond consists of one σ bond and one π bond, contributing to the planar geometry.
• The molecule's geometry can affect properties like polarity and reactivity.

Recognizing trigonal planar molecules is crucial for predicting their chemical behavior and interactions in various organic reactions.

Tetrahedral Geometry

Tetrahedral geometry is a common geometry seen in organic chemistry, particularly in molecules like ethane (C₂H₆). This geometry arises from sp³ hybridization, where one s-orbital and three p-orbitals of a carbon atom mix to create four hybrid orbitals.

These orbitals are oriented in a way that they point to the corners of a tetrahedron, with bond angles close to 109.5 degrees. For ethane, each carbon atom forms four sigma bonds, one with the other carbon and three with hydrogen atoms, resulting in a three-dimensional tetrahedral shape.

• Each carbon atom’s four sp³ hybrid orbitals form bonds pointing toward the vertices of a tetrahedron.
• Bond angles are approximately 109.5 degrees, reducing electron pair repulsion.
• The tetrahedral shape is integral to understanding the spatial arrangement of atoms in a molecule and their resultant properties.

The idea of tetrahedral molecular geometry is a key concept for envisioning the arrangement of atoms in many organic compounds, thus being a fundamental principle for students learning organic chemistry.