Problem 13 - General Chemistry: Principles and Modern Applications

Question

Indicate which of the following molecules and ions are linear, which are planar, and which are neither. Then propose hybridization schemes for the central atoms. (a) \(\mathrm{Cl}_{2} \mathrm{C}=\mathrm{CCl}_{2} ;(\mathrm{b}) \mathrm{N} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{N} ;(\mathrm{c}) \mathrm{F}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{N}\) (d) \([\mathrm{S}-\mathrm{C} \equiv \mathrm{N}]^{-}\)

Step-by-Step Solution

Answer

(a) Planar, sp2 hybridized central atom. (b) Linear, sp hybridized central atom. (c) Neither, sp3 hybridized for the first central atom and sp for the second. (d) Linear, sp hybridized central atom.

Step 1: Determine Geometry of Molecules

Analyze the structure of given molecules or ions in each part of the problem. (a) \(\mathrm{Cl}_{2} \mathrm{C}=\mathrm{CCl}_{2}\): The central atom is a carbon represented by \(C=\). This molecule is planar due to the sp2 hybridization. (b) \(\mathrm{N} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{N}\): Here, the molecule is linear with the central atom being carbon, due to sp hybridization. (c) \(\mathrm{F}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{N}\): We have two central atoms here the first being an sp3 hybridized carbon making the molecule 'neither' planar nor linear. The second carbon atom is sp hybridized and forms a linear portion of the molecule. (d) \([\mathrm{S}-\mathrm{C} \equiv \mathrm{N}]^{-}\): The molecule is linear with sp hybridization.

Step 2: Propose Hybridization Scheme

Determine the hybridization type for each central atom. (a) The central carbon facilitating a double bond with another carbon and single bonds with chlorine atoms is sp2 hybridized. (b) The central carbon atom linked with two nitrogen atoms with three bond pairs is sp hybridized. (c) The first central carbon atom linked with three fluorine atoms and another carbon atom is sp3 hybridized. The second carbon atom linked to the first carbon and nitrogen atom with three bond pairs is sp hybridized. (d) The central carbon linked to sulfur and nitrogen with three bond pairs is sp hybridized.

Key Concepts

Hybridization

Hybridization is a concept in chemistry that helps explain how atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals determine the geometry of a molecule. For example, in the molecule \( \mathrm{Cl}_{2} \mathrm{C}=\mathrm{CCl}_{2} \), the carbon atoms are \( sp^2 \) hybridized. This means that one s orbital and two p orbitals combine to form three equivalent \( sp^2 \) orbitals.
The hybridization type dictates the molecular shape.

• \( sp \) hybridization typically results in a linear shape.
• \( sp^2 \) hybridization leads to a trigonal planar shape.
• \( sp^3 \) hybridization forms a tetrahedral shape.

Understanding hybridization helps predict the geometry of molecules.

Linear Molecules

Linear molecules are those in which the atoms are arranged in a straight line. This often results from \( sp \) hybridization. For example, in \( \mathrm{N} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{N} \), both carbons are \( sp \) hybridized, making the molecule linear.
A molecule is linear if the angle between adjacent bonds around the central atom is 180 degrees. This straight arrangement can involve:

• Triple bonds, as seen in acetylene (\( \mathrm{C}_2 \mathrm{H}_2 \))
• A mix of single and triple bonds

Linear shapes are key in understanding molecular vibrations and interactions.

Planar Molecules

Planar molecules have all their atoms in a single plane, often due to \( sp^2 \) hybridization. The molecule \( \mathrm{Cl}_{2} \mathrm{C}=\mathrm{CCl}_{2} \) is a good example of this. Its geometry is described as trigonal planar because the \( sp^2 \) hybridization forms angles of 120 degrees.
Such planar arrangements affect the molecule’s reactivity and physical properties.

• Common in benzene rings or other aromatic systems
• Provide stability through conjugated systems

Planar geometries lead to significant implications in chemical reactions.

Geometry Determination

Determining the geometry of a molecule involves analyzing the arrangement of atoms and the types of bonds present. By understanding the hybridization of the central atom, one can predict the molecular shape. For example:

• Identify the hybridization of the central atom, such as \( sp, sp^2, \) or \( sp^3 \).
• Use the hybridization to predict the geometric arrangement.
  
• Consider resonance and multiple bonds for accurate geometry.

Geometry determination is crucial for understanding chemical properties and reactivity patterns. It provides insight into behavior and interactions in various environments.