Question

Sketch the probable geometric shape of a molecule of (a) \(\mathrm{N}_{2} \mathrm{O}_{4}\left(\mathrm{O}_{2} \mathrm{NNO}_{2}\right) ;\) (b) \(\mathrm{C}_{2} \mathrm{N}_{2}(\mathrm{NCCN}) ;\) (c) \(\mathrm{C}_{2} \mathrm{H}_{6}\) \(\left(\mathrm{H}_{3} \mathrm{CCH}_{3}\right) ;(\mathrm{d}) \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\left(\mathrm{H}_{3} \mathrm{COCH}_{3}\right)\).

Short answer

(a) The shape of \$\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{O}_{2} \mathrm{NNO}_{2})\$ is trigonal pyramidal. (b) The shape of \$\mathrm{C}_{2} \mathrm{N}_{2}(\mathrm{NCCN})\$ is linear. (c) The shape of \$\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{H}_{3} \mathrm{CCH}_{3})\$ is tetrahedral. (d) The shape of \$\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}(\mathrm{H}_{3} \mathrm{COCH}_{3})\$ is trigonal pyramidal.

Step-by-step solution

Draw the Lewis Structure for each molecule

(a) For \$\mathrm{N}_{2} \mathrm{O}_{4}\left(\mathrm{O}_{2} \mathrm{NNO}_{2}\right)\$, start by identifying the central atom (N) and arrange other atoms around it. Then fill in the valence electrons, making sure each atom besides hydrogen has an octet.(b) For \$\mathrm{C}_{2} \mathrm{N}_{2}(\mathrm{NCCN})\$, similarly identify the central atoms (C) and arrange N atoms around them. Then fill in the valence electrons.(c) For \$\mathrm{C}_{2} \mathrm{H}_{6}(\$\mathrm{H}_{3} \mathrm{CCH}_{3}\$)\$, identify the central atoms (C) and arrange H atoms around them. Then fill in the valence electrons.(d) For \$\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}(\mathrm{H}_{3} \mathrm{COCH}_{3})\$, identify the central atoms (C) and arrange H and O atoms around them. Then fill in the valence electrons.

Apply the VSEPR theory to identify shape

(a) For \$\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{O}_{2} \mathrm{NNO}_{2})\$, the N atom is surrounded by one lone pair and three atoms. Therefore, its electron pair geometry is tetrahedral and its molecular shape is trigonal pyramidal.(b) For \$\mathrm{C}_{2} \mathrm{N}_{2}(\mathrm{NCCN})\$, the C atoms are surrounded by two atoms. Therefore, its electron pair geometry is linear and its molecular shape is linear.(c) For \$\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{H}_{3} \mathrm{CCH}_{3})\$, each C atom is surrounded by three atoms. Therefore, its electron pair geometry is tetrahedral and its molecular shape is tetrahedral.(d) For \$\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}(\mathrm{H}_{3} \mathrm{COCH}_{3})\$, the C atom attached to O is surrounded by three atoms and a lone pair. Therefore, its electron pair geometry is tetrahedral and its molecular shape is trigonal pyramidal.

Key concepts

Lewis Structures

Lewis structures are essential tools used in chemistry to represent molecules and ions. They depict how atoms are connected and show the arrangement of valence electrons around atoms in a molecule. These diagrams can help predict the geometry, reactivity, and polarity of a molecule.

When drawing a Lewis structure, follow these steps:

• Identify the central atom, usually the least electronegative (except hydrogen).
• Arrange the other atoms around the central atom.
• Count the total number of valence electrons available from all atoms in the molecule.
• Draw single bonds between the central atom and surrounding atoms, and subtract bonded electrons from the total count.
• Distribute remaining electrons to satisfy the octet rule (or duet for hydrogen) for each atom.
• If there are not enough electrons to fulfill the octet rule, form double or triple bonds as necessary.

Using Lewis structures, we can represent molecules like \(_2\) \(\mathrm{O}_4\), \(\mathrm{C}_2\) \(\mathrm{N}_2\), \(\mathrm{C}_2\) \(\mathrm{H}_6\), and \(\mathrm{C}_2\) \(\mathrm{H}_6\) \(\mathrm{O}\) and understand their chemical behavior better.

VSEPR Theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory is used to predict the geometry of molecules. It helps us understand how the shape of a molecule is influenced by electron pairs around the central atom. The basic idea is that electron pairs, both bonding and non-bonding, repel each other and will arrange themselves as far apart as possible to minimize repulsion.

Key principles of VSEPR include:

• Electron pairs (bonding and lone pairs) will adopt a spatial arrangement that minimizes repulsive forces.
• Lone pairs create stronger repulsive forces than bonding pairs, which can slightly alter predicted geometric angles.
• The number of regions of electron density around the central atom determines the electron pair geometry.

By applying VSEPR theory, we can determine that the molecule \(\mathrm{C}_2\) \(\mathrm{N}_2\) is linear, \(\mathrm{N}_2\) \(\mathrm{O}_4\) assumes a tetrahedral electron geometry resulting in a trigonal pyramidal shape, while \(\mathrm{C}_2\) \(\mathrm{H}_6\) and \(\mathrm{C}_2\) \(\mathrm{H}_6\) \(\mathrm{O}\) have tetrahedral arrangements.

Electron Pair Geometry

Electron pair geometry considers the spatial arrangement of all electron pairs around the central atom, which includes both bonding pairs (those involved in bonds) and lone pairs (those not participating in bonds).

For example:

• If a central atom is surrounded by four regions of electron density, like in \(\mathrm{CH}_4\), the electron pair geometry is tetrahedral.
• For \(\mathrm{C}_2\) \(\mathrm{H}_6\) where carbon atoms have four electron domains around them in total, the geometry is tetrahedral.
• In cases like \(\mathrm{C}_2\) \(\mathrm{N}_2\), linear geometry occurs due to two regions of electron density around each carbon.

Electron pair geometry gives a broad overview of the molecule's structure by focusing on all electron regions, crucial for further determining the molecule's specific shape. It does not differentiate between bond pairs and lone pairs; hence, both influence the geometry but are treated equally.

Molecular Shape

Molecular shape specifically refers to the arrangement of only the atoms within a molecule, ignoring the lone electron pairs. Whereas electron pair geometry considers all electron clouds, molecular shape is determined by the positions of the atoms alone.

This subtle yet significant difference means:

• An atom's lone pair can distort the observed shape from the predicted geometry. For example, in \(\mathrm{N}_2\) \(\mathrm{O}_4\), the presence of a lone pair of electrons on the central nitrogen changes the shape from tetrahedral to trigonal pyramidal.
• In \(\mathrm{C}_2\) \(\mathrm{H}_6\), the absence of lone pairs allows the molecular shape to reflect the electron pair geometry, rendering it tetrahedral.
• In linear molecules like \(\mathrm{C}_2\) \(\mathrm{N}_2\), the shape is unaffected by lone pairs because the central atoms are only bonded to two atoms.

By understanding molecular shape, one can predict a molecule’s interactions and reactivity based on the three-dimensional spatial arrangement of its atoms.