Question

The connections in \(\mathrm{CH}_{3} \mathrm{NO}_{2}\) are: (a) Put in the remaining valence electrons to complete the Lewis dot diagram. (b) Using lines, solid wedges, and dashed wedges, draw the three-dimensional shape of this molecule. Indicate the numeric value of all bond angles.

Short answer

The Lewis dot structure for CH3NO2 has a total of 24 valence electrons, forming the following bonds: N-C, N-O (2), and C-H (3). After distributing the remaining valence electrons, the molecule has a bent geometry with approximate bond angles of C-N-O at 120° and N-O-O at 117°. The 3D shape of the molecule includes solid lines for bonds in the plane, solid wedges for bonds coming out of the plane, and dashed wedges for bonds going into the plane.

Step-by-step solution

Calculate the total number of valence electrons

To create the Lewis dot diagram for CH3NO2, first, we have to calculate the total number of valence electrons present in the molecule. Valence electrons for each atom: - Carbon (C): 4 - Hydrogen (H): 1 (each, but 3 total for CH3) - Nitrogen (N): 5 - Oxygen (O): 6 (each, but 12 total for O2) Adding all these valence electrons together, we get: Total valence electrons = 4 (C) + 3 (H) + 5 (N) + 12 (O2) = 24 valence electrons

Arrange the atoms and start forming the bonds

Now, let's arrange the atoms and start forming the bonds using the valence electrons. Put the central atom, Nitrogen, in the middle, and attach the Carbon (CH3) group and the two Oxygen atoms. Place Hydrogens around Carbon. Use a pair of electrons to form a bond between each adjacent pair of atoms: - N and C - N and one Oxygen - N and another Oxygen - C and each Hydrogen (3 bonds total) We've used 10 electrons (5 electron pairs) so far to form these bonds.

Distribute the remaining valence electrons

We have 24 - 10 = 14 valence electrons left. Now, distribute these electrons in pairs to complete the octets of the outer atoms. Start with the Oxygen atoms first (since they are more electronegative than Nitrogen or Carbon). Each Oxygen atom requires three more electron pairs to complete the octet. We've now used \(6\times 2+5\times 2 = 22\) electrons out of 24. Finally, add the remaining 2 electrons to the Nitrogen atom as a lone pair. Now we have a complete Lewis structure for CH3NO2.

Drawing the three-dimensional shape of the molecule

To draw the 3D shape of CH3NO2, use the following guidelines: - Solid lines represent bonds in the plane. - Solid wedges represent bonds coming out of the plane towards you. - Dashed wedges represent bonds going into the plane away from you. In this case, consider the following 3D arrangement: - Central N atom connects to the O atoms using solid lines (plane) forming a N-O single bond to each. - The N-C bond is also in the plane, represented by a solid line. - The three H atoms connected to the C atom should be shown using two solid wedges and one dashed wedge.

Indicate the numeric value of bond angles

The bond angles will be based on the molecular geometry according to the VSEPR theory. In this case, the central Nitrogen atom has two single bonds (with C and O atoms), another single bond with O, and a lone pair of electrons. According to the VSEPR theory, this arrangement will have a bent (angular) molecular geometry. The approximate bond angles are: - C-N-O (in the same plane): 120° - N-O-O: 117° (due to the lone pair on N) With this information, the Lewis dot structure and three-dimensional shape of the CH3NO2 molecule are complete.

Key concepts

Valence Electrons

Valence electrons are the electrons found in the outermost shell of an atom. These are crucial because they are involved in chemical bonds. In the molecule \(\mathrm{CH}_3\mathrm{NO}_2\), calculating the total number of valence electrons helps in constructing the Lewis structure. Here's how it breaks down:

• Carbon (C) has 4 valence electrons,
• Hydrogen (H) has 1 valence electron, but for \(\mathrm{CH}_3\), we have 3 hydrogen atoms, giving us 3 electrons from hydrogen,
• Nitrogen (N) has 5 valence electrons,
• Oxygen (O) has 6 valence electrons, but with two oxygen atoms, this amounts to 12 electrons.

Adding these values gives us a total of 24 valence electrons for \(\mathrm{CH}_3\mathrm{NO}_2\). Understanding this total allows us to arrange the atoms properly to form bonds, achieving a stable molecule.

Molecular Geometry

Molecular geometry refers to the three-dimensional shape a molecule assumes. The arrangement of atoms in space can affect physical and chemical properties. In \(\mathrm{CH}_3\mathrm{NO}_2\), nitrogen is the central atom, surrounded by other atoms following certain geometric patterns.
The nitrogen atom in this molecule attaches to a carbon atom, forming a N-C bond. It also connects to two oxygen atoms with N-O bonds. The arrangement is defined by nitrogen's hybridization and the repulsions between electron pairs. \[\mathrm{CH}_3\mathrm{NO}_2\] adopts a bent shape around nitrogen, influenced by lone pairs, resulting in specific bond angles. Understanding these geometric arrangements is critical for predicting reactivity and properties.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is an essential model in predicting the shape of a molecule. It is based on the idea that electron pairs around a central atom will repel one another, arranging themselves as far apart as possible.
In the case of \(\mathrm{CH}_3\mathrm{NO}_2\), the VSEPR theory helps us understand how nitrogen, with its lone pair and bonds to carbon and oxygen atoms, results in specific molecular geometry.

• Nitrogen forms two single bonds with each oxygen and carbon, and has a lone pair, which affects the spatial arrangement.
• The lone pair exerts repulsive forces, distorting the ideal angles slightly, often resulting in a bent configuration.

The VSEPR model allows us to predict bond angles and visualize the 3D structure of [\mathrm{CH}_3\mathrm{NO}_2].

Bond Angles

Bond angles are the angles formed between adjacent bonds at an atom. These angles are indicative of the molecular geometry and can be affected by the presence of lone pairs or differing bond lengths. In \(\mathrm{CH}_3\mathrm{NO}_2\), bond angles are determined by both the atomic arrangement and electron repulsions.
For example, the bond angle between carbon, nitrogen, and oxygen (C-N-O) in the molecule is approximately 120° due to the planar arrangement. However, the lone pair on nitrogen pushes bonds closer, making the N-O-O angle slightly less, near 117°.
It's important to recognize these angles to understand the shape of the molecule, which influences reactivity and interaction with other molecules.