Question

Using the VSEPR theory, predict the molecular structure of each of the following molecules or ions containing multiple bonds. a. \(\mathrm{CO}_{3}^{2-}\) b. HNO \(_{3}\) (hydrogen is bonded to oxygen) c. \(\mathrm{NO}_{2}^{-}\) d. \(\mathrm{C}_{2} \mathrm{H}_{2}\)

Short answer

The molecular structures for the given molecules or ions are as follows: a. \(\mathrm{CO}_{3}^{2-}\): trigonal planar with one double bond to O. b. HNO\(_{3}\): trigonal planar with two double bonds to O; H is bonded to one O. c. \(\mathrm{NO}_{2}^{-}\): bent with one double bond to O. d. \(\mathrm{C}_{2} \mathrm{H}_{2}\): linear with a triple bond between C atoms; each C is bonded to one H.

Step-by-step solution

For each molecule or ion, we identify the central atom: a. \(\mathrm{CO}_{3}^{2-}\) Central atom: C b. HNO \(_{3}\) Central atom: N c. \(\mathrm{NO}_{2}^{-}\) Central atom: N d. \(\mathrm{C}_{2} \mathrm{H}_{2}\) Central atoms: Two C atoms #Step 2: Determine the electron-domain geometry#

We will determine the electron-domain geometry for each central atom: a. C in \(\mathrm{CO}_{3}^{2-}\): three bonding domains (O atoms) and zero lone pairs. Electron-domain geometry: trigonal planar. b. N in HNO \(_{3}\): three bonding domains (O atoms) and zero lone pairs. Electron-domain geometry: trigonal planar. c. N in \(\mathrm{NO}_{2}^{-}\): two bonding domains (O atoms) and one lone pair. Electron-domain geometry: trigonal planar. d. Each C in \(\mathrm{C}_{2} \mathrm{H}_{2}\): two bonding domains (H and another C atom) and zero lone pairs. Electron-domain geometry: linear. #Step 3: Determine the molecular geometry#

Now, we will determine the molecular geometry for each central atom: a. C in \(\mathrm{CO}_{3}^{2-}\): molecular geometry - trigonal planar. b. N in HNO \(_{3}\): molecular geometry - trigonal planar. c. N in \(\mathrm{NO}_{2}^{-}\): molecular geometry - bent. d. Each C in \(\mathrm{C}_{2} \mathrm{H}_{2}\): molecular geometry - linear. #Step 4: Identify the multiple bonds and combine them with the molecular structure#

Finally, we identify the multiple bonds and combine them with the molecular geometry: a. \(\mathrm{CO}_{3}^{2-}\): C is double-bonded to one O and single bonded with other two O atoms. Structure: trigonal planar with one double bond. b. HNO \(_{3}\): N is single-bonded to one O (which is bonded to H) and double-bonded to the other two O atoms. Structure: trigonal planar with two double bonds. c. \(\mathrm{NO}_{2}^{-}\): N is single-bonded to one O and double-bonded to the other O atom. Structure: bent with one double bond. d. \(\mathrm{C}_{2} \mathrm{H}_{2}\): Each C is single-bonded to H and triple-bonded to the other C atom. Structure: linear with a triple bond between C atoms.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It is determined by the number and type of bonds between atoms as well as any lone pairs of electrons. Understanding molecular geometry is crucial as it affects the molecule's properties, such as polarity, reactivity, and interaction with other molecules.
For molecules such as \(\mathrm{CO}_3^{2-}\), HNO \(_3\), and \(\mathrm{NO}_2^{-}\), identifying the central atom and applying VSEPR theory helps predict their shapes. For example:

• Upon determining the electron domains around a center atom in \(\mathrm{CO}_3^{2-}\), the molecular geometry is trigonal planar.
• In \(\mathrm{NO}_2^{-}\), a lone pair on nitrogen forces the geometry to be bent, despite a trigonal planar electron-domain geometry.

These shapes arise as atoms arrange themselves to minimize repulsion, balancing bonded atoms and lone pairs around the central atom.

Electron-Domain Geometry

The concept of electron-domain geometry involves the spatial arrangement of all electron domains (including bonds and lone pairs) around a central atom. VSEPR theory helps predict the electron-domain geometry by treating multiple bonds and lone pairs as a single "domain" or "region." This concept provides a foundation for understanding molecular geometry.
Consider the examples:

• In \(CO_3^{2-}\), the three oxygen atoms bonded to carbon create three electron domains, resulting in a trigonal planar electron-domain geometry.
• For \(\mathrm{C}_2\mathrm{H}_2\), each carbon atom involves two electron domains—one with hydrogen and one shared with the other carbon—leading to a linear electron-domain geometry.

VSEPR theory shows that lone pairs affect the arrangement by occupying space and pushing bonding pairs closer together, altering the electron-domain geometry perception.

Multiple Bonds

In chemistry, multiple bonds involve the sharing of more than one pair of electrons between two atoms. Double and triple bonds count as single electron domains in VSEPR theory. They play a crucial role in determining molecular geometry and properties.
Analyzing the examples:

• In \(\mathrm{CO}_3^{2-}\), carbon forms one double bond with an oxygen and single bonds with the other two oxygens, which contributes to its trigonal planar structure.
• The nitrogen in \(\mathrm{NO}_2^{-}\) shares electrons via one single and one double bond with the oxygens, influencing its bent shape.
• In ethyne (\(\mathrm{C}_2\mathrm{H}_2\)), the central triple bond between carbon atoms dictates the linear structure, showing the significant impact of multiple bonds on geometry.

Understanding multiple bonds is essential for predicting and rationalizing molecular behavior and interactions.

Trigonal Planar

A trigonal planar geometry is a molecular shape that occurs when a central atom is bonded to three other atoms and has no lone pairs. All atoms lie in a single plane, resulting in an angle of 120 degrees between them. This geometry is often seen with electron domain configurations of the central atom that include three bonding pairs.

• In molecules such as \(\mathrm{CO}_3^{2-}\) and HNO \(_3\), the central atom forms bonds with three peripheral atoms, without any lone pairs, leading to a trigonal planar geometry.

VSEPR theory explains this configuration resulting from the repulsion between the bonding electron pairs, seen in compounds where sterics and formal charges stabilize the planar form. Recognizing trigonal planar geometry helps in predicting molecular interactions and reactivity.

Linear Geometry

Linear geometry describes a molecular shape where all atoms are arranged in a straight line. This configuration results in a bond angle of 180 degrees and is found in simple diatomic molecules, as well as in those with two bonded atoms and no lone pairs surrounding a central atom.

• A classic example is ethyne (\(\mathrm{C}_2\mathrm{H}_2\)), where each carbon atom is bonded linearly to hydrogen and through a triple bond to another carbon, showcasing the linear nature.
• Linear geometry also appears in molecules like \(\mathrm{BeCl}_2\) and \(\mathrm{CS}_2\), where central atoms lack lone pairs, maintaining a linear shape through equal bond repulsion.

Understanding linear geometry aids in visualizing the arrangement of electron-rich regions around a central atom, framing how molecules interact chemically and physically.